Enhancing Evolutionary Algorithms by Efficient Population Initialization for Constrained Problems Saber Elsayed * , Ruhul Sarker * , Noha Hamza * , Carlos A. Coello Coello † and Efr´ en Mezura-Montes ‡ * School of Engineering and Information Technolog University of New South Wales Canberra, Australia Email: {s.elsayed,r.sarker,n.hamza @unsw.edu.au} † Depto. de Computaci´ on, CINVESTAV-IPN, Mexico Email: ccoello@cs.cinvestav.mx ‡ Artificial Intelligence Research Center University of Veracruz, Mexico Email:emezura@uv.mx Abstract—One of the challenges that appear in solving constrained optimization problems is to quickly locate the search areas of interest. Although the initial solutions of any optimization algorithm have a significant effect on its performance, none of the existing initialization methods can provide direct information about the objective function and constraints of the problem to be solved. In this paper, a technique for generating initial solutions is proposed, which provides useful information about the behavior of both the objective function and the constraints. Based on such information, an automatic mechanism for selecting individuals, from the search areas of interest, is introduced. The proposed method is adopted with different evolutionary algorithms and tested on the CEC2006 and the CEC2010 test problems. The results obtained show the benefits of the proposed method in enhancing the performance, and reducing the average computational time, of several algorithms with respect to their versions adopting other initialization techniques Index Terms—constrained optimization problems, population initialization, evolutionary algorithms I. I NTRODUCTION Many engineering, business, computer science and defense decision processes require solving optimization problems in the presence of constraints. Such problems are known as constrained optimization problems (COPs). A COP may contain different types of variables and constraints. These problems become more challenging if they possess difficult characteristics, such as multi-modality, high dimensionality, and small feasible regions [1]. Formally, a COP can be expressed as: minimize f ( − → x ) subject to: c k ( − → x ) ≤ 0,k =1, 2,...,K h e ( − → x )=0,e =1, 2,...,E L j ≤x j ≤U j ,j =1, 2,...,D (1) where − → x =[x 1 ,x 2 , ..., x D ] is a vector with D decision variables, f ( − → x ) the objective function, c k ( − → x ) the k th inequality constraint, h e ( − → x ) the e th equality constraint and each x j has a lower limit (L j ) and an upper limit (U j ). Over the years, the solution of COPs has attracted a considerable amount of research. Among the currently available approaches to deal with COPs, evolutionary algorithms (EAs), such as genetic algorithms (GAs) [2] and differential evolution (DE) [3], have become very popular. Normally, the first step in such algorithms is to generate an initial set of solutions to evolve. Due to the influence of such solutions in the performance of an EA, a considerable number of new initialization methods has been developed, with the main aim of uniformly cover the search space. The most popular technique for generating a population of individuals is the pseudo-random number generator (PRNG) [4] which generates a sequence of of random numbers [4], in which the solutions are scattered according to a uniform distribution, or to any other statistical distribution. This initialization method is simple, but it has difficulties when the dimensionality increases [5] because it tends to fail in the generation of points that are fully distributed [4], [6]. Based on chaos theory [7], the chaotic number generator (CNG) [8] has been proposed for its use with EAs [8]. Among seven chaotic maps used with DE, the variant with the sinus map outperformed all the other variants [8]. As a type of space-filling method, uniform experimental design (UED) [9] searches for points to be uniformly distributed in a given range. However, evaluating such a large population is expensive for both small- and large-scale problems. This shortcoming was the motivation for introducing orthogonal design. An orthogonal array aims to specify a set of combinations spread uniformly over the space of all possible combinations. In the literature, such an initialization method enhanced the performance of several optimization approaches, such as DE [10]. Latin hypercube sampling (LHS) [11] divides the variables into a fixed number of intervals (creating grids) 978-1-7281-6929-3/20/$31.00 ©2020 IEEE