In this paper, we explore the capabilities of different types of evolution strategies (ES) to solve global optimization problems with constraints. The aim is to highlight the idea that the selection of the search engine is more critical than the selection of the constraint-handling mechanism, which can be very simple indeed. We show how using just three simple comparison criteria based on feasibility, the simple evolution strategy can be led to the feasible region of the search space and find the global optimum solution (or a very good approximation of it). Different ES including a variation of a (μ+1) − ES and with or without correlated mutation were implemented. Such approaches were tested using a well-known test suite for constrained optimization. Furthermore, the most competitive version found (among those five) was compared against three state-of-the-art approaches and it was also compared against a GA using the same constraint-handling approach. Finally, our evolution strategy was used to solve some engineering design problems.

Most real-world problems involve some type of optimization problems that are often constrained. Numerous researchers have investigated several techniques to deal with constrained single-objective and multi-objective evolutionary optimization in many fields, including theory and application. This presented study provides a novel analysis of scholarly literature on constraint-handling techniques for single-objective and multi-objective population-based algorithms according to the most relevant journals and articles. As a contribution to this study, the paper reviews the main ideas of the most state-of-the-art constraint handling techniques in population-based optimization, and then the study addresses the bibliometric analysis, with a focus on multi-objective, in the field. The extracted papers include research articles, reviews, book/book chapters, and conference papers published between 2000 and 2021 for analysis. The results indicate that the constraint-handling techniques for multi-objective optimization have received much less attention compared with single-objective optimization. The most promising algorithms for such optimization were determined to be genetic algorithms, differential evolutionary algorithms, and particle swarm intelligence. Additionally, “Engineering,” “Computer Science,” and “ Mathematics” were identified as the top three research fields in which future research work is anticipated to increase.