Game of Patterns and Genetic Algorithms Under a Comparative Study

Abstract

In this article we present a comparison of the performance between a metaheuristic optimization method, Game of Patterns (GofP), so-called by the author, and the well-known genetic algorithms (GAs), through two implementations, namely: the GA of Scilab (SGA); and the GA of the R Project for Statistical Computing (RGA). For this purpose, we have selected a set of multimodal objective functions in the n-dimensional Euclidean space \(\mathbb {R}^{n}\) with a unique global minimum. For comparing both metaheuristic optimization approaches, a performance indicator of quality, denoted Q(p, n, s), was defined, which allows us to measure the quality of the obtained global optimal solution for each pth problem, in the n-dimensional space, when it is solved by each metaheuristic optimization method \(s\in \{\texttt {GofP},\texttt {SGA},\texttt {RGA}\}\). The indicator Q(p, n, s) then depends on: the number of evaluations of the pth optimization problem in the Euclidean space \(\mathbb {R}^{n}\), which has required the s metaheuristic optimization method for identifying the global minimum; and the distance between the location of its respective unique global minimum and the location of the minimum that has been identified by the s metaheuristic optimization method. The paper also offers a brief explanation of the GofP method, which has been developed for solving unconstrained mixed integer problems in the \(n\times m\)-dimensional Euclidean space \(\mathbb {R}^{n}\times \mathbb {Z}^{m}\).