Beekeeping

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Beekeeping, tacuinum sanitatis casanatensis (14th century)

 

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Beekeeping in Serbia

Beekeeping (or apiculture) is the maintenance of bee colonies, commonly in man-made hives, by humans. Most such bees are honey bees in the genus Apis, but other honey-producing bees such as Melipona stingless bees are also kept. A beekeeper (or apiarist) keeps bees in order to collect their honey and other products that the hive produce (including beeswax, propolis, flower pollen, bee pollen, and royal jelly), to pollinate crops, or to produce bees for sale to other beekeepers. A location where bees are kept is called an apiary or "bee yard".

History

Early history

Honey seeker depicted on 8,000-year-old cave painting near Valencia, Spain

 

Depictions of humans collecting honey from wild bees date to 10,000 years ago. Beekeeping in pottery vessels began about 9,000 years ago in North Africa. Domestication of bees is shown in Egyptian art from around 4,500 years ago. Simple hives and smoke were used and honey was stored in jars, some of which were found in the tombs of pharaohs such as Tutankhamun. It wasn't until the 18th century that European understanding of the colonies and biology of bees allowed the construction of the movable comb hive so that honey could be harvested without destroying the entire colony. 

At some point humans began to attempt to maintain colonies of wild bees in artificial hives made from hollow logs, wooden boxes, pottery vessels, and woven straw baskets or "skeps". Traces of beeswax are found in potsherds throughout the Middle East beginning about 7000 BCE.

Honeybees were kept in Egypt from antiquity. On the walls of the sun temple of Nyuserre Ini from the Fifth Dynasty, before 2422 BCE, workers are depicted blowing smoke into hives as they are removing honeycombs. Inscriptions detailing the production of honey are found on the tomb of Pabasa from the Twenty-sixth Dynasty (c. 650 BCE), depicting pouring honey in jars and cylindrical hives. Sealed pots of honey were found in the grave goods of pharaohs such as Tutankhamun.

Stele showing Shamash-resh-ușur praying to the gods Adad and Ishtar with an inscription about beekeeping in Babylonian cuneiform

I am Shamash-resh-ușur, the governor of Suhu and the land of Mari. Bees that collect honey, which none of my ancestors had ever seen or brought into the land of Suhu, I brought down from the mountain of the men of Habha, and made them settle in the orchards of the town 'Gabbari-built-it'. They collect honey and wax, and I know how to melt the honey and wax – and the gardeners know too. Whoever comes in the future, may he ask the old men of the town, (who will say) thus: "They are the buildings of Shamash-resh-ușur, the governor of Suhu, who introduced honey bees into the land of Suhu."

— translated text from stele, (Dalley, 2002)

In prehistoric Greece (Crete and Mycenae), there existed a system of high-status apiculture, as can be concluded from the finds of hives, smoking pots, honey extractors and other beekeeping paraphernalia in Knossos. Beekeeping was considered a highly valued industry controlled by beekeeping overseers—owners of gold rings depicting apiculture scenes rather than religious ones as they have been reinterpreted recently, contra Sir Arthur Evans.

Archaeological finds relating to beekeeping have been discovered at Rehov, a Bronze and Iron Age archaeological site in the Jordan Valley, Israel. Thirty intact hives, made of straw and unbaked clay, were discovered by archaeologist Amihai Mazar in the ruins of the city, dating from about 900 BCE. The hives were found in orderly rows, three high, in a manner that could have accommodated around 100 hives, held more than 1 million bees and had a potential annual yield of 500 kilograms of honey and 70 kilograms of beeswax, according to Mazar, and are evidence that an advanced honey industry existed in ancient Israel 3,000 years ago.

The Beekeepers, 1568, by Pieter Bruegel the Elder

In ancient Greece, aspects of the lives of bees and beekeeping are discussed at length by Aristotle. Beekeeping was also documented by the Roman writers Virgil, Gaius Julius Hyginus, Varro, and Columella.

Beekeeping has also been practiced in ancient China since antiquity. In the book "Golden Rules of Business Success" written by Fan Li (or Tao Zhu Gong) during the Spring and Autumn period there are sections describing the art of beekeeping, stressing the importance of the quality of the wooden box used and how this can affect the quality of the honey. The Chinese word for honey (蜜 mì, reconstructed Old Chinese pronunciation *mjit) was borrowed from Indo-European proto-Tocharian language, the source of "honey", from proto-Tocharian *ḿət(ə) (where *ḿ is palatalized; cf. Tocharian B mit), cognate with English mead.

The ancient Maya domesticated a separate species of stingless bee. The use of stingless bees is referred to as meliponiculture, named after bees of the tribe Meliponini—such as Melipona quadrifasciata in Brazil. This variation of bee keeping still occurs around the world today. For instance, in Australia, the stingless bee Tetragonula carbonaria is kept for production of their honey.

Scientific study of honey bees

It was not until the 18th century that European natural philosophers undertook the scientific study of bee colonies and began to understand the complex and hidden world of bee biology. Preeminent among these scientific pioneers were Swammerdam, René Antoine Ferchault de Réaumur, Charles Bonnet, and François Huber. Swammerdam and Réaumur were among the first to use a microscope and dissection to understand the internal biology of honey bees. Réaumur was among the first to construct a glass walled observation hive to better observe activities within hives. He observed queens laying eggs in open cells, but still had no idea of how a queen was fertilized; nobody had ever witnessed the mating of a queen and drone and many theories held that queens were "self-fertile," while others believed that a vapor or "miasma" emanating from the drones fertilized queens without direct physical contact. Huber was the first to prove by observation and experiment that queens are physically inseminated by drones outside the confines of hives, usually a great distance away. 

Following Réaumur's design, Huber built improved glass-walled observation hives and sectional hives that could be opened like the leaves of a book. This allowed inspecting individual wax combs and greatly improved direct observation of hive activity. Although he went blind before he was twenty, Huber employed a secretary, François Burnens, to make daily observations, conduct careful experiments, and keep accurate notes over more than twenty years. Huber confirmed that a hive consists of one queen who is the mother of all the female workers and male drones in the colony. He was also the first to confirm that mating with drones takes place outside of hives and that queens are inseminated by a number of successive matings with male drones, high in the air at a great distance from their hive. Together, he and Burnens dissected bees under the microscope and were among the first to describe the ovaries and spermatheca, or sperm store, of queens as well as the penis of male drones. Huber is universally regarded as "the father of modern bee-science" and his "Nouvelles Observations sur Les Abeilles (or "New Observations on Bees")  revealed all the basic scientific truths for the biology and ecology of honeybees.

Invention of the movable comb hive

Rural beekeeping in the 16th century

Early forms of honey collecting entailed the destruction of the entire colony when the honey was harvested. The wild hive was crudely broken into, using smoke to suppress the bees, the honeycombs were torn out and smashed up — along with the eggs, larvae and honey they contained. The liquid honey from the destroyed brood nest was strained through a sieve or basket. This was destructive and unhygienic, but for hunter-gatherer societies this did not matter, since the honey was generally consumed immediately and there were always more wild colonies to exploit. But in settled societies the destruction of the bee colony meant the loss of a valuable resource; this drawback made beekeeping both inefficient and something of a "stop and start" activity. There could be no continuity of production and no possibility of selective breeding, since each bee colony was destroyed at harvest time, along with its precious queen.

During the medieval period abbeys and monasteries were centers of beekeeping, since beeswax was highly prized for candles and fermented honey was used to make alcoholic mead in areas of Europe where vines would not grow. The 18th and 19th centuries saw successive stages of a revolution in beekeeping, which allowed the bees themselves to be preserved when taking the harvest.

Intermediate stages in the transition from the old beekeeping to the new were recorded for example by Thomas Wildman in 1768/1770, who described advances over the destructive old skep-based beekeeping so that the bees no longer had to be killed to harvest the honey. Wildman for example fixed a parallel array of wooden bars across the top of a straw hive or skep (with a separate straw top to be fixed on later) "so that there are in all seven bars of deal" [in a 10-inch-diameter (250 mm) hive] "to which the bees fix their combs". He also described using such hives in a multi-storey configuration, foreshadowing the modern use of supers: he described adding (at a proper time) successive straw hives below, and eventually removing the ones above when free of brood and filled with honey, so that the bees could be separately preserved at the harvest for a following season. Wildman also described a further development, using hives with "sliding frames" for the bees to build their comb, foreshadowing more modern uses of movable-comb hives. Wildman's book acknowledged the advances in knowledge of bees previously made by Swammerdam, Maraldi, and de Réaumur—he included a lengthy translation of Réaumur's account of the natural history of bees—and he also described the initiatives of others in designing hives for the preservation of bee-life when taking the harvest, citing in particular reports from Brittany dating from the 1750s, due to Comte de la Bourdonnaye. However, the forerunners of the modern hives with movable frames that are mainly used today are considered the traditional basket top bar (movable comb) hives of Greece, known as “Greek beehives”. The oldest testimony on their use dates back to 1669 although it is probable that their use is more than 3000 years old.

