Multi-objective Bonobo Optimizer (MOBO): an intelligent heuristic for multi-criteria optimization
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Multi-objective Bonobo Optimizer (MOBO): an intelligent heuristic for multi-criteria optimization Amit Kumar Das1 · Ankit Kumar Nikum2 · Siva Vignesh Krishnan1 · Dilip Kumar Pratihar1 Received: 5 November 2019 / Revised: 29 July 2020 / Accepted: 31 July 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract Non-traditional optimization tools have proved their potential in solving various types of optimization problems. These problems deal with either single objective or multiple/many objectives. Bonobo Optimizer (BO) is an intelligent and adaptive metaheuristic optimization algorithm inspired from the social behavior and reproductive strategies of bonobos. There is no study in the literature to extend this BO to solve multi-objective optimization problems. This paper presents a Multi-objective Bonobo Optimizer (MOBO) to solve different optimization problems. Three different versions of MOBO are proposed in this paper, each using a different method, such as non-dominated sorting with adaptation of grid approach; a ranking scheme for sorting of population with crowding distance approach; decomposition technique, wherein the solutions are obtained by dividing a multi-objective problem into a number of single-objective problems. The performances of all three different versions of the proposed MOBO had been tested on a set of thirty diversified benchmark test functions, and the results were compared with that of four other well-known multi-objective optimization techniques available in the literature. The obtained results showed that the first two versions of the proposed algorithms either outperformed or performed competitively in terms of convergence and diversity compared to the others. However, the third version of the proposed techniques was found to have the poor performance. Keywords Multi-objective optimization · Bonobo Optimizer · Intelligent algorithm · Multi-objective Bonobo Optimizer · Multi-criteria optimization
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Dilip Kumar Pratihar [email protected] Amit Kumar Das [email protected] Ankit Kumar Nikum [email protected] Siva Vignesh Krishnan [email protected]
1
Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur 721302, India
2
Department of Mechanical Engineering, SVNIT, Surat 395007, India
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A. K. Das et al.
1 Introduction Multi-objective optimization problems (MOPs) are referred to those ones, which have more than one objectives. A multi-objective optimization problem characterized by M(≥ 2) objectives, n variables, J-equality and K-inequality constraints can be formulated as follows (assuming minimization problem, without loss of generality): Minimize F(X ) ( f 1 (x), . . . , f M (x))T
(1)
subject to g j (x) 0,
j 1, . . . , J
h k (x) ≤ 0, k 1, . . . , K where x (x1 , . . . , xn )T and xiL ≤ xi ≤ xiU , i 1, . . . , n A decision maker (DM) is a person, who gives preference information to obtain Pareto-front. MOPs can be classified based on the role of DM as follows: • No preference method, where there is
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