A New Arithmetic Optimization Algorithm for Solving Real-World Multiobjective CEC-2021 Constrained Optimization Problems: Diversity Analysis and Validations

Abstract

In this paper, a new Multi-Objective Arithmetic Optimization Algorithm (MOAOA) is proposed for solving Real-World constrained Multi-objective Optimization Problems (RWMOPs). Such problems can be found in different areas, including mechanical engineering, chemical engineering, process and synthesis, and power electronics systems. MOAOA is inspired by the distribution behavior of the main arithmetic operators in mathematics. The proposed multi-objective version is formulated and developed from the recently introduced single-objective Arithmetic Optimization Algorithm (AOA) through an elitist nondominance sorting and crowding distance-based mechanism. For the performance evaluation of MOAOA, a set of 35 constrained RWMOPs and five ZDT unconstrained problems are considered. For the fitness and efficiency evaluation of the proposed MOAOA, the results obtained from the MOAOA are compared with four other state-of-the-art multi-objective algorithms. In addition, five performance indicators, such as Hyper-Volume (HV), Spread (SP), Inverse Generalized Distance (IGD), Runtime (RT), and Generalized Distance (GD), are calculated for the rigorous evaluation of the performance and feasibility study of the MOAOA. The findings demonstrate the superiority of the MOAOA over other algorithms with high accuracy and coverage across all objectives. This paper also considers the Wilcoxon signed-rank test (WSRT) for the statistical investigation of the experimental study. The coverage, diversity, computational cost, and convergence behavior achieved by MOAOA show its high efficiency in solving ZDT and RWMOPs problems. INDEX TERMS Arithmetic Optimization Algorithm (AOA); CEC-2021 real-world problems; Constrained optimization; Multi-Objective Arithmetic Optimization Algorithm (MOAOA). I. INTRODUCTIONRecently, computer technology advancements have increased the quality of addressing complex problems and decreased the time and cost of producing the optimal solution. However, human input is yet needed to determine the best of different solutions. Significant efforts can be seen in the literature to produce a system that optimally solves the given problem without any human effort [1]. One of the most reliable methods to accomplish this depends on optimization techniques. In many instances, most engineering problems, such as city programming, program management, investment decision, control system design, engineering

Sizing and Energy Management of Parking Lots of Electric Vehicles Based on Battery Storage with Wind Resources in Distribution Network

“…Figure 1 depicts the hierarchy of AOs along with the exploration and operation phases. In the AOA based on Figure 1, top-down dominance has a decreasing trend [23,24].…”

“…In this study, the formulation of an arithmetic optimization algorithm (AOA) is described based on exploration and exploitation phases. This optimization method is inspired by arithmetic operators (AOs) in mathematics such as multiplication (M), division (D), subtraction (S), and addition (A) and can solve optimization problems without the need for their derivatives [23,24].…”

“…When the function of operator D ends, operator M is activated (r2 is a random number). The position update equations are defined as follows for the exploration phase [23,24]:…”

“…The decision variables include the number of electric vehicles in the parking lots and the wind turbine number in the distribution network. The arithmetic optimization algorithm (AOA), which is inspired by arithmetic operators in mathematics [23,24], is applied to determine the optimization variables by considering the objective function and operation constraints. The motivation of using the AOA is the high capability of this method to solve the optimization problem, quickly achieving the global optimal solution [19,20].…”

An Electric Fish-Based Arithmetic Optimization Algorithm for Feature Selection

“…The AOA is inspired by mathematical operations and proposed by Abualigah et al [25]. It has been adopted in several applications, such as proton exchange membrane fuel cells by extreme learning machine [26], multilevel thresholding segmentation [27], real-world multiobjective problem [28], and damage assessment in FGM composite plates [29].…”