Lorenzo Langstroth
(1810–1895)

The 19th century saw this revolution in beekeeping practice completed through the perfection of the movable comb hive by the American Lorenzo Lorraine Langstroth. Langstroth was the first person to make practical use of Huber's earlier discovery that there was a specific spatial measurement between the wax combs, later called the bee space, which bees do not block with wax, but keep as a free passage. Having determined this bee space (between 5 and 8 mm, or 1/4 to 3/8"), Langstroth then designed a series of wooden frames within a rectangular hive box, carefully maintaining the correct space between successive frames, and found that the bees would build parallel honeycombs in the box without bonding them to each other or to the hive walls. This enables the beekeeper to slide any frame out of the hive for inspection, without harming the bees or the comb, protecting the eggs, larvae and pupae contained within the cells. It also meant that combs containing honey could be gently removed and the honey extracted without destroying the comb. The emptied honey combs could then be returned to the bees intact for refilling. Langstroth's book, The Hive and Honey-bee, published in 1853, described his rediscovery of the bee space and the development of his patent movable comb hive.

The invention and development of the movable-comb-hive fostered the growth of commercial honey production on a large scale in both Europe and the US.

Evolution of hive designs

Bees at the hive entrance

Langstroth's design for movable comb hives was seized upon by apiarists and inventors on both sides of the Atlantic and a wide range of moveable comb hives were designed and perfected in England, France, Germany and the United States. Classic designs evolved in each country: Dadant hives and Langstroth hives are still dominant in the US; in France the De-Layens trough-hive became popular and in the UK a British National hive became standard as late as the 1930s although in Scotland the smaller Smith hive is still popular. In some Scandinavian countries and in Russia the traditional trough hive persisted until late in the 20th century and is still kept in some areas. However, the Langstroth and Dadant designs remain ubiquitous in the US and also in many parts of Europe, though Sweden, Denmark, Germany, France and Italy all have their own national hive designs. Regional variations of hive evolved to reflect the climate, floral productivity and the reproductive characteristics of the various subspecies of native honey bee in each bio-region.

Honey-laden honeycomb in a wooden frame

The differences in hive dimensions are insignificant in comparison to the common factors in all these hives: they are all square or rectangular; they all use movable wooden frames; they all consist of a floor, brood-box, honey super, crown-board and roof. Hives have traditionally been constructed of cedar, pine, or cypress wood, but in recent years hives made from injection molded dense polystyrene have become increasingly important.

Hives also use queen excluders between the brood-box and honey supers to keep the queen from laying eggs in cells next to those containing honey intended for consumption. Also, with the advent in the 20th century of mite pests, hive floors are often replaced for part of (or the whole) year with a wire mesh and removable tray.

Flow Hive 2 with honey pouring into jars

 

In 2015 the Flow Hive system was invented in Australia by Cedar Anderson and his father Stuart Anderson, allowing honey to be extracted without expensive centrifuge equipment.

Pioneers of practical and commercial beekeeping

The 19th century produced an explosion of innovators and inventors who perfected the design and production of beehives, systems of management and husbandry, stock improvement by selective breeding, honey extraction and marketing. Preeminent among these innovators were:

Petro Prokopovych used frames with channels in the side of the woodwork; these were packed side by side in boxes that were stacked one on top of the other. The bees traveled from frame to frame and box to box via the channels. The channels were similar to the cut outs in the sides of modern wooden sections (1814).

Jan Dzierżon was the father of modern apiology and apiculture. All modern beehives are descendants of his design.

François Huber made significant discoveries regarding the bee life-cycle and communication between bees. Despite being blind, Huber brought to light a large amount of information regarding the queen bee's mating habits and her communication with the rest of the hive. His work was published as New Observations on the Natural History of Bees.

L. L. Langstroth revered as the "father of American apiculture"; no other individual has influenced modern beekeeping practice more than Lorenzo Lorraine Langstroth. His classic book The Hive and Honey-bee was published in 1853.

Moses Quinby often termed "the father of commercial beekeeping in the United States", author of Mysteries of Bee-Keeping Explained. He invented the Bee smoker in 1873.

Amos Root author of the A B C of Bee Culture, which has been continuously revised and remains in print. Root pioneered the manufacture of hives and the distribution of bee-packages in the United States. 

A. J. Cook author of The Bee-Keepers' Guide; or Manual of the Apiary, 1876.

Dr. C.C. Miller was one of the first entrepreneurs to actually make a living from apiculture. By 1878 he made beekeeping his sole business activity. His book, Fifty Years Among the Bees, remains a classic and his influence on bee management persists to this day.

Honey Extractor

Franz Hruschka was an Italian military officer who made one crucial invention that catalyzed the commercial honey industry. In 1865 he invented a simple machine for extracting honey from the comb by means of centrifugal force. His original idea was simply to support combs in a metal framework and then spin them around within a container to collect honey as it was thrown out by centrifugal force. This meant that honeycombs could be returned to a hive undamaged but empty, saving the bees a vast amount of work, time, and materials. This single invention greatly improved the efficiency of honey harvesting and catalysed the modern honey industry.

Walter T. Kelley was an American pioneer of modern beekeeping in the early and mid-20th century. He greatly improved upon beekeeping equipment and clothing and went on to manufacture these items as well as other equipment. His company sold via catalog worldwide and his book, How to Keep Bees & Sell Honey, an introductory book of apiculture and marketing, allowed for a boom in beekeeping following World War II. 

In the U.K. practical beekeeping was led in the early 20th century by a few men, pre-eminently Brother Adam and his Buckfast bee and R.O.B. Manley, author of many titles, including Honey Production in the British Isles and inventor of the Manley frame, still universally popular in the U.K. Other notable British pioneers include William Herrod-Hempsall and Gale.

Dr. Ahmed Zaky Abushady (1892–1955), was an Egyptian poet, medical doctor, bacteriologist and bee scientist who was active in England and in Egypt in the early part of the twentieth century. In 1919, Abushady patented a removable, standardized aluminum honeycomb. In 1919 he also founded The Apis Club in Benson, Oxfordshire, and its periodical Bee World, which was to be edited by Annie D. Betts and later by Dr. Eva Crane. The Apis Club was transitioned to the International Bee Research Association (IBRA). Its archives are held in the National Library of Wales. In Egypt in the 1930s, Abushady established The Bee Kingdom League and its organ, The Bee Kingdom.

In India, R. N. Mattoo was the pioneer worker in starting beekeeping with Indian honeybee, (Apis cerana indica) in the early 1930s. Beekeeping with European honeybee, (Apis mellifera) was started by Dr. A. S. Atwal and his team members, O. P. Sharma and N. P. Goyal in Punjab in the early 1960s. It remained confined to Punjab and Himachal Pradesh up to the late 1970s. Later on in 1982, Dr. R. C. Sihag, working at Haryana Agricultural University, Hisar (Haryana), introduced and established this honeybee in Haryana and standardized its management practices for semi-arid-subtropical climates. On the basis of these practices, beekeeping with this honeybee could be extended to the rest of the country. Now beekeeping with Apis mellifera predominates in India.

Traditional beekeeping

Wooden hives in Stripeikiai honeymaking museum, Lithuania

 

Beekeeping at Kawah Ijen Mountain, Indonesia

Fixed comb hives

A fixed comb hive is a hive in which the combs cannot be removed or manipulated for management or harvesting without permanently damaging the comb. Almost any hollow structure can be used for this purpose, such as a log gum, skep, wooden box, or a clay pot or tube. Fixed comb hives are no longer in common use in industrialized countries, and are illegal in places that require movable combs to inspect for problems such as varroa and American foulbrood. In many developing countries fixed comb hives are widely used and, because they can be made from any locally available material .

Beekeeping using fixed comb hives is an essential part of the livelihoods of many communities in poor countries. The charity Bees for Development recognizes that local skills to manage bees in fixed comb hives^[26] are widespread in Africa, Asia, and South America. Internal size of fixed comb hives range from 32.7 liters (2000 cubic inches) typical of the clay tube hives used in Egypt to 282 liters (17209 cubic inches) for the Perone hive. Straw skeps, bee gums, and unframed box hives are unlawful in most US states, as the comb and brood cannot be inspected for diseases. However, skeps are still used for collecting swarms by hobbyists in the UK, before moving them into standard hives. Quinby used box hives to produce so much honey that he saturated the New York market in the 1860s. His writings contain excellent advice for management of bees in fixed comb hives.

