Evolutionary multimodal optimization

Abstract: Multimodal optimization amounts to finding multiple global and local optima (as opposed to a single solution) of a function, so that the user can have a better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be switched to another suitable one while still maintaining the optimal system performance. Evolutionary Algorithms (EAs), due to their population-based approaches, are able to detect multiple solutions within a population in a single simulation run and have a clear advantage over the classical optimization techniques, which need multiple restarts and multiple runs in the hope that a different solution may be discovered every run, with no guarantee however. Numerous evolutionary optimization techniques have been developed since late 1970s for locating multiple optima (global or local). These techniques are commonly referred to as “niching” methods. Niching can be incorporated into a standard EA to promote and maintain formation of multiple stable subpopulations within a single population, with an aim to locate multiple globally optimal or suboptimal solutions simultaneously. This article is the first of its kind to present a comprehensive review of the basic concepts related to real-parameter evolutionary multimodal optimization, a survey of the major niching techniques, a detailed account of the adaptation of EAs from diverse paradigms to tackle multimodal problems, benchmark problems and performance measures.

Abstract: In real life, we often need to find multiple optimally sustainable solutions of an optimization problem Evolutionary multimodal optimization algorithms can be very helpful in such cases They detect and maintain multiple optimal solutions during the run by incorporating specialized niching operations in their actual framework Differential evolution (DE) is a powerful evolutionary algorithm (EA) well-known for its ability and efficiency as a single peak global optimizer for continuous spaces This article suggests a niching scheme integrated with DE for achieving a stable and efficient niching behavior by combining the newly proposed parent-centric mutation operator with synchronous crowding replacement rule The proposed approach is designed by considering the difficulties associated with the problem dependent niching parameters (like niche radius) and does not make use of such control parameter The mutation operator helps to maintain the population diversity at an optimum level by using well-defined local neighborhoods Based on a comparative study involving 13 well-known state-of-the-art niching EAs tested on an extensive collection of benchmarks, we observe a consistent statistical superiority enjoyed by our proposed niching algorithm

Abstract: Neighborhood information plays an important role in improving the performance of evolutionary computation in various optimization scenarios, particularly in the context of multimodal optimization. Several neighborhood concepts, i.e., index-based neighborhood, nearest neighborhood, and fuzzy neighborhood, have been studied and engaged in the design of niching methods. However, the use of these neighborhood concepts requires the specification of some problem-related parameters, which is difficult to determine without a prior knowledge. In this paper, we introduce a new neighborhood concept based on a geometrical construction called Voronoi diagram. The new concept offers two advantages at the expense of increasing the computational complexity to a higher level. It eliminates the need of additional parameters and it is more informative than the existing ones. The information provided by the Voronoi neighbors of an individual can be exploited to estimate the evolutionary state. Based on the information, we divide the population into three groups and assign each group a different reproduction strategy to support the exploration and exploitation of the search space. We show the use of the concept in the design of an effective evolutionary algorithm for multimodal optimization. The experiments have been conducted to investigate the performance of the algorithm. The results reveal that the proposed algorithm compare favorably with the state-of-the-art algorithms designed based on other types of neighborhood concepts.