Statistical Analysis and Comparison of the Performance of Meta-Heuristic Methods Based on their Powerfulness and Effectiveness
Subject Areas : Machine learning
Mehrdad Rohani
1
,
Hassan Farsi
2
*
,
Seyed Hamid Zahiri
3
1 - Univerrsity of Birjand
2 - University of Birjand
3 - University of Birjand
Keywords: Effectiveness, Meta-heuristic Algorithms, Optimization, Powerfulness, Statistical Analysis.,
Abstract :
In this paper, the performance of meta-heuristic algorithms is compared using statistical analysis based on new criteria (powerfulness and effectiveness). Due to the large number of meta-heuristic methods reported so far, choosing one of them by researchers has always been challenging. In fact, the user does not know which of these methods are able to solve his complex problem. In this paper, in order to compare the performance of several methods from different categories of meta-heuristic methods new criteria are proposed. In fact, by using these criteria, the user is able to choose an effective method for his problem. For this reason, statistical analysis is conducted on each of these methods to clarify the application of each of these methods for the users. Also, powerfulness and effectiveness criteria are defined to compare the performance of the meta-heuristic methods to introduce suitable substrate and suitable quantitative parameters for this purpose. The results of these criteria clearly show the ability of each method for different applications and problems.
[1] R. Bellman, "Dynamic Programming", Science, Vol. 153, No. 3731, 1966, pp. 34-37.
[2] W. Kuo, V. R. Prasad, F. A. Tillman, and C.-L. Hwang, Optimal Reliability Design: Fundamentals and Applications, Cambridge University Press, 2001.
[3] J. A. Snyman, Practical Mathematical Optimization. Springer, 2005.
[4] I. BoussaïD, J. Lepagnot, and P. Siarry, "A Survey on Optimization Metaheuristics", Information Sciences, Vol. 237, 2013, pp. 82-117.
[5] A. Sezavar, H. Farsi, and S. Mohamadzadeh, "A Modified Grasshopper Optimization Algorithm Combined with CNN for Content Based Image Retrieval", International Journal of Engineering, Vol. 32, No. 7, 2019, pp. 924-930.
[6] A. H. Hosseinian and V. Baradaran, "A Multi-Objective Multi-Agent Optimization Algorithm for the Community Detection Problem", J. Inform. Syst. Telecommun, Vol. 6, No. 1,2019, pp. 169-179.
[7] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization By Simulated Annealing", Science, Vol. 220, No. 4598, 1983, pp. 671-680.
[8] J. R. Koza and J. R. Koza, Genetic Programming, On the Programming of Computers :Natural Selection MIT press, 1992.
[9] A. Walker, J. Hallam, and D. Willshaw, "Bee-Havior in a Mobile Robot: The Construction of a Self-Organized Cognitive Map and Its Use in Robot Navigation within a Complex, Natural Environment", IEEE International Conference on Neural Networks, 1993, pp. 1451-1456.
[10] F. Glover, "Tabu Search for Nonlinear and Parametric Optimization (With Links to Genetic Algorithms)", Discrete Applied Mathematics, Vol. 49, No. 1-3, 1994, pp. 231-255.
[11] J. Kennedy and R. Eberhart, "Particle Swarm Optimization", in Proceedings of ICNN'95-International Conference on Neural Networks, 1995, Vol. 4, pp. 1942-1948.
[12] K. M. Passino, "Biomimicry of Bacterial Foraging for Distributed Optimization and Control", IEEE control systems magazine, Vol. 22, No. 3, 2002, pp. 52-67.
[13] D. Simon, "Biogeography-Based Optimization", IEEE Transactions on Evolutionary Computation, Vol. 12, No. 6, 2008, pp. 702-713.
[14] S. Mirjalili, S. M. Mirjalili, and A. Lewis, "Grey Wolf Optimizer", Advances in Engineering Software, Vol. 69, 2014, pp. 46-61.
[15] S. Mirjalili, "The Ant Lion Optimizer", Advances in Engineering Software, Vol. 83, 2015, pp. 80-98.
[16] S. Mirjalili, "Moth-flame Optimization Algorithm: A Novel Nature-Inspired Heuristic Paradigm", Knowledge-Based Systems, Vol. 89, 2015, pp. 228-249.
[17] S. Mirjalili "Dragonfly Algorithm: a New Meta-Heuristic Optimization Technique for Solving Single-Objective, Discrete, and Multi-Objective Problems", Neural Computing and Applications, Vol. 27, No. 4, 2016, pp. 1053-1073.
[18] S. Mirjalili, S. M. Mirjalili, and A. Hatamlou, "Multi-Verse Optimizer: a Nature-Inspired Algorithm for Global Optimization", Neural Computing and Applications, Vol. 27, No. 2, pp. 495-513, 2016.
[19] S. Mirjalili, "SCA: a Sine Cosine Algorithm for Solving Optimization Problems", Knowledge-Based Systems, Vol. 96, 2016, pp. 120-133.
[20] S. Mirjalili and A. Lewis, "The Whale Optimization Algorithm", Advances in Engineering Software, Vol. 95, 2016, pp. 51-67.
[21] S. Mirjalili, A. H. Gandomi, S. Z. Mirjalili, S. Saremi, H. Faris, and S. M. Mirjalili, "Salp Swarm Algorithm: A Bio-Unspired Optimizer for Engineering Design Problems", Advances in Engineering Software, Vol. 114, 2017, pp. 163-191.
[22] S. M. Almufti, "Historical Survey on Metaheuristics Algorithms", International Journal of Scientific World, Vol. 7, No. 1, 2019, pp. 1.
[23] S. Shirke and R. Udayakumar, "Evaluation of Crow Search Algorithm (CSA) for Optimization in Discrete Applications", International Conference on Trends in Electronics and Informatics (ICOEI), 2019, pp. 584-589.
[24] M. Dorigo and G. Di Caro, "Ant Colony Optimization: a New Meta-Heuristic", in Proceedings of the Congress on Evolutionary Computation-CEC99, Vol. 2, 1999, pp. 1470-1477.
[25] M. Clerc, Particle Swarm Optimization. John Wiley & Sons, 2010.
[26] J. G. Digalakis and K. G. Margaritis, "On Benchmarking Functions for Genetic Algorithms", International Journal of Computer Mathematics, Vol. 77, No. 4, 2001, pp. 481-506.
[27] M. Molga and C. Smutnicki, "Test Functions for Optimization Needs", Test Functions for Optimization Needs, Vol. 101, 2005, pp. 48.
[28] X.-S. Yang, "Firefly Algorithm, Stochastic Test Functions and Design Optimisation," International Journal of Bio-Inspired Computation, Vol. 2, No. 2, 2010, pp. 78-84.
[29] D. Molina, J. Poyatos, J. Del Ser, S. García, A. Hussain, and F. Herrera, "Comprehensive Taxonomies of Nature-and Bio-inspired Optimization: Inspiration Versus Algorithmic Behavior, Critical Analysis Recommendations", Cognitive Computation, Vol. 12, No. 5, 2020, pp. 897-9339.