Modern beekeeping

Topbar hives

Top bar hives have been widely adopted in Africa where they are used to keep tropical honeybee ecotypes. Their advantages include being light weight, adaptable, easy to harvest honey, and less stressful for the bees. Disadvantages include combs that are fragile and cannot usually be extracted and returned to the bees to be refilled and that they cannot easily be expanded for additional honey storage. 

A growing number of amateur beekeepers are adopting various top-bar hives similar to the type commonly found in Africa. Top bar hives were originally used as a traditional beekeeping method in Greece and Vietnam with a history dating back over 2000 years. These hives have no frames and the honey-filled comb is not returned after extraction. Because of this, the production of honey is likely to be somewhat less than that of a frame and super based hive such as Langstroth or Dadant. Top bar hives are mostly kept by people who are more interested in having bees in their garden than in honey production per se. Some of the most well known top-bar hive designs are the Kenyan Top Bar Hive with sloping sides, the Tanzanian Top Bar Hive with straight sides, and Vertical Top Bar Hives, such as the Warre or "People's Hive" designed by Abbe Warre in the mid-1900s.

The initial costs and equipment requirements are typically much less than other hive designs. Scrap wood or #2 or #3 pine can often be used to build a nice hive. Top-bar hives also offer some advantages to interacting with the bees and the amount of weight that must be lifted is greatly reduced. Top-bar hives are being widely used in developing countries in Africa and Asia as a result of the Bees for Development program. Since 2011, a growing number of beekeepers in the U.S. are using various top-bar hives.

Vertical stackable hives

There are three types of vertical stackable hives: hanging or top-access frame, sliding or side-access frame, and top bar. 

Hanging frame hives include Langstroth, the British National, Dadant, Layens, and Rose, differing primarily by size or number of frames. The Langstroth was the first successful top-opened hive with movable frames. Many other hive designs are based on the principle of bee space first described by Langstroth, and is a descendant of Jan Dzierzon's Polish hive designs. Langstroth hives are the most common size in the United States and much of the world; the British National is the most common size in the United Kingdom; Dadant and Modified Dadant hives are widely used in France and Italy, and Layens by some beekeepers, where their large size is an advantage. Square Dadant hives–often called 12 frame Dadant or Brother Adam hives–are used in large parts of Germany and other parts of Europe by commercial beekeepers. 

Any hanging frame hive design can be built as a sliding frame design. The AZ Hive, the original sliding frame design, integrates hives using Langstroth-sized frames into a honey house so as to streamline the workflow of honey harvest by localization of labor, similar to cellular manufacturing. The honey house can be a portable trailer, allowing the beekeeper to haul the hives to a site and provide pollination services.

Top bar stackable hives simply use top bars instead of full frames. The most common type is the Warre hive, although any hive with hanging frames can be made into a top bar stackable hive by using only the top bar and not the whole frame. This may work less-well with larger frames, where crosscomb and attachment can occur more-readily.

Protective clothing

Beekeepers often wear protective clothing to protect themselves from stings

Most beekeepers also wear some protective clothing. Novice beekeepers usually wear gloves and a hooded suit or hat and veil. Experienced beekeepers sometimes elect not to use gloves because they inhibit delicate manipulations. The face and neck are the most important areas to protect, so most beekeepers wear at least a veil. Defensive bees are attracted to the breath, and a sting on the face can lead to much more pain and swelling than a sting elsewhere, while a sting on a bare hand can usually be quickly removed by fingernail scrape to reduce the amount of venom injected.

Traditionally beekeeping clothing was pale colored and this is still very common today. This is because of the natural color of cotton and cost of coloring was an expense not warranted for workwear, though some consider this is to provide better differentiation from the colony's natural predators (such as bears and skunks) which tend to be dark-colored. It is now known that bees see in ultraviolet and are also attracted to scent. So the type of fabric conditioner used has more impact than the color of the fabric.

'Stings' retained in clothing fabric continue to pump out an alarm pheromone that attracts aggressive action and further stinging attacks. Washing suits regularly, and rinsing gloved hands in vinegar minimizes attraction.

Smoker

Bee smoker with heat shield and hook

 

Smoke is the beekeeper's third line of defense. Most beekeepers use a "smoker"—a device designed to generate smoke from the incomplete combustion of various fuels. Smoke calms bees; it initiates a feeding response in anticipation of possible hive abandonment due to fire. Smoke also masks alarm pheromones released by guard bees or when bees are squashed in an inspection. The ensuing confusion creates an opportunity for the beekeeper to open the hive and work without triggering a defensive reaction. In addition, when a bee consumes honey the bee's abdomen distends, supposedly making it difficult to make the necessary flexes to sting, though this has not been tested scientifically.

Many types of fuel can be used in a smoker as long as it is natural and not contaminated with harmful substances. These fuels include hessian, twine, burlap, pine needles, corrugated cardboard, and mostly rotten or punky wood. Indian beekeepers, especially in Kerala, often use coconut fibers as they are readily available, safe, and of negligible expense. Some beekeeping supply sources also sell commercial fuels like pulped paper and compressed cotton, or even aerosol cans of smoke. Other beekeepers use sumac as fuel because it ejects lots of smoke and doesn't have an odor.

Some beekeepers are using "liquid smoke" as a safer, more convenient alternative. It is a water-based solution that is sprayed onto the bees from a plastic spray bottle.

Torpor may also be induced by the introduction of chilled air into the hive – while chilled carbon dioxide may have harmful long-term effects.

Effects of stings and of protective measures

Some beekeepers believe that the more stings a beekeeper receives, the less irritation each causes, and they consider it important for safety of the beekeeper to be stung a few times a season. Beekeepers have high levels of antibodies (mainly IgG) reacting to the major antigen of bee venom, phospholipase A2 (PLA). Antibodies correlate with the frequency of bee stings.

The entry of venom into the body from bee-stings may also be hindered and reduced by protective clothing that allows the wearer to remove stings and venom sacs with a simple tug on the clothing. Although the stinger is barbed, a worker bee is less likely to become lodged into clothing than human skin. 

If a beekeeper is stung by a bee, there are many protective measures that should be taken in order to make sure the affected area does not become too irritated. The first cautionary step that should be taken following a bee sting is removing the stinger without squeezing the attached venom glands. A quick scrape with a fingernail is effective and intuitive. This step is effective in making sure that the venom injected does not spread, so the side effects of the sting will go away sooner. Washing the affected area with soap and water is also a good way to stop the spread of venom. The last step that needs to be taken is to apply ice or a cold compress to the stung area.

Natural beekeeping

The natural beekeeping movement believes that bee hives are weakened by modern beekeeping and agricultural practices, such as crop spraying, hive movement, frequent hive inspections, artificial insemination of queens, routine medication, and sugar water feeding.

Practitioners of "natural beekeeping" tend to use variations of the top-bar hive, which is a simple design that retains the concept of having a movable comb without the use of frames or a foundation. The horizontal top-bar hive, as championed by Marty Hardison, Michael Bush, Philip Chandler, Dennis Murrell and others, can be seen as a modernization of hollow log hives, with the addition of wooden bars of specific width from which bees hang their combs. Its widespread adoption in recent years can be attributed to the publication in 2007 of The Barefoot Beekeeper by Philip Chandler, which challenged many aspects of modern beekeeping and offered the horizontal top-bar hive as a viable alternative to the ubiquitous Langstroth-style movable-frame hive. 

The most popular vertical top-bar hive is the Warré hive, based on a design by the French priest Abbé Émile Warré (1867–1951) and popularized by Dr. David Heaf in his English translation of Warré's book L'Apiculture pour Tous as Beekeeping For All.

Honey bee in Toronto

Urban or backyard beekeeping

Related to natural beekeeping, urban beekeeping is an attempt to revert to a less industrialized way of obtaining honey by utilizing small-scale colonies that pollinate urban gardens. Urban apiculture has undergone a renaissance in the first decade of the 21st century, and urban beekeeping is seen by many as a growing trend.

Some have found that "city bees" are actually healthier than "rural bees" because there are fewer pesticides and greater biodiversity in the urban gardens. Urban bees may fail to find forage, however, and homeowners can use their landscapes to help feed local bee populations by planting flowers that provide nectar and pollen. An environment of year-round, uninterrupted bloom creates an ideal environment for colony reproduction.

