A novel population initialization strategy for accelerating Levy flights based multi-verse optimizer

Article type: Research Article

Authors: Ahmad, Sohail^a | Sulaiman, Muhammad^{a; *} | Kumam, Poom^{b; c; e; *} | Hussain, Zubair^a | Asif Jan, Muhammad^d | Mashwani, Wali Khan^d | Ullah, Masih^a

Affiliations: [a] Department of Mathematics, Abdul Wali Khan University Mardan, KP, Pakistan | [b] KMUTT-Fixed Point Research Laboratory, Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thrung Khru, Bangkok, Thailand | [c] KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thrung Khru, Bangkok, Thailand | [d] Institute of Numerical Sciences, Kohat University of Science and Technology, Kohat, Pakistan | [e] Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Correspondence: [*] Corresponding authors. Muhammad Sulaiman, Department of Mathematics, Abdul Wali Khan University Mardan, KP, Pakistan. E-mail: [email protected] and Poom Kumam, E-mail: [email protected].

Abstract: In this paper, we have designed a new optimization technique, which is named as the Improved Multi-verse Algorithm with Levy Flights (ILFMVO) algorithm. The quality of the population is an important factor that can directly or indirectly affect the strength of an algorithm in searching for the given search space for an optimal solution. Also, having an initialization of the initial population with randomly generated candidate solutions is not an effective idea in every case, especially when the search space is large. Hence, we have updated the Levy flights based Multi-verse Optimizer (LFMVO) by dividing initialization into two parts. To investigate the ability of ILFMVO, we have solved a constrained economic dispatch problem with a non-smooth, non-convex cost functions of three, six, and twenty thermal generator systems and two design engineering problems with nonlinear objectives and complex nonlinear constraints. We have compared our results with other standard algorithms. We have presented the sensitivity analysis to check the robustness and stability of our approach. The outcome demonstrated that ILFMVO has better accuracy, stability, and convergence.

Keywords: Antlion optimizer, Economic load dispatch, Design engineering problems, Firefly algorithm, Improved Multi-verse optimizer with Levy flights, Lambda iteration, Particle swarm optimization

DOI: 10.3233/JIFS-190112

Journal: Journal of Intelligent & Fuzzy Systems, vol. 39, no. 1, pp. 1-17, 2020