Abstract
Over the last few decades, optimization problems have gained special attention in the world of computing, mainly because thanks to them, complex problems, which could only be addressed through approaches, now can be solved. In the wild, biodiversity is manifested by subtle differences in the individuals genetic code and consequently in the evolution of species. This approach is intended to apply to solving optimization problems through multimodal evolutionary algorithms. Standard evolutionary algorithms are not able to find more than a local optimum in the case of multimodal functions due to stochastic errors are committed (an individual randomly move one class to another) and that the population has a finite size (finite diversity). For this reason, in this work, a detailed study of the techniques of solving multimodal problems by using spatial evolutionary algorithms is done. In addition, the design details of new mechanisms for spatial evolutionary algorithms that allow us to reallocate the space of solutions are introduced. Thus, we will be able to deal with the resolution of complex problems with multiple local or global solutions.
Highlights
Many interesting problems in the literature have more than a locally optimal solution, leading to the possibility that there are multiple local or global optimums within the solutions search space
We review the range of options to find a variety of good solutions for multimodal problems avoiding premature convergence, from implicit approach, going through explicit solutions, to algorithms applied to multi-criteria optimization problem solving
We have done an introduction to evolutionary algorithms for solving multimodal problems and to the application of these techniques when it comes to solving multi-criteria optimization problems
Summary
Many interesting problems in the literature have more than a locally optimal solution, leading to the possibility that there are multiple local or global optimums within the solutions search space. They are called multimodal problems [1]. There are cases in which all global maximums have the same hierarchy, either because they have the same value or because a criterion for identifying which of them is better than the previous ones cannot be defined, as can be seen in the Figure 1: This happens in the so-called multi-criteria or multi-objective optimization problems: in this case, the solutions are scored with regard to several variables or criteria where both have the same importance. The multi-criteria optimization is defined as the problem of finding a vector of decision variables that satisfy some constraints and optimize a vector function whose elements representing the objective function
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