Multimodal optimization by artificial weed colonies enhanced with localized group search optimizers

Abstract

Multimodal optimization aims at 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 approach 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. This article proposes a hybrid two-stage optimization technique that firstly employs Invasive Weed Optimization (IWO), an ecologically inspired algorithm to find the promising Euclidean sub-regions surrounding multiple global and local optima. IWO is run for 80% of the total budget of function evaluations (FEs), and consecutively the search is intensified by using a modified Group Search Optimizer (GSO), in each detected sub-region. GSO, invoked in each sub-region discovered with IWO, is continued for 20% of the total budget of FEs. Both IWO and GSO have been modified from their original forms to meet the demands of the multimodal problems used in this work. Performance of the proposed algorithm is compared with a number of state-of-the-art multimodal optimization algorithms over a benchmark-suite comprising of 21 basic multimodal problems and 7 composite multimodal problems. A practical multimodal optimization problem concerning the design of dielectric composites has also been used to test the performance of the algorithm. Experimental results suggest that the proposed technique is able to provide better and more consistent performance over the existing well-known multimodal algorithms for majority of the test problems without incurring any serious computational burden.