Urban beekeepers are testing modern types of beehives, testing for urban contest and ease of use. In 2015 the FlowHive appeared and in 2018 Beeing, a hive made in Italy, that allows the beekeeper to extract honey without having contact with the bees. 

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MIT's ''Synthetic Apiary'' project raises colonies entirely indoors

Indoor beekeeping

Modern beekeepers have experimented with raising bees indoors, in a controlled environment or in indoor observation hives. This may be done for reasons of space and monitoring, or in the off-season. In the off-season, large commercial beekeepers may move colonies to "wintering" warehouses, with fixed temperature, light and humidity. This helps the bees remain healthy, but relatively dormant. These relatively dormant or "wintered" bees survive on stored honey, and new bees are not born.

Experiments in raising bees for longer durations indoors have looked into more detailed and varying environment controls. In 2015, MIT's Synthetic Apiary project simulated springtime inside a closed environment, for a number of hives over the course of a winter. They provided food sources and simulated long days, and saw activity and reproduction levels comparable to the levels seen outdoors in warm weather. They concluded that such an indoor apiary could be sustained year-round if needed.

Bee colonies

Species

There are more than 20,000 species of wild bees. Many species are solitary (e.g., mason bees, leafcutter bees (Megachilidae), carpenter bees and other ground-nesting bees). Many others rear their young in burrows and small colonies (e.g., bumblebees and stingless bees). Some honey bees are wild e.g. the little honeybee (Apis florea), giant honeybee (Apis dorsata) and rock bee (Apis laboriosa). Beekeeping, or apiculture, is concerned with the practical management of the social species of honey bees, which live in large colonies of up to 100,000 individuals. In Europe and America the species universally managed by beekeepers is the Western honey bee (Apis mellifera). This species has several sub-species or regional varieties, such as the Italian bee (Apis mellifera ligustica), European dark bee (Apis mellifera mellifera), and the Carniolan honey bee (Apis mellifera carnica). In the tropics, other species of social bees are managed for honey production, including the Asiatic honey bee (Apis cerana).

Castes

A colony of bees consists of three castes of bee:

• a queen bee, which is normally the only breeding female in the colony;
• a large number of female worker bees, typically 30,000–50,000 in number;
• a number of male drones, ranging from thousands in a strong hive in spring to very few during dearth or cold season.

Queen bee (center)

The queen is the only sexually mature female in the hive and all of the female worker bees and male drones are her offspring. The queen may live for up to three years or more and may be capable of laying half a million eggs or more in her lifetime. At the peak of the breeding season, late spring to summer, a good queen may be capable of laying 3,000 eggs in one day, more than her own body weight. This would be exceptional however; a prolific queen might peak at 2,000 eggs a day, but a more average queen might lay just 1,500 eggs per day. The queen is raised from a normal worker egg, but is fed a larger amount of royal jelly than a normal worker bee, resulting in a radically different growth and metamorphosis. The queen influences the colony by the production and dissemination of a variety of pheromones or "queen substances". One of these chemicals suppresses the development of ovaries in all the female worker bees in the hive and prevents them from laying eggs.

Mating of queens

The queen emerges from her cell after 15 days of development and she remains in the hive for 3–7 days before venturing out on a mating flight. Mating flight is otherwise known as "nuptial flight". Her first orientation flight may only last a few seconds, just enough to mark the position of the hive. Subsequent mating flights may last from 5 minutes to 30 minutes, and she may mate with a number of male drones on each flight. Over several matings, possibly a dozen or more, the queen receives and stores enough sperm from a succession of drones to fertilize hundreds of thousands of eggs. If she does not manage to leave the hive to mate—possibly due to bad weather or being trapped in part of the hive—she remains infertile and becomes a drone layer, incapable of producing female worker bees. Worker bees sometimes kill a non-performing queen and produce another. Without a properly performing queen, the hive is doomed.

Mating takes place at some distance from the hive and often several hundred feet in the air; it is thought that this separates the strongest drones from the weaker ones, ensuring that only the fastest and strongest drones get to pass on their genes.

Worker bees

Worker bee

Most of the bees in a hive are female worker bees. At the height of summer when activity in the hive is frantic and work goes on non-stop, the life of a worker bee may be as short as 6 weeks; in late autumn, when no brood is being raised and no nectar is being harvested, a young bee may live for 16 weeks, right through the winter.

Over the course of their lives, worker bees' duties are dictated by age. For the first few weeks of their lifespan, they perform basic chores within the hive: cleaning empty brood cells, removing debris and other housekeeping tasks, making wax for building or repairing comb, and feeding larvae. Later, they may ventilate the hive or guard the entrance. Older workers leave the hive daily, weather permitting, to forage for nectar, pollen, water, and propolis. 

Period	Work activity
Days 1–3	Cleaning cells and incubation
Day 3–6	Feeding older larvae
Day 6–10	Feeding younger larvae
Day 8–16	Receiving nectar and pollen from field bees
Day 12–18	Beeswax making and cell building
Day 14 onwards	Entrance guards; nectar, pollen, water and propolis foraging; robbing other hives

Drones

Larger drones compared to smaller workers

Drones are the largest bees in the hive (except for the queen), at almost twice the size of a worker bee. Note in the picture that they have much larger eyes than the workers have, presumably to better locate the queen during the mating flight. They do not work, do not forage for pollen or nectar, are unable to sting, and have no other known function than to mate with new queens and fertilize them on their mating flights. A bee colony generally starts to raise drones a few weeks before building queen cells so they can supersede a failing queen or prepare for swarming. When queen-raising for the season is over, bees in colder climates drive drones out of the hive to die, biting and tearing their legs and wings.

Differing stages of development

Stage of development	Queen	Worker	Drone
Egg	3 days	3 days	3 days
Larva (successive molts)	8 days	10 days	13 days
Cell Capped	day 8	day 8	day 10
Pupa	4 days	8 days	8 days
Total	15 days	21 days	24 days

Structure of a bee colony

A domesticated bee colony is normally housed in a rectangular hive body, within which eight to ten parallel frames house the vertical plates of honeycomb that contain the eggs, larvae, pupae and food for the colony. If one were to cut a vertical cross-section through the hive from side to side, the brood nest would appear as a roughly ovoid ball spanning 5–8 frames of comb. The two outside combs at each side of the hive tend to be exclusively used for long-term storage of honey and pollen.

Within the central brood nest, a single frame of comb typically has a central disk of eggs, larvae and sealed brood cells that may extend almost to the edges of the frame. Immediately above the brood patch an arch of pollen-filled cells extends from side to side, and above that again a broader arch of honey-filled cells extends to the frame tops. The pollen is protein-rich food for developing larvae, while honey is also food but largely energy rich rather than protein rich. The nurse bees that care for the developing brood secrete a special food called "royal jelly" after feeding themselves on honey and pollen. The amount of royal jelly fed to a larva determines whether it develops into a worker bee or a queen. 

Apart from the honey stored within the central brood frames, the bees store surplus honey in combs above the brood nest. In modern hives the beekeeper places separate boxes, called "supers", above the brood box, in which a series of shallower combs is provided for storage of honey. This enables the beekeeper to remove some of the supers in the late summer, and to extract the surplus honey harvest, without damaging the colony of bees and its brood nest below. If all the honey is taken, including the amount of honey needed to survive winter, the beekeeper must replace these stores by feeding the bees sugar or corn syrup in autumn.

Annual cycle of a bee colony

The development of a bee colony follows an annual cycle of growth that begins in spring with a rapid expansion of the brood nest, as soon as pollen is available for feeding larvae. Some production of brood may begin as early as January, even in a cold winter, but breeding accelerates towards a peak in May (in the northern hemisphere), producing an abundance of harvesting bees synchronized to the main nectar flow in that region. Each race of bees times this build-up slightly differently, depending on how the flora of its original region blooms. Some regions of Europe have two nectar flows: one in late spring and another in late August. Other regions have only a single nectar flow. The skill of the beekeeper lies in predicting when the nectar flow will occur in his area and in trying to ensure that his colonies achieve a maximum population of harvesters at exactly the right time.

The key factor in this is the prevention or skillful management of the swarming impulse. If a colony swarms unexpectedly and the beekeeper does not manage to capture the resulting swarm, he is likely to harvest significantly less honey from that hive, since he has lost half his worker bees at a single stroke. If, however, he can use the swarming impulse to breed a new queen but keep all the bees in the colony together, he maximizes his chances of a good harvest. It takes many years of learning and experience to be able to manage all these aspects successfully, though owing to variable circumstances many beginners often achieve a good honey harvest.

