# A New Optimization Algorithm Inspired from the Mating Behavior of Barnacles: Barnacles Mating Optimizer Algorithms (BMO)

1. Introduction

Optimization is the process of finding the best combination of variables or parameters that fulfill the constraints to achieve the objective function whether for minimization or maximization purposes. The objective function is normally formulated based on applications or problems to be solved and it can be in terms of cost, efficiency, profits etc. Here, the Barnacles Mating Optimizer (BMO) algorithm is presented to solve optimization problems. The main inspiration of BMO is originated from the mating behavior of barnacles in nature. Barnacles are hermaphroditic micro-organisms which have both male and female sex reproductions. Barnacles are filter feeders (also known as suspension feeders) that feed on food particles that they strain out of the water. The shell of the barnacle is made up of a number of plates (usually 6), with feathery leg-like appendages that draw water into their shell so that they can feed [1] .To create new off-springs, they must be fertilized by a neighbor. The fertilized eggs hatch into larvae and its role to find suitable place to settle. Once it has found potentially suitable spot, they have reached their adult form barnacles continue to grow by adding new material to their heavily calcified plates.

A barnacle is a type of arthropod constituting the infraclass Cirripedia in the subphylum Crustacea, and is hence related to crabs and lobsters. Barnacles are exclusively marine, and tend to live in shallow and tidal waters, typically in erosive settings.  In some barnacles, the cement glands are fixed to a long, muscular stalk, but in most they are part of a flat membrane or calcified plate. A ring of plates surrounds the body, homologous with the carapace of other crustaceans. These consist of the  rostrum, two lateral plates, two carinolaterals, and a carina [2]. In sessile barnacles, the apex of the ring of plates is covered by an  operculum, which may be recessed into the carapace. The plates are held together by various means, depending on species, in some cases being solidly fused. Barnacles can play an important role in estimating paleo-water depths. The degree of disarticluation of fossils suggests the distance they have been transported, and since many species have narrow ranges of water depths, it can be assumed that the animals lived in shallow water and broke up as they were washed down-slope. The completeness of fossils, and nature of damage, can thus be used to constrain the tectonic history of regions [3].

2. Inspiration of Barnacles mating optimizer algorithm (BMO)

Barnacles Mating Optimizer (BMO) algorithm a novel bio-inspired optimization algorithm to solve optimization problems. The proposed algorithm mimics the mating behavior of barnacles in nature for solving optimization problems. Although barnacles are hermaphrodites, carrying both male and female genitalia, they rarely have mating with themselves. Instead, they use their extraordinarily long penises to reach out and find a mate within striking distance [4]. In Barnacles ovaries are located in the base or stalk and may extend into the mantle, while the tests are towards the back of the head, often extending into the thorax [5]. Self mating also possible has been in the rare cases in barnacles they cannot leave their shells to mate. Barnacles can also reproducing through a method called sperm casting, which male barnacle release his sperm into the water and female pick it up and fertilize their eggs this technique is called sperm casting or self-mating behavior of barnacles.

3. Barnacles Mating Algorithm

Barnacles are micro-organisms existed since Jurassic times. They live intidal poolson mussels, rocks and pier pilings [6]. Barnacles can swim at births and when they reach adult stage, they attach themselves to objects in the water and grow a shell [7]. Most of the barnacles are hermaphroditic, which means that they have both male and female reproductions. The most interesting fact about barnacles is they are famous for their long penises, including some of the longest in animals relative to their body (Barazandeh et al., 2013), which is seven to eight times the length of their bodies in order to cope with the changing tides and sedentary lifestyle. A barnacle’s mating group consists of all the neighbors within reach of its penis and all its potential competitors for mates. Another unique characteristic of barnacles is their capability for tenacious underwater adhesion by secreting proteinaceous substances. However, in this paper, the mating process of barnacles will be used as an inspiration in developing a new novel optimization algorithm.

In barnacles the cement glands are fixed to a long, muscular stalk, but in most they are part of a flat membrane or calcified plate. A ring of plates surrounds the body, homologous with the carapace of other crustaceans. The barnacle uses it’s cirri to feed the food it collects into its mouth [8]. The cirrus are instrumental in the collecting and feeding for the goose barnacle. From the mouth, the food travels down a short esophagus, into the animal’s digestive gland. The food is stored in the barnacle’s gut or stomach for some time, and then is excreted back into the ocean as waste through the anus [9].

