The method of deformed stars as a population algorithm for global optimization. (English) Zbl 1512.90182
Zgurovsky, Michael (ed.) et al., System analysis & intelligent computing. Theory and applications. Cham: Springer. Stud. Comput. Intell. 1022, 229-247 (2022).
Summary: In this paper, a new method of deformed stars for global optimization based on the ideas and principles of the evolutionary paradigm was proposed. The two-dimensional case was developed and then extended for \(n\)-dimensional case. This method is based on the assumption of rational use of potential solutions groups, which allows increasing the rate of convergence and the accuracy of result. Populations of potential solutions are used to optimize the multivariable function, as well as their transformation, the operations of deformation, rotation and compression. The obtained results of experiments allow us to conclude that the proposed method is applicable to solving problems of finding optimal (suboptimal) values, including non-differentiated functions. The advantages of the developed method in comparison of genetic algorithms, evolutionary strategies and differential evolution as the most typical evolutionary algorithms were shown. The experiments were conducted using several well-known functions for global optimization (Ackley’s function, Rosenbrock’s saddle, Rastrigin’s function).
For the entire collection see [Zbl 1485.68014].
For the entire collection see [Zbl 1485.68014].
MSC:
| 90C26 | Nonconvex programming, global optimization |
| 68W50 | Evolutionary algorithms, genetic algorithms (computational aspects) |
| 90C59 | Approximation methods and heuristics in mathematical programming |
Software:
WCAReferences:
| [1] | Storn, R.; Price, K., Differential evolution—a simple and efficient heuristic for global optimization over continuous, J. Global Optim., 11, 341-359 (1997) · Zbl 0888.90135 · doi:10.1023/A:1008202821328 |
| [2] | Geen, ZW; Kim, JH; Loganathan, GV, A new heuristic optimization algorithm: Harmony search, SIMULATION, 76, 2, 60-68 (2001) · doi:10.1177/003754970107600201 |
| [3] | Yang, X.-S., Deb, S.: Cuckoo search via Levy flights. In: Proceedings of World Congress on Nature and Biological Inspired Computing, pp. 201-214. IEEE Publications, India, USA (2009) |
| [4] | Cheng, M-Y; Prayogo, D., Symbiotic organisms search: a new metaheuristic optimization algorithm, Comput. Struct., 139, 98-112 (2014) · doi:10.1016/j.compstruc.2014.03.007 |
| [5] | Vasconcelos, J.A., Ramirez, R.H.C., Takahashi, R.R.: Saldanha improvements in genetic algorithms. IEEE Trans. Mag. 37(5) (2001) |
| [6] | Yang, X.-S.: Firefly algorithms for multimodal optimization. In: Stochastic Algorithms: Foundations and Applications, SAGA, Lecture Notes in Computer Sciences, vol. 5792, pp. 169-178 (2009) · Zbl 1260.90164 |
| [7] | Eskandar, H.; Sadollah, A.; Bahreininejad, A.; Hamdi, M., Water cycle algorithm—a novel metaheuristic optimization method for solving constrained engineering optimization problems, Comput. Struct., 110-111, 151-166 (2012) · doi:10.1016/j.compstruc.2012.07.010 |
| [8] | Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1) (1997) |
| [9] | Glover, F., Heuristics for integer programming using surrogate constraints, Decis. Sci., 8, 1, 156-166 (1977) · doi:10.1111/j.1540-5915.1977.tb01074.x |
| [10] | Glover, F., Tabu search—Part I, ORSA J. Comput., 1, 190-206 (1989) · Zbl 0753.90054 · doi:10.1287/ijoc.1.3.190 |
| [11] | Guha, D., Roy, P.K., Banerjee, S.: Load frequency control of large scale power system using quasi-oppositional grey wolf optimization algorithm. Eng. Sci. Technol. Int. J. 19(4) (2015) |
| [12] | Dorigo, M., Stützle, T.: Ant Colony Optimization. A Bradford Book, 1st edn. First Printing (2004) · Zbl 1092.90066 |
| [13] | Snytyuk, V.: Method of deformed stars for multi-extremal optimization. One- and two-dimensional cases. In: International Conferences Mathematical Modeling and Simulation of Systems. MODS 2019, Advances in Intelligent Systems and Computing, vol. 1019. Springer, Cham (2019) |
| [14] | Bull, L.; Holland, O.; Blackmore, S., On meme-gene coevolution, Artif. Life, 6, 227-235 (2000) · doi:10.1162/106454600568852 |
| [15] | Antonevych, M., Didyk, A., Snytyuk, V.: Choice of better parameters for method of deformed stars in n-dimensional case, Kyiv, IT & I, 17-20 (2020) |
| [16] | Tmienova, N., Snytyuk, V.: Method of deformed stars for global optimization. In: 2020 IEEE 2nd International Conference on System Analysis & Intelligent Computing (SAIC), pp. 259-262 (2020) |
| [17] | Beyer, H-G; Schwefel, H-P, Evolution strategies: a comprehensive introduction, J. Nat. Comput., 1, 1, 3-52 (2002) · Zbl 1014.68134 · doi:10.1023/A:1015059928466 |
| [18] | Srinivas, M.; Patnaik, LM, Genetic algorithms: a survey, Computer, 27, 6, 17-26 (1994) · doi:10.1109/2.294849 |
| [19] | Hestenes, D., New Foundations for Classical Mechanics (1999), Dordrecht: Kluwer Academic Publishers, Dordrecht · Zbl 0932.70001 |
| [20] | Antonevych, M., Didyk, A., Snytyuk, V.: Optimization of functions of two variables by deformed stars method. In: 2019 IEEE International Conference on Advanced Trends in Information Theory (ATIT), Kyiv, Ukraine, pp. 475-480 (2019) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
