Abstract This paper develops Penguin Search Optimisation Algorithm (PeSOA), a new metaheuristic algorithm which is inspired by the foraging behaviours of penguins. A population of penguins located in the solution space of the given search and optimisation problem is divided into groups and tasked with finding optimal solutions. The penguins of a group perform simultaneous dives and work as a team to collaboratively feed on fish the energy content of which corresponds to the fitness of candidate solutions. Fish stocks have higher fitness and concentration near areas of solution optima and thus drive the search. Penguins can migrate to other places if their original habitat lacks food. We identify two forms of penguin communication both intra-group and inter-group which are useful in designing intensification and diversification strategies. An efficient intensification strategy allows fast convergence to a local optimum, whereas an effective diversification strategy avoids cyclic behaviour around local optima and explores more effectively the space of potential solutions. The proposed PeSOA algorithm has been validated on a well-known set of benchmark functions. Comparative performances with six other nature-inspired metaheuristics show that the PeSOA performs favourably in these tests. A run-time analysis shows that the performance obtained by the PeSOA is very stable at any time of the evolution horizon, making the PeSOA a viable approach for real world applications.

References

[1] Aarts E. and Korst J., Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing, Wiley, 1988.

[2] Ammi M. and Chikhi S., “Cooperative Parallel Metaheuristics based Penguin Optimization Search for Solving the Vehicle Routing Problem,” International Journal of Applied Metaheuristic Computing, vol. 7, no. 1, pp. 1-18, 2016.

[3] Dorigo M. and Birattari M., In Encyclopedia of Machine Learning, Springer US, 2010.

[4] Davis L., Handbook of Genetic Algorithms, New York: Nostrand Reinhold, 1991.

[5] Feo T. and Resende M., “Greedy Randomized Adaptive Search Procedures,” Journal of Global Optimization, vol. 6, no. 2, pp. 109-133, 1995.

[6] Gheraibia Y., Moussaoui A., Djenouri Y., Kabir S., Yin P., and Mazouzi S., “Penguin Search Optimisation Algorithm for Finding Optimal Spaced Seeds,” International Journal of Software Science and Computational Intelligence, vol. 7, no. 2, pp. 85-99, 2015.

[7] Gheraibia Y., Moussaoui M., Azevedo S., Parker D., Papadopoulos Y., and Walker M., “Can Aquatic Flightless Birds Allocate Automotive Safety Requirements?” in Proceeding of IEEE 7th International Conference on Intelligent Computing and Information Systems, Cairo, pp. 1-6, 2015.

[8] Gheraibia Y. and Moussaoui A., In RecentTrends in Applied Artificial Intelligence, Springer Berlin Heidelberg, 2013.

[9] Green K., Williams R., and Green M., “Foraging Ecology and Diving Behaviour of Macaroni Penguins Eudyptes Chrysolophus at Heard Island,” Marine Ornithology, vol. 26, no. 1, pp. 27-34, 1998.

[10] Glover F., “Tabu Search,” ORSA Journal on Computing, vol. 1, no. 3, pp. 190-206, 1989.

[11] Houston A. and McNamara J., “A General Theory of Central Place Foraging for Single-Prey Loaders,” Theoretical Population Biology, vol. 28, no. 3, pp. 233-262, 1985.

[12] Hanuise N., Bost C., Huin W., Auber A., Halsey L., and Handrich Y., “Measuring Foraging Activity in A Deep-Diving Bird,” The Journal of Experimental Biology, vol. 213, no. 22, pp. 3874- 3880, 2010.

[13] Jadwiszczak P., “Penguin Past: The Current State of Knowledge,” Polish Polar Research, vol. 30, no.1, pp. 3-28, 2009.

[14] Kennedy J., In Encyclopedia of Machine Learning, Springer, 2010.

[15] Karaboga D., An Idea Based on Honey Bee Swarm For Numerical Optimization, Technical Report-tr06, Erciyes University, 2005.

[16] Laguna M. and Marti R., “Experimental Testing of Advanced Scatter Search Designs for Global Optimization of Multimodal Functions,” Journal of Global Optimization, vol. 33, no. 2, pp. 235- 255, 2005.

[17] MacArthur R. and Pianka E., “On optimal Use of A Patchy Environment,” The University of 378 The International Arab Journal of Information Technology, Vol. 16, No. 3, May 2019 Chicago Press, vol. 100, no. 9, pp. 603-609, 1966.

[18] Mori Y., “Optimal Diving Behaviour for Foraging in Relation to Body Size,” Journal of Evolutionary Biology, vol. 15, no. 2, pp. 269-276, 2002.

[19] Oliveira H. and Vasconcelos G., “A Hybrid Search Method for The Vehicle Routing Problem With Time Windows,” Annals of Operations Research, vol. 180, no. 1, pp. 125-144, 2010.

[20] Qingmiao W. and Shiguang J., “ACO-Based BW Algorithm for Parameter Estimation of Hidden Markov Models,” International Journal of Computer Applications in Technology, vol. 41, no. 3, pp. 281-286, 2011.

[21] Reilly P., “Penguins of the World,” Journal of Oxford University Press, vol. 21, no. 3, pp. 1-32, 1994.

[22] Rengeswaran B., Mathaiyan N., and Kandasamy P., “Cuckoo Search with Mutation for Biclustering of Microarray Gene Expression Data,” The International Arab Journal of Information Technology, vol. 14, no. 3, pp. 300- 306, 2017.

[23] Storn R. and Price K., “Differential Evolution-A Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces,” Journal of Global Optimization, vol. 11, vol. 4, pp. 341- 359, 1997.