4. Lifecycle of BMO:

The egg produced by barnacles fertilize into nauplius larvae which gray takes six months and more to develop into adult barnacles. Usually their lifecycle completes in four steps as:

• Nauplius stage
• Cyprid stage
• Adult stage
• Juvenile stage

4.1. Nauplius stage

In this stage, fertilized eggs hatch into one-eyed larvae known as Nauplius. It is initially brooded by the parent and are finally released for free-swimming. Our observations of the life cycle stages of barnacles, described six nauplius stages (N1 – N6) followed by the cyprid stage, which upon attachment metamorphoses to the juvenile form under controlled conditions, an average of nine days elapsed from the appearance of the egg masses in the parental capitulum to the release of N1 larvae[10]. Under the described culture conditions, 27 days elapsed from the first appearance of egg masses to the first cyprid larvae. Eighteen days elapsed from N1 release to cyprid appearance. Consider the enormity of the twelvefold increase in length of the O. cor nauplii, N1 – N6, in just eighteen days.

4.2. Cyprid stage

In this stage, larva role is to find a suitable place to settle. Its stage is from day to weeks, once it has found potentially suitable spot it attaches head first using its antennules and a secreted glycoprotein us substances. The cyprid larva is the last larval stage before adulthood. It is not a feeding stage; its role is to find a suitable place to settle, since the adults are sessile n that time period the naupliar stages capture, ingest, digest, and store enough food reserves to  the cyprid larval stage, which is non-feeding Cyprid has reversible and irreversible adhesion with temporary and perment in nature.

4.3. Adult stage

In this stage, once metamorphosis is over and they have reached their adult form barnacles continue to grow by adding new material to their heavily calcified plates. . It takes more than 6 months for the barnacle larvae to start developing into the hardier adult barnacles.

Adult barnacles feed with their legs, cement themselves to rocks head first, live their adult life in the same spot, eat plankton, have a “door” that can be closed at low tide to keep predators out and water in.

4.4. Juvenile Stage

In this stage, eventually, the larvae change into cypris form, and attach on other hard surfaces to form new barnacles. Our observations of the life cycle stages of barnacles   described six nauplius stages (N1 – N6) followed by the cyprid stage, which upon attachment metamorphoses to the juvenile form). While the patchy material is often less expansive in day 3-5 juveniles than it is in newly metamorphosed juveniles energize the cyprid activities of swimming and exploration, essential to host identification, settlement and attachment and support metamorphosis to yet another body morph, the juvenile.

5. Steps for BMO

• Initialization
• Selection process
• Reproduction

5.1. Initialization

The evaluation of the number of control variables and the number of population or number of barnacles is done initially, and the sorting process is performed to locate the best solution.

5.2. Selection process

The selection process is done randomly but it will be restricted to the penis length of the barnacle, population. Each barnacle may contribute its sperm as well as to receive sperm from other barnacle and each barnacle only can be fertilized by one barnacle only at one time even though in real life, the female can probably be fertilized by more than one male (Barazandeh et al., 2013) [11].

5.3. Reproduction

The reproduction process proposed in BMO is slightly different compared to other evolutionary algorithms. The BMO is mainly emphasizing on the inheritance characteristics or genotype frequencies of barnacles’ parents in producing the offspring based on Hardy–Weinberg principle.

6. Numerical example for BMO Algorithm

7. Flow Chart of BMO

8. Applications of BMO

• Power system[13]
• Economic dispatch problem[14]
• Lighting archive[15]
• Data visualization[16]

9. Advantages of BMO

• Extensive comparative studies with other algorithms are conducted and from the simulation results it is observed that BMO generally provides better result and exhibits huge potential of BMO in solving real optimization problems [17].
• BMO balances the exploitation and exploration to generate a new off spring towards the global optimal solution [18].
• BMO is mainly emphasing on the inheritance characteristics or genotype frequencies of barnacles parents in producing the off spring based on Hardy-Weinberg principle [19].
• The results showed that BMO was able to provide very competitive results compared to recent algorithms and obtaining the global optima for unimodal functions, exploration ability for multi-modal functions as well as ability to avoid local optima in composite functions.
• Modern approaches are flexible and high efficency which can be used for different kind of problems.