Formation of new colonies

Colony reproduction: swarming and supersedure

A swarm about to land

All colonies are totally dependent on their queen, who is the only egg-layer. However, even the best queens live only a few years and one or two years longevity is the norm. She can choose whether or not to fertilize an egg as she lays it; if she does so, it develops into a female worker bee; if she lays an unfertilized egg it becomes a male drone. She decides which type of egg to lay depending on the size of the open brood cell she encounters on the comb. In a small worker cell, she lays a fertilized egg; if she finds a larger drone cell, she lays an unfertilized drone egg. 

All the time that the queen is fertile and laying eggs she produces a variety of pheromones, which control the behavior of the bees in the hive. These are commonly called queen substance, but there are various pheromones with different functions. As the queen ages, she begins to run out of stored sperm, and her pheromones begin to fail. 

Inevitably, the queen begins to falter, and the bees decide to replace her by creating a new queen from one of her worker eggs. They may do this because she has been damaged (lost a leg or an antenna), because she has run out of sperm and cannot lay fertilized eggs (has become a "drone laying queen"), or because her pheromones have dwindled to where they cannot control all the bees in the hive. At this juncture, the bees produce one or more queen cells by modifying existing worker cells that contain a normal female egg. They then pursue one of two ways to replace the queen: supersedure, replacing or superseding the queen without swarming, or swarm cell production, dividing the hive into two colonies through swarming. 

Supersedure is highly valued as a behavioral trait by beekeepers. A hive that supersedes its old queen does not lose any stock. Instead it creates a new queen and the old one fades away or is killed when the new queen emerges. In these hives, the bees produce just one or two queen cells, characteristically in the center of the face of a broodcomb. 

Swarm cell production involves creating many queen cells, typically a dozen or more. These are located around the edges of a broodcomb, often at the sides and the bottom. 

New wax combs between basement joists

Once either process has begun, the old queen leaves the hive with the hatching of the first queen cells. She leaves accompanied by a large number of bees, predominantly young bees (wax-secretors), who form the basis of the new hive. Scouts are sent out from the swarm to find suitable hollow trees or rock crevices. As soon as one is found, the entire swarm moves in. Within a matter of hours, they build new wax brood combs, using honey stores that the young bees have filled themselves with before leaving the old hive. Only young bees can secrete wax from special abdominal segments, and this is why swarms tend to contain more young bees. Often a number of virgin queens accompany the first swarm (the "prime swarm"), and the old queen is replaced as soon as a daughter queen mates and begins laying. Otherwise, she is quickly superseded in the new home.

Different sub-species of Apis mellifera exhibit differing swarming characteristics. In general the more northerly black races are said to swarm less and supersede more, whereas the more southerly yellow and grey varieties are said to swarm more frequently. The truth is complicated because of the prevalence of cross-breeding and hybridization of the sub species.

Factors that trigger swarming

Some beekeepers may monitor their colonies carefully in spring and watch for the appearance of queen cells, which are a dramatic signal that the colony is determined to swarm.

A swarm attached to a branch

 

This swarm looks for shelter. A beekeeper may capture it and introduce it into a new hive, helping meet this need. Otherwise, it returns to a feral state, in which case it finds shelter in a hollow tree, excavation, abandoned chimney, or even behind shutters. 

A small after-swarm has less chance of survival and may threaten the original hive's survival if the number of individuals left is unsustainable. When a hive swarms despite the beekeeper's preventative efforts, a good management practice is to give the reduced hive a couple frames of open brood with eggs. This helps replenish the hive more quickly and gives a second opportunity to raise a queen if there is a mating failure. 

Each race or sub-species of honey bee has its own swarming characteristics. Italian bees are very prolific and inclined to swarm; Northern European black bees have a strong tendency to supersede their old queen without swarming. These differences are the result of differing evolutionary pressures in the regions where each sub-species evolved.

Artificial swarming

When a colony accidentally loses its queen, it is said to be "queenless". The workers realize that the queen is absent after as little as an hour, as her pheromones fade in the hive. Instinctively, the workers select cells containing eggs aged less than three days and enlarge these cells dramatically to form "emergency queen cells". These appear similar to large peanut-like structures about an inch long that hang from the center or side of the brood combs. The developing larva in a queen cell is fed differently from an ordinary worker-bee; in addition to the normal honey and pollen, she receives a great deal of royal jelly, a special food secreted by young "nurse bees" from the hypopharyngeal gland. This special food dramatically alters the growth and development of the larva so that, after metamorphosis and pupation, it emerges from the cell as a queen bee. The queen is the only bee in a colony which has fully developed ovaries, and she secretes a pheromone which suppresses the normal development of ovaries in all her workers.

Beekeepers use the ability of the bees to produce new queens to increase their colonies in a procedure called splitting a colony. To do this, they remove several brood combs from a healthy hive, taking care to leave the old queen behind. These combs must contain eggs or larvae less than three days old and be covered by young nurse bees, which care for the brood and keep it warm. These brood combs and attendant nurse bees are then placed into a small "nucleus hive" with other combs containing honey and pollen. As soon as the nurse bees find themselves in this new hive and realize they have no queen, they set about constructing emergency queen cells using the eggs or larvae they have in the combs with them.

Losses

Diseases

The common agents of disease that affect adult honey bees include fungi, bacteria, protozoa, viruses, parasites, and poisons. The gross symptoms displayed by affected adult bees are very similar, whatever the cause, making it difficult for the apiarist to ascertain the causes of problems without microscopic identification of microorganisms or chemical analysis of poisons. Since 2006 colony losses from colony collapse disorder have been increasing across the world although the causes of the syndrome are, as yet, unknown. In the US, commercial beekeepers have been increasing the number of hives to deal with higher rates of attrition.

Parasites

Galleria mellonella and Achroia grisella “wax moth” larvae that hatch, tunnel through, and destroy comb that contains bee larvae and their honey stores. The tunnels they create are lined with silk, which entangles and starves emerging bees. Destruction of honeycombs also results in honey leaking and being wasted. A healthy hive can manage wax moths, but weak colonies, unoccupied hives, and stored frames can be decimated.

Small hive beetle (Aethina tumida) is native to Africa but has now spread to most continents. It is a serious pest among honey bees unadapted to it.

Varroa destructor, the Varroa mite, is an established pest of two species of honey bee through many parts of the world, and is blamed by many researchers as a leading cause of CCD.

Acarapis woodi, the tracheal mite, infests the trachea of honey bees.

Predators

Most predators prefer not to eat honeybees due to their unpleasant sting, but they still have some predators. These include large animals such as skunks or bears, which are after the honey and brood in the nest as well as the adult bees themselves. Some birds will also eat bees (for example, bee-eaters, which are named for their bee-centric diet), as do some robber flies, such as Mallophora ruficauda, which is a pest of apiculture in South America due to its habit of eating workers while they are foraging in meadows.

World apiculture

According to U.N. FAO data, the world's beehive stock rose from around 50 million in 1961 to around 83 million in 2014, which comes to about 1.3% average annual growth. Average annual growth has accelerated to 1.9% since 2009. 

World's stock of beehives from 1961 to 2014

Ant colony optimization algorithms

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Ant_colony_optimization_algorithms 

Ant behavior was the inspiration for the metaheuristic optimization technique

 

When a colony of ants is confronted with the choice of reaching their food via two different routes of which one is much shorter than the other, their choice is entirely random. However, those who use the shorter route reach the food faster and therefore go back and forth more often between the anthill and the food.

 

In computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems which can be reduced to finding good paths through graphs. Artificial Ants stand for multi-agent methods inspired by the behavior of real ants. The pheromone-based communication of biological ants is often the predominant paradigm used. Combinations of Artificial Ants and local search algorithms have become a method of choice for numerous optimization tasks involving some sort of graph, e.g., vehicle routing and internet routing. The burgeoning activity in this field has led to conferences dedicated solely to Artificial Ants, and to numerous commercial applications by specialized companies such as AntOptima.

As an example, Ant colony optimization is a class of optimization algorithms modeled on the actions of an ant colony. Artificial 'ants' (e.g. simulation agents) locate optimal solutions by moving through a parameter space representing all possible solutions. Real ants lay down pheromones directing each other to resources while exploring their environment. The simulated 'ants' similarly record their positions and the quality of their solutions, so that in later simulation iterations more ants locate better solutions. One variation on this approach is the bees algorithm, which is more analogous to the foraging patterns of the honey bee, another social insect. 

This algorithm is a member of the ant colony algorithms family, in swarm intelligence methods, and it constitutes some metaheuristic optimizations. Initially proposed by Marco Dorigo in 1992 in his PhD thesis, the first algorithm was aiming to search for an optimal path in a graph, based on the behavior of ants seeking a path between their colony and a source of food. The original idea has since diversified to solve a wider class of numerical problems, and as a result, several problems have emerged, drawing on various aspects of the behavior of ants. From a broader perspective, ACO performs a model-based search and shares some similarities with estimation of distribution algorithms.

