Abstract
In multi-mode heuristic optimization, the output fitness of an algorithm cannot converge to the global optimal value if its search points have not converged to the region with optimal solution. Generally, more samplings and more converged points in this optimal region may result in a higher probability of fitness convergence toward the optimal value. However, studies focus mainly on fitness convergence rather than region convergence (RC) of search points. This is partly because, for most objective functions, it is usually hard to track the region of search points in dynamic optimization. To remedy this, a novel analysis method is proposed using the double-well function (DWF), since it has a unique fitness landscape that makes it convenient to trace these points. First, a mathematical analysis of the DWF is given to explore its landscape. Then, RC is defined and discussed using DWF. On these bases, experiments are conducted and analyzed using Particle Swarm Optimization (PSO), and much useful information about its RC is revealed. Besides, this method can be used to analyze the RC of similar optimization algorithms as well.
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References
Yang, X.: Nature-Inspired Computation and Swarm Intelligence: Algorithms, Theory and Applications. Elsevier Ltd., Amsterdam (2020)
Dechanupaprittha, S., Jamroen, C.: Self-learning PSO based optimal EVs charging power control strategy for frequency stabilization considering frequency deviation and impact on EV owner. Sustain. Energy Grids Netw. 26, 100463 (2021)
Latifa, N.B., Aguili, T.: Optimization of coupled periodic antenna using genetic algorithm with Floquet modal analysis and MoM-GEC. Open J. Antennas Propag. 10(1), 1–15 (2022)
Wang, P., Yang, G.: Using double well function as a benchmark function for optimization algorithm. In: 2021 IEEE Congress on Evolutionary Computation, pp. 886–892. IEEE, New York (2021)
Liang, J., Qu, B., Suganthan, P.N.: Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective real-parameter numerical optimization. Technical report. Zhengzhou University, Zhengzhou, China and Nanyang Technological University, Singapore (2013)
Awad, N.H., Ali, M.Z., Liang, J., Qu, B., Suganthan, P.N.: Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective real-parameter numerical optimization. Technical report. Nanyang Technological University, Singapore, Jordan University of Science and Technology, Jordan, and Zhengzhou University, Zhengzhou, China (2016)
Cristian, I.T.: The particle swarm optimization algorithm: convergence analysis and parameter selection. Inf. Process. Lett. 85(6), 317–325 (2003)
Sun, J., Wu, X., Palade, V., Fang, W., Lai, C.-H., Xu, W.: Convergence analysis and improvements of quantum-behaved particle swarm optimization. Inf. Sci. 193, 81–103 (2012)
Chen, S., Peng, G., He, X., Yang, X.: Global convergence analysis of the bat algorithm using a Markovian framework and dynamical system theory. Expert Syst. Appl. 114, 173–182 (2018)
Kononova, A.V., Corne, D.W., Wilde, P.D., Shneer, V., Caraffini, F.: Structural bias in population-based algorithms. Inf. Sci. 298, 468–490 (2015)
Fan, S.: A new extracting formula and a new distinguishing means on the one variable cubic equation. Nat. Sci. J. Hainan Teach. Coll. 2(2), 91–98 (1989)
Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence, pp. 69–73. IEEE, New York (1998)
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Yang, G., Wang, P., Yin, X. (2023). A Region Convergence Analysis for Multi-mode Stochastic Optimization Based on Double-Well Function. In: Huang, DS., Premaratne, P., Jin, B., Qu, B., Jo, KH., Hussain, A. (eds) Advanced Intelligent Computing Technology and Applications. ICIC 2023. Lecture Notes in Computer Science, vol 14086. Springer, Singapore. https://doi.org/10.1007/978-981-99-4755-3_1
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DOI: https://doi.org/10.1007/978-981-99-4755-3_1
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