[24] Stützle T. and Dorigo M., “ACO Algorithms for the Traveling Salesman Problem, Journal of Evolutionary Algorithms in Engineering and Computer Science,” vol. 15, no. 4, pp.163-183., 1999.

[25] Takahashi A., Sato K., Nishikawa J., Watanuki Y., and Naito Y., “Synchronous Diving Behaviour of Adélie Penguins,” Journal of Ethology, vol. 22, no. 1, pp. 5-11, 2004.

[26] Tremblay Y. and Cherel Y., Synchronous under the Water Foraging Behaviour in Penguins, The Condor, pp. 179-185, 1999.

[27] Tolga M. and Smutnicki C., “Test Functions for Optimization Needs,” Computer and Information Science, pp. 1-43, 2005.

[28] Yang X., “Firefly Algorithms for Multimodal Optimization,” in Proceedings of Stochastic Algorithms: Foundations and Applications, Sapporo, pp. 169-178, 2009.

[29] Yang X. and Deb S., “Engineering Optimization By Cuckoo Search,” International Journal of Mathematical Modelling and Numerical Optimization, vol. 1, no. 4, pp. 330-343, 2010.

[30] Yang X., in Nature Inspired Cooperative Strategies for Optimization, Springer Berlin Heidelberg, 2010.

[31] Wang X., Wang S., and Ma J., “An Improved Co-Evolutionary Particle Swarm Optimization for Wireless Sensor Networks with Dynamic Deployment,” Sensors, vol. 7, no. 3, pp. 354-370, 2007. PeSOA: Penguins Search Optimisation Algorithm for Global Optimisation Problems 379 Youcef Gheraibia received the Ph.D. degree in computer engineering from the University of Annaba, Algeria, in 2016. He is a member of the dependable system group at the University of Hull, he is actually working in a EU2020 Project supported by EU. From 2013 to 2017, he was a lecturer with the University of Souk Areas, Algeria, where he is currently a member of the LRIM Laboratory. He is working on topics related to artificial intelligence and optimisation, with application on dependability, safety monitoring, and autonomous system. Abdeoulahab Moussaoui is Professor at Ferhat Abbas University. He received his BSc in Computer Science in 1990 from the Department of Computer Science from the University of Science and Technology of HouariBoumedienne (USTHB), Algeria. He also received and MSc in Space Engineering in 1991 from University of Science and Technology of Oran (USTO). He received also an MSc degree in Machine Learning from Reims University (France) since 1992 and Master's degree in Computer Science in 1995 from University of SidiBel-abbes, Algeria and PhD degree in Computer Science from Ferhat Abbas University, Algeria where he obtains a status of full-professor in Computer Science. He is IEEE Member and AJIT, IJMMIA & IJSC Referee. His researches are in the areas of clustering algorithms and multivariate image classification applications. His current research interests include the fuzzy neuronal network and non- parametric classification using unsupervised knowledge system applied to biomedical image segmentation and bioinformatics. Peng-Yeng Yin received his B.S., M.S. and Ph.D. degrees in Computer Science from National Chiao Tung University, Hsinchu, Taiwan. From 1993 to 1994, he was a visiting scholar at the Department of Electrical Engineering, University of Maryland, College Park, and the Department of Radiology, Georgetown University, Washington D.C. In 2000, he was a visiting Professor in the Visualization and Intelligent Systems Laboratory (VISLab) at the Department of Electrical Engineering, University of California, Riverside (UCR). From 2006 to 2007, he was a visiting Professor at Leeds School of Business, University of Colorado. And in 2015, he was a visiting Professor at Graduate School of Engineering, Osaka University, Japan. He is currently a Distinguished Professor of the Department of Information Management, National Chi Nan University, Taiwan, and he was the department head during 2004 and 2006, and the Dean of the office of R&D for the university from 2008 to 2012. Dr. Yin received the Overseas Research Fellowship from Ministry of Education in 1993, Overseas Research Fellowships from National Science Council in 2000 and 2015. He is a member of the Phi Tau Phi Scholastic Honor Society and listed in Who’s Who in the World, Who’s Who in Science and Engineering, and Who’s Who in Asia. Dr. Yin has published more than 140 academic articles in reputable journals and conferences including European Journal of Operational Research, Decision Support Systems, Annals of Operations Research, IEEE Trans. on Pattern Analysis and Machine Intelligence, IEEE Trans. on Knowledge and Data Engineering, IEEE Trans. on Education, etc. He is the Editor-in-Chief of the International Journal of Applied Metaheuristic Computing and has been on the Editorial Board of Journal of Computer Information Systems, Applied Mathematics & Information Sciences, Mathematical Problems in Engineering, International Journal of Advanced Robotic Systems, and served as a program committee member in many international conferences. He has also edited four books in pattern recognition and metaheuristic computing. His current research interests include artificial intelligence, evolutionary computation, educational informatics, metaheuristics, pattern recognition, image processing, machine learning, software engineering, computational intelligence, and operations research. Yiannis Papadopoulos Professor Yiannis Papadopoulosis leader of the Dependable Systems research group at the University of Hull. He pioneered the HiP-HOPS model- based dependability analysis and optimisation method and contributed to the EAST-ADL automotive design language, working with Volvo, Honda, Continental, Honeywell and DNV-GL, among others. He is actively involved in two technical committees of IFAC (TC 1.3 & 5.1). Contact him at Y.I.Papadopoulos@hull.ac.uk. Smaine Mazouzi he is a professor at 20 Août 1955 University of Skikda. He received his M.S. and Ph.D. degrees in Computer Science from University of Constantine, respectively, in 1996 and 2008. His fields of interest are pattern recognition, machine vision, and computer security. His current research concerns using distributed and complex systems modeled as multi-agent systems in image understanding and intrusion detection.