Overview

In the natural world, ants of some species (initially) wander randomly, and upon finding food return to their colony while laying down pheromone trails. If other ants find such a path, they are likely not to keep travelling at random, but instead to follow the trail, returning and reinforcing it if they eventually find food (see Ant communication).

Over time, however, the pheromone trail starts to evaporate, thus reducing its attractive strength. The more time it takes for an ant to travel down the path and back again, the more time the pheromones have to evaporate. A short path, by comparison, gets marched over more frequently, and thus the pheromone density becomes higher on shorter paths than longer ones. Pheromone evaporation also has the advantage of avoiding the convergence to a locally optimal solution. If there were no evaporation at all, the paths chosen by the first ants would tend to be excessively attractive to the following ones. In that case, the exploration of the solution space would be constrained. The influence of pheromone evaporation in real ant systems is unclear, but it is very important in artificial systems.

The overall result is that when one ant finds a good (i.e., short) path from the colony to a food source, other ants are more likely to follow that path, and positive feedback eventually leads to many ants following a single path. The idea of the ant colony algorithm is to mimic this behavior with "simulated ants" walking around the graph representing the problem to solve.

Ambient networks of intelligent objects

New concepts are required since “intelligence” is no longer centralized but can be found throughout all minuscule objects. Anthropocentric concepts have been known to lead to the production of IT systems in which data processing, control units and calculating forces are centralized. These centralized units have continually increased their performance and can be compared to the human brain. The model of the brain has become the ultimate vision of computers. Ambient networks of intelligent objects and, sooner or later, a new generation of information systems which are even more diffused and based on nanotechnology, will profoundly change this concept. Small devices that can be compared to insects do not dispose of a high intelligence on their own. Indeed, their intelligence can be classed as fairly limited. It is, for example, impossible to integrate a high performance calculator with the power to solve any kind of mathematical problem into a biochip that is implanted into the human body or integrated in an intelligent tag which is designed to trace commercial articles. However, once those objects are interconnected they dispose of a form of intelligence that can be compared to a colony of ants or bees. In the case of certain problems, this type of intelligence can be superior to the reasoning of a centralized system similar to the brain.

Nature offers several examples of how minuscule organisms, if they all follow the same basic rule, can create a form of collective intelligence on the macroscopic level. Colonies of social insects perfectly illustrate this model which greatly differs from human societies. This model is based on the co-operation of independent units with simple and unpredictable behavior. They move through their surrounding area to carry out certain tasks and only possess a very limited amount of information to do so. A colony of ants, for example, represents numerous qualities that can also be applied to a network of ambient objects. Colonies of ants have a very high capacity to adapt themselves to changes in the environment as well as an enormous strength in dealing with situations where one individual fails to carry out a given task. This kind of flexibility would also be very useful for mobile networks of objects which are perpetually developing. Parcels of information that move from a computer to a digital object behave in the same way as ants would do. They move through the network and pass from one knot to the next with the objective of arriving at their final destination as quickly as possible.

Artificial pheromone system

Pheromone-based communication is one of the most effective ways of communication which is widely observed in nature. Pheromone is used by social insects such as bees, ants and termites; both for inter-agent and agent-swarm communications. Due to its feasibility, artificial pheromones have been adopted in multi-robot and swarm robotic systems. Pheromone-based communication was implemented by different means such as chemical or physical (RFID tags, light, sound) ways. However, those implementations were not able to replicate all the aspects of pheromones as seen in nature. 

Using projected light was presented in an 2007 IEEE paper by Garnier, Simon, et al. as an experimental setup to study pheromone-based communication with micro autonomous robots. Another study that proposed a novel pheromone communication method, COSΦ, for a swarm robotic system is based on precise and fast visual localization. The system allows simulation of a virtually unlimited number of different pheromones and provides the result of their interaction as a gray-scale image on a horizontal LCD screen that the robots move on. In order to demonstrate the pheromone communication method, Colias autonomous micro robot was deployed as the swarm robotic platform.

Algorithm and formulae

In the ant colony optimization algorithms, an artificial ant is a simple computational agent that searches for good solutions to a given optimization problem. To apply an ant colony algorithm, the optimization problem needs to be converted into the problem of finding the shortest path on a weighted graph. In the first step of each iteration, each ant stochastically constructs a solution, i.e. the order in which the edges in the graph should be followed. In the second step, the paths found by the different ants are compared. The last step consists of updating the pheromone levels on each edge.

procedure ACO_MetaHeuristic is
    while not_termination do
        generateSolutions()
        daemonActions()
        pheromoneUpdate()
    repeat
end procedure

Edge selection

Each ant needs to construct a solution to move through the graph. To select the next edge in its tour, an ant will consider the length of each edge available from its current position, as well as the corresponding pheromone level. At each step of the algorithm, each ant moves from a state ${\displaystyle x}$ to state ${\displaystyle y}$, corresponding to a more complete intermediate solution. Thus, each ant ${\displaystyle k}$ computes a set ${\displaystyle A_{k}(x)}$ of feasible expansions to its current state in each iteration, and moves to one of these in probability. For ant ${\displaystyle k}$, the probability ${\displaystyle p_{xy}^{k}}$ of moving from state ${\displaystyle x}$ to state ${\displaystyle y}$ depends on the combination of two values, the attractiveness ${\displaystyle \eta _{xy}}$ of the move, as computed by some heuristic indicating the a priori desirability of that move and the trail level ${\displaystyle \tau _{xy}}$ of the move, indicating how proficient it has been in the past to make that particular move. The trail level represents a posteriori indication of the desirability of that move.

In general, the ${\displaystyle k}$th ant moves from state ${\displaystyle x}$ to state ${\displaystyle y}$ with probability 

${\displaystyle p_{xy}^{k}={\frac {(\tau _{xy}^{\alpha })(\eta _{xy}^{\beta })}{\sum _{z\in \mathrm {allowed} _{x}}(\tau _{xz}^{\alpha })(\eta _{xz}^{\beta })}}}$

where is the amount of pheromone deposited for transition from state ${\displaystyle x}$ to ${\displaystyle y}$, 0 ≤ ${\displaystyle \alpha }$ is a parameter to control the influence of ${\displaystyle \tau _{xy}}$, ${\displaystyle \eta _{xy}}$ is the desirability of state transition ${\displaystyle xy}$ (a priori knowledge, typically ${\displaystyle 1/d_{xy}}$, where ${\displaystyle d}$ is the distance) and ${\displaystyle \beta }$ ≥ 1 is a parameter to control the influence of ${\displaystyle \eta _{xy}}$. ${\displaystyle \tau _{xz}}$ and ${\displaystyle \eta _{xz}}$ represent the trail level and attractiveness for the other possible state transitions.

Pheromone update

Trails are usually updated when all ants have completed their solution, increasing or decreasing the level of trails corresponding to moves that were part of "good" or "bad" solutions, respectively. An example of a global pheromone updating rule is 

${\displaystyle \tau _{xy}\leftarrow (1-\rho )\tau _{xy}+\sum _{k}\Delta \tau _{xy}^{k}}$

where ${\displaystyle \tau _{xy}}$ is the amount of pheromone deposited for a state transition ${\displaystyle xy}$, ${\displaystyle \rho }$ is the pheromone evaporation coefficient and ${\displaystyle \Delta \tau _{xy}^{k}}$ is the amount of pheromone deposited by ${\displaystyle k}$th ant, typically given for a TSP problem (with moves corresponding to arcs of the graph) by 

${\displaystyle \Delta \tau _{xy}^{k}={\begin{cases}Q/L_{k}&{\mbox{if ant }}k{\mbox{ uses curve }}xy{\mbox{ in its tour}}\\0&{\mbox{otherwise}}\end{cases}}}$

where ${\displaystyle L_{k}}$ is the cost of the ${\displaystyle k}$th ant's tour (typically length) and ${\displaystyle Q}$ is a constant.

Common extensions

Here are some of the most popular variations of ACO algorithms.

Ant System (AS)

The Ant System is the first ACO algorithm. This algorithm corresponds to the one presented above. It was developed by Dorigo.

Ant Colony System (ACS)

In the Ant Colony System algorithm, the original Ant System was modified in three aspects: (i) the edge selection is biased towards exploitation (i.e. favoring the probability of selecting the shortest edges with a large amount of pheromone); (ii) while building a solution, ants change the pheromone level of the edges they are selecting by applying a local pheromone updating rule; (iii) at the end of each iteration, only the best ant is allowed to update the trails by applying a modified global pheromone updating rule.

