Multi-objective orthogonal opposition-based crow search algorithm for large-scale multi-objective optimization

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ORIGINAL ARTICLE

Multi-objective orthogonal opposition-based crow search algorithm for large-scale multi-objective optimization Rizk M. Rizk-Allah1 • Aboul Ella Hassanien2



Adam Slowik3

Received: 11 June 2019 / Accepted: 7 February 2020 Ó Springer-Verlag London Ltd., part of Springer Nature 2020

Abstract Many engineering optimization problems are typically multi-objective in their natures and multidisciplinary with a large number of decision variables. Furthermore, Pareto dominance loses its effectiveness in such situations. Thus, developing a robust optimization algorithm undoubtedly becomes a true challenge. This paper proposes a multi-objective orthogonal opposition-based crow search algorithm (M2O-CSA) for solving large-scale multi-objective optimization problems (LSMOPs). In the M2O-CSA, a multi-orthogonal opposition strategy is employed to mitigate the conflicts among the convergence and distribution of solutions. First, two individuals are randomly chosen to undergo the crossover stage and then orthogonal array is presented to obtain nine individuals. Then individuals are used in the opposition stage to improve the diversity of solutions. The effectiveness of the proposed M2O-CSA is investigated by implementing it on different dimensions of multi-objective optimization problems (MOPs). The Pareto front solutions of these MOPs have various characteristics such as convex, non-convex and discrete. It is also applied to solve multi-objective design applications with distinctive features such as four bar truss (FBT) design, welded beam (WB) deign, disk brake (DB) design, and speed reduced (SR) design, where they involve different characteristics. In this context, a new decision making tool based on multi-objective optimization on the basis of ratio analysis (MOORA) technique is employed to help the designer for extracting the operating point as the best compromise or satisfactory solution to execute the candidate engineering design. Simulation results affirm that the proposed M2O-CSA works efficiently and effectively. Keywords Crow search algorithm  Orthogonal  Opposition  Multi-objective optimization  Metaheuristic  Engineering designs  MOORA

1 Introduction

Rizk M. Rizk-Allah and Aboul Ella Hassanien: Scientific Research Group in Egypt. & Aboul Ella Hassanien [email protected] http://www.egyptscience.net Rizk M. Rizk-Allah http://www.egyptscience.net 1

Faculty of Engineering, Menoufia University, Shebin El-Kom, Egypt

2

Faculty of Computers and Artificial Intelligence, Cairo University, Cairo, Egypt

3

Department of Electronics and Computer Science, Koszalin University of Technology, Koszalin, Poland

In almost real design applications, the designer often faces the problem of achieving many design targets. These targets are often conflicting and incommensurable and needed to be optimized simultaneously. The process of optimizing multiple targets (objectives) is denoted by a multi-objective optimization problem (MOP). In this regard, there is no