Constrained niching using differential evolution

Abstract

The work presented here involves development and detailed investigations of niching methods for multimodal optimization of constrained functions. There is a lack of investigations in the literature on constrained multimodal optimization, hence a number of constrained niching algorithms have been developed here that leverage existing differential evolution-based niching methods with a feasibility rules-domination selection procedure. Furthermore, a suite of 18 benchmark functions has been developed and are presented in this paper; nine newly developed functions are incorporated with nine existing functions from the literature. Optimization results on these analytical functions using the constrained niching algorithms are presented, with analysis provided on the ability to locate multiple global optima, the convergence speed and constraint handling nature of the methods. The differential evolution strategy is also investigated, with SHADE and L-SHADE strategies considered. Finally, a dimensionality study also compares against the only other known constrained niching algorithm. Results indicate that all of the algorithms developed and tested generally perform well for low dimensional, low modality problems, but that local neighbourhood-based methods show the best results across the suite of functions tested. When high-dimensional problems are considered, using the L-SHADE strategy yields excellent results. An accompanying supplementary data file is provided with the manuscript.has also been successfully applied to DE [51]. The ensemble approach takes any number of constraint handling techniques and adaptively applies them to exploit the individual performance of each technique. Mezura-Montes et al.[52] investigated the effect of different mutation strategies in DE on constrained optimization. They highlighted the fact that much work in solving CNOPs using DE uses the feasibility rules of Deb [14], and as such, used this to handle the constraints.Commonly, population diversity is a requirement of EAs, such that design space exploration is achieved, with diversity decreasing through the optimization to exploit the global optimum within the space. On the other hand, while diversity is important for unimodal optimization, this is not necessarily the main driver of niching techniques. Niching requires a more careful balance of diversity to be able to locate and maintain strong and stable niches, and therefore exploit all the optima in the design space. Comprehensive reviews on niching techniques have been provided by Das et al.[53] and more recently by Li et al. [25] (the reader is particularly guided to the review of Li et al. for discussions of niching using SIAs as well as EAs), and a short review is presented here with particular attention paid to niching using EAs.One of the earliest bodies of work on maintaining population diversity, and therefore implicitly also multimodal optimization, was by de Jong [17], who introduced the classical idea of crowding. Crowding compares the fitness of close individuals and attemp...

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