Elitist Ant System

In this algorithm, the global best solution deposits pheromone on its trail after every iteration (even if this trial has not been revisited), along with all the other ants.

Max-Min Ant System (MMAS)

This algorithm controls the maximum and minimum pheromone amounts on each trail. Only the global best tour or the iteration best tour are allowed to add pheromone to its trail. To avoid stagnation of the search algorithm, the range of possible pheromone amounts on each trail is limited to an interval [τ_max,τ_min]. All edges are initialized to τ_max to force a higher exploration of solutions. The trails are reinitialized to τ_max when nearing stagnation.

Rank-based Ant System (ASrank)

All solutions are ranked according to their length. Only a fixed number of the best ants in this iteration are allowed to update their trials. The amount of pheromone deposited is weighted for each solution, such that solutions with shorter paths deposit more pheromone than the solutions with longer paths.

Continuous Orthogonal Ant Colony (COAC)

The pheromone deposit mechanism of COAC is to enable ants to search for solutions collaboratively and effectively. By using an orthogonal design method, ants in the feasible domain can explore their chosen regions rapidly and efficiently, with enhanced global search capability and accuracy. The orthogonal design method and the adaptive radius adjustment method can also be extended to other optimization algorithms for delivering wider advantages in solving practical problems.

Recursive Ant Colony Optimization

It is a recursive form of ant system which divides the whole search domain into several sub-domains and solves the objective on these subdomains. The results from all the subdomains are compared and the best few of them are promoted for the next level. The subdomains corresponding to the selected results are further subdivided and the process is repeated until an output of desired precision is obtained. This method has been tested on ill-posed geophysical inversion problems and works well.

Convergence

For some versions of the algorithm, it is possible to prove that it is convergent (i.e., it is able to find the global optimum in finite time). The first evidence of convergence for an ant colony algorithm was made in 2000, the graph-based ant system algorithm, and later on for the ACS and MMAS algorithms. Like most metaheuristics, it is very difficult to estimate the theoretical speed of convergence. A performance analysis of a continuous ant colony algorithm with respect to its various parameters (edge selection strategy, distance measure metric, and pheromone evaporation rate) showed that its performance and rate of convergence are sensitive to the chosen parameter values, and especially to the value of the pheromone evaporation rate. In 2004, Zlochin and his colleagues showed that COAC-type algorithms could be assimilated methods of stochastic gradient descent, on the cross-entropy and estimation of distribution algorithm. They proposed these metaheuristics as a "research-based model".

Applications

Knapsack problem: The ants prefer the smaller drop of honey over the more abundant, but less nutritious, sugar

Ant colony optimization algorithms have been applied to many combinatorial optimization problems, ranging from quadratic assignment to protein folding or routing vehicles and a lot of derived methods have been adapted to dynamic problems in real variables, stochastic problems, multi-targets and parallel implementations. It has also been used to produce near-optimal solutions to the travelling salesman problem. They have an advantage over simulated annealing and genetic algorithm approaches of similar problems when the graph may change dynamically; the ant colony algorithm can be run continuously and adapt to changes in real time. This is of interest in network routing and urban transportation systems.

The first ACO algorithm was called the ant system and it was aimed to solve the travelling salesman problem, in which the goal is to find the shortest round-trip to link a series of cities. The general algorithm is relatively simple and based on a set of ants, each making one of the possible round-trips along the cities. At each stage, the ant chooses to move from one city to another according to some rules:

1. It must visit each city exactly once;
2. A distant city has less chance of being chosen (the visibility);
3. The more intense the pheromone trail laid out on an edge between two cities, the greater the probability that that edge will be chosen;
4. Having completed its journey, the ant deposits more pheromones on all edges it traversed, if the journey is short;
5. After each iteration, trails of pheromones evaporate.

Scheduling problem

• Sequential Ordering Problem (SOP) 
• Job-shop scheduling problem (JSP)
• Open-shop scheduling problem (OSP)
• Permutation flow shop problem (PFSP)
• Single machine total tardiness problem (SMTTP)
• Single machine total weighted tardiness problem (SMTWTP)
• Resource-constrained project scheduling problem (RCPSP)
• Group-shop scheduling problem (GSP)
• Single-machine total tardiness problem with sequence dependent setup times (SMTTPDST)^[43]
• Multistage flowshop scheduling problem (MFSP) with sequence dependent setup/changeover times

Vehicle routing problem

• Capacitated vehicle routing problem (CVRP)
• Multi-depot vehicle routing problem (MDVRP)
• Period vehicle routing problem (PVRP)
• Split delivery vehicle routing problem (SDVRP)
• Stochastic vehicle routing problem (SVRP)
• Vehicle routing problem with pick-up and delivery (VRPPD)
• Vehicle routing problem with time windows (VRPTW)
• Time dependent vehicle routing problem with time windows (TDVRPTW)
• Vehicle routing problem with time windows and multiple service workers (VRPTWMS)

Assignment problem

• Quadratic assignment problem (QAP)
• Generalized assignment problem (GAP)
• Frequency assignment problem (FAP)
• Redundancy allocation problem (RAP)

Set problem

• Set cover problem (SCP)
• Partition problem (SPP)
• Weight constrained graph tree partition problem (WCGTPP)
• Arc-weighted l-cardinality tree problem (AWlCTP)
• Multiple knapsack problem (MKP)
• Maximum independent set problem (MIS)

Device sizing problem in nanoelectronics physical design

• Ant colony optimization (ACO) based optimization of 45 nm CMOS-based sense amplifier circuit could converge to optimal solutions in very minimal time.
• Ant colony optimization (ACO) based reversible circuit synthesis could improve efficiency significantly.

Antennas optimization and synthesis

Loopback vibrators 10×10, synthesized by means of ACO algorithm

 

Unloopback vibrators 10×10, synthesized by means of ACO algorithm

 

To optimize the form of antennas, ant colony algorithms can be used. As example can be considered antennas RFID-tags based on ant colony algorithms (ACO)., loopback and unloopback vibrators 10×10

Image processing

The ACO algorithm is used in image processing for image edge detection and edge linking.

• Edge detection:

The graph here is the 2-D image and the ants traverse from one pixel depositing pheromone.The movement of ants from one pixel to another is directed by the local variation of the image's intensity values. This movement causes the highest density of the pheromone to be deposited at the edges.

The following are the steps involved in edge detection using ACO:

Step1: Initialization:Randomly place ${\displaystyle K}$ ants on the image ${\displaystyle I_{M_{1}M_{2}}}$ where ${\displaystyle K=(M_{1}*M_{2})^{\tfrac {1}{2}}}$ . Pheromone matrix ${\displaystyle \tau _{(i,j)}}$ are initialized with a random value. The major challenge in the initialization process is determining the heuristic matrix. 

There are various methods to determine the heuristic matrix. For the below example the heuristic matrix was calculated based on the local statistics: the local statistics at the pixel position (i,j). 

${\displaystyle \eta _{(i,j)}={\tfrac {1}{Z}}*Vc*I_{(i,j)}}$

 Where ${\displaystyle I}$ is the image of size ${\displaystyle M_{1}*M_{2}}$
${\displaystyle Z=\sum _{i=1:M_{1}}\sum _{j=1:M_{2}}Vc(I_{i,j})}$,which is a normalization factor

${\displaystyle {\begin{aligned}Vc(I_{i,j})=&f\left(\left\vert I_{(i-2,j-1)}-I_{(i+2,j+1)}\right\vert +\left\vert I_{(i-2,j+1)}-I_{(i+2,j-1)}\right\vert \right.\\&+\left\vert I_{(i-1,j-2)}-I_{(i+1,j+2)}\right\vert +\left\vert I_{(i-1,j-1)}-I_{(i+1,j+1)}\right\vert \\&+\left\vert I_{(i-1,j)}-I_{(i+1,j)}\right\vert +\left\vert I_{(i-1,j+1)}-I_{(i-1,j-1)}\right\vert \\&+\left.\left\vert I_{(i-1,j+2)}-I_{(i-1,j-2)}\right\vert +\left\vert I_{(i,j-1)}-I_{(i,j+1)}\right\vert \right)\end{aligned}}}$

${\displaystyle f(\cdot )}$ can be calculated using the following functions:
${\displaystyle f(x)=\lambda x,\quad {\text{for x ≥ 0; (1)}}}$
${\displaystyle f(x)=\lambda x^{2},\quad {\text{for x ≥ 0; (2)}}}$
${\displaystyle f(x)={\begin{cases}\sin({\frac {\pi x}{2\lambda }}),&{\text{for 0 ≤ x ≤}}\lambda {\text{; (3)}}\\0,&{\text{else}}\end{cases}}}$
${\displaystyle f(x)={\begin{cases}\pi x\sin({\frac {\pi x}{2\lambda }}),&{\text{for 0 ≤ x ≤}}\lambda {\text{; (4)}}\\0,&{\text{else}}\end{cases}}}$
The parameter ${\displaystyle \lambda }$ in each of above functions adjusts the functions’ respective shapes.