Reference

[1] Sulaiman M, Mustaffa Z, Saari M, Daniyal H (2020) Barnacles Mating Optimizer: A new bio-inspired algorithm for solving engineering optimization problems. Engineering Applications of Artificial Intelligence 87:103330. doi: 10.1016/j.engappai.2019.103330

[2] Crisp, D. J. in Marine Biodeterioration: An Interdisciplinary Study (eds Costlow, J. D. & Tipper, R. C.) 103–126 (Naval Institute Press, Annapolis, MD, 1984).

[3] Yamaguchi S, Yusa Y, Yamato S et al. (2008) Mating group size and evolutionarily stable pattern of sexuality in barnacles. Journal of Theoretical Biology 253:61-73. doi: 10.1016/j.jtbi.2008.01.025.

[4]  S. Yamaguchi, E. L. Charnov, K. Sawada, and Y. Yusa, “Sexual Systems and Life History of Barnacles: A Theoretical Perspective,” Integrative and Comparative Biology, vol. 52, pp. 356-365, 2012.

[5]  M. Barazandeh, C. S. Davis, C. J. Neufeld, D. W. Coltman, and A. R. Palmer, “Something Darwin didn’t know about barnacles: spermcast mating in a common stalked species,” Proceedings of the Royal Society B: Biological Sciences, vol. 285, 2013.

[6] Ruppert, Edward E.; Fox, Richard, S.; Barnes, Robert D. (2004). Invertebrate Zoology (7th ed.). Cengage Learning. p. 683. ISBN 978-81-315-0104-7

[7] E. Bourget (1987). Barnacle shells: composition, structure, and growth. pp. 267–285. In A. J. Southward (ed.), 1987.

[8] B. A. Foster & J. S. Buckeridge (1987). Barnacle palaeontology. pp. 41–63. In A. J. Southward (ed.), 1987.

[9] Harley C, Pankey M, Wares J et al. (2006) Color Polymorphism and Genetic Structure in the Sea Star Pisaster ochraceus. The Biological Bulletin 211:248-262. doi: 10.2307/4134547.

[10] von Oertzen J (1989) Marine Biodeterioration: An interdisciplinary study. Eds. J. D. Costlow and R. C. Tipper. — 384 pp., 164 figs. Annapolis, Maryland: Naval Institute Press 1984. ISBN 0-87021-530-2. Internationale Revue der gesamten Hydrobiologie und Hydrographie 74:232-232. doi: 10.1002/iroh.19890740222

[11] Mechanism of Fertilization: Plants to Humans, edited by Brian Dale

[12]  Donald Thomas Anderson (1994). “Larval development and metamorphosis”. Barnacles: Structure, Function, Development and Evolution. Springer. pp. 197–246. ISBN 978-0-412-44420-3.

[13]  D. Karaboga and B. Akay, “Artificial Bee Colony (ABC) Algorithm onTraining Artificial Neural Networks,” in Proceedings of the 15th IEEE on Signal Processing and Communications Applications (SIU), 2007,pp. 1-4.

[14]  M. H. Sulaiman, H. Daniyal, and M. W. Mustafa, “Modified Firefly Algorithm in solving economic dispatch problems with practical constraints,” in 2012 IEEE International Conference on Power and Energy (PECon), 2012, pp. 157-161.

[15] William A. Newman (2007). “Cirripedia”. In Sol Felty Light; James T. Carlton (eds.). The Light and Smith Manual: Intertidal Invertebrates from Central California to Oregon (4th ed.). University of California Press. pp. 475–484. ISBN 978-0-520-23939-5.

[16] D. H. Wolpert and W. G. Macready, “No free lunch theorems for optimization,” IEEE Transactions on Evolutionary Computation, vol. 1, pp. 67-82,

[17]  B. Mahdad and K. Srairi, “Differential evolution based dynamic decomposed strategy for solution of large practical economic dispatch,” in 2011 10th International Conference on Environment and Electrical Engineering, 2011, pp. 1-5.

[18] D. H. Wolpert and W. G. Macready, “No free lunch theorems for optimization,” IEEE Transactions on Evolutionary Computation, vol. 1, pp. 67-82, 1997.

[19]  A. W. F. Edwards, “G. H. Hardy (1908) and Hardy–Weinberg Equilibrium,” Genetics, vol. 179, pp. 1143-1150, 2008

.[20]. S. Mirjalili, A. H. Gandomi, S. Z. Mirjalili, S. Saremi, H. Faris, and S.M. Mirjalili, “Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems,” Advances in Engineering Software, vol.114, pp. 163-191, 2017/12/01/ 2017.

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