Step 2 Construction process: 

The ant's movement is based on 4-connected pixels or 8-connected pixels. The probability with which the ant moves is given by the probability equation ${\displaystyle P_{x,y}}$
 

Step 3 and Step 5 Update process: 

The pheromone matrix is updated twice. in step 3 the trail of the ant (given by ${\displaystyle \tau _{(x,y)}}$ ) is updated where as in step 5 the evaporation rate of the trail is updated which is given by the below equation.
${\displaystyle \tau _{new}\leftarrow (1-\psi )\tau _{old}+\psi \tau _{0}}$, where ${\displaystyle \psi }$ is the pheromone decay coefficient ${\displaystyle 0<\tau <1 annotation="">$

Step 7 Decision Process:Once the K ants have moved a fixed distance L for N iteration, the decision whether it is an edge or not is based on the threshold T on the pheromone matrixτ. Threshold for the below example is calculated based on Otsu's method.

Image Edge detected using ACO:
 

The images below are generated using different functions given by the equation (1) to (4).

• Edge linking: ACO has also been proven effective in edge linking algorithms too.

Other applications

• Bankruptcy prediction
• Classification
• Connection-oriented network routing
• Connectionless network routing
• Data mining
• Discounted cash flows in project scheduling
• Distributed information retrieval
• Energy and electricity network design
• Grid workflow scheduling problem
• Inhibitory peptide design for protein protein interactions
• Intelligent testing system
• Power electronic circuit design
• Protein folding
• System identification

Definition difficulty

With an ACO algorithm, the shortest path in a graph, between two points A and B, is built from a combination of several paths. It is not easy to give a precise definition of what algorithm is or is not an ant colony, because the definition may vary according to the authors and uses. Broadly speaking, ant colony algorithms are regarded as populated metaheuristics with each solution represented by an ant moving in the search space. Ants mark the best solutions and take account of previous markings to optimize their search. They can be seen as probabilistic multi-agent algorithms using a probability distribution to make the transition between each iteration. In their versions for combinatorial problems, they use an iterative construction of solutions. According to some authors, the thing which distinguishes ACO algorithms from other relatives (such as algorithms to estimate the distribution or particle swarm optimization) is precisely their constructive aspect. In combinatorial problems, it is possible that the best solution eventually be found, even though no ant would prove effective. Thus, in the example of the Travelling salesman problem, it is not necessary that an ant actually travels the shortest route: the shortest route can be built from the strongest segments of the best solutions. However, this definition can be problematic in the case of problems in real variables, where no structure of 'neighbours' exists. The collective behaviour of social insects remains a source of inspiration for researchers. The wide variety of algorithms (for optimization or not) seeking self-organization in biological systems has led to the concept of "swarm intelligence", which is a very general framework in which ant colony algorithms fit.

Stigmergy algorithms

There is in practice a large number of algorithms claiming to be "ant colonies", without always sharing the general framework of optimization by canonical ant colonies. In practice, the use of an exchange of information between ants via the environment (a principle called "stigmergy") is deemed enough for an algorithm to belong to the class of ant colony algorithms. This principle has led some authors to create the term "value" to organize methods and behavior based on search of food, sorting larvae, division of labour and cooperative transportation.

Related methods

• Genetic algorithms (GA) maintain a pool of solutions rather than just one. The process of finding superior solutions mimics that of evolution, with solutions being combined or mutated to alter the pool of solutions, with solutions of inferior quality being discarded.
• An estimation of distribution algorithm (EDA) is an evolutionary algorithm that substitutes traditional reproduction operators by model-guided operators. Such models are learned from the population by employing machine learning techniques and represented as probabilistic graphical models, from which new solutions can be sampled or generated from guided-crossover.
• Simulated annealing (SA) is a related global optimization technique which traverses the search space by generating neighboring solutions of the current solution. A superior neighbor is always accepted. An inferior neighbor is accepted probabilistically based on the difference in quality and a temperature parameter. The temperature parameter is modified as the algorithm progresses to alter the nature of the search.
• Reactive search optimization focuses on combining machine learning with optimization, by adding an internal feedback loop to self-tune the free parameters of an algorithm to the characteristics of the problem, of the instance, and of the local situation around the current solution.
• Tabu search (TS) is similar to simulated annealing in that both traverse the solution space by testing mutations of an individual solution. While simulated annealing generates only one mutated solution, tabu search generates many mutated solutions and moves to the solution with the lowest fitness of those generated. To prevent cycling and encourage greater movement through the solution space, a tabu list is maintained of partial or complete solutions. It is forbidden to move to a solution that contains elements of the tabu list, which is updated as the solution traverses the solution space.
• Artificial immune system (AIS) algorithms are modeled on vertebrate immune systems.
• Particle swarm optimization (PSO), a swarm intelligence method
• Intelligent water drops (IWD), a swarm-based optimization algorithm based on natural water drops flowing in rivers
• Gravitational search algorithm (GSA), a swarm intelligence method
• Ant colony clustering method (ACCM), a method that make use of clustering approach, extending the ACO.
• Stochastic diffusion search (SDS), an agent-based probabilistic global search and optimization technique best suited to problems where the objective function can be decomposed into multiple independent partial-functions

History

The inventors are Frans Moyson and Bernard Manderick. Pioneers of the field include Marco Dorigo, Luca Maria Gambardella.

Chronology of COA algorithms

Chronology of ant colony optimization algorithms.

• 1959, Pierre-Paul Grassé invented the theory of stigmergy to explain the behavior of nest building in termites;
• 1983, Deneubourg and his colleagues studied the collective behavior of ants;
• 1988, and Moyson Manderick have an article on self-organization among ants;
• 1989, the work of Goss, Aron, Deneubourg and Pasteels on the collective behavior of Argentine ants, which will give the idea of ant colony optimization algorithms;
• 1989, implementation of a model of behavior for food by Ebling and his colleagues;
• 1991, M. Dorigo proposed the ant system in his doctoral thesis (which was published in 1992). A technical report extracted from the thesis and co-authored by V. Maniezzo and A. Colorni was published five years later;
• 1994, Appleby and Steward of British Telecommunications Plc published the first application to telecommunications networks
• 1995, Gambardella and Dorigo proposed ant-q, the preliminary version of ant colony system as first estension of ant system
• 1996, Gambardella and Dorigo proposed ant colony system 
• 1996, publication of the article on ant system
• 1996, Hoos and Stützle invent the max-min ant system
• 1997, Dorigo and Gambardella proposed ant colony system hybrized with local search
• 1997, Schoonderwoerd and his colleagues published an improved application to telecommunication networks
• 1998, Dorigo launches first conference dedicated to the ACO algorithms
• 1998, Stützle proposes initial parallel implementations
• 1999, Gambardella, Taillard and Agazzi proposed macs-vrptw, first multi ant colony system applied to vehicle routing problems with time windows
• 1999, Bonabeau, Dorigo and Theraulaz publish a book dealing mainly with artificial ants
• 2000, special issue of the Future Generation Computer Systems journal on ant algorithms
• 2000, first applications to the scheduling, scheduling sequence and the satisfaction of constraints
• 2000, Gutjahr provides the first evidence of convergence for an algorithm of ant colonies
• 2001, the first use of COA algorithms by companies (Eurobios and AntOptima)
• 2001, Iredi and his colleagues published the first multi-objective algorithm
• 2002, first applications in the design of schedule, Bayesian networks
• 2002, Bianchi and her colleagues suggested the first algorithm for stochastic problem
• 2004, Dorigo and Stützle publish the Ant Colony Optimization book with MIT Press 
• 2004, Zlochin and Dorigo show that some algorithms are equivalent to the stochastic gradient descent, the cross-entropy method and algorithms to estimate distribution
• 2005, first applications to protein folding problems
• 2012, Prabhakar and colleagues publish research relating to the operation of individual ants communicating in tandem without pheromones, mirroring the principles of computer network organization. The communication model has been compared to the Transmission Control Protocol
• 2016, first application to peptide sequence design
• 2017, successful integration of the multi-criteria decision-making method PROMETHEE into the ACO algorithm (HUMANT algorithm)