Multimodal Optimization with k-Cluster Big Bang-Big Crunch Algorithm and Postprocessing Methods for Identification and Quantification of Optima
This addresses the problem of finding multiple solutions in engineering optimization for researchers, but it is incremental as it builds on existing evolutionary algorithms with clustering and post-processing enhancements.
The paper tackled multimodal optimization by proposing k-BBBC, a clustering-based extension of the Big Bang-Big Crunch algorithm, and post-processing methods for identifying and quantifying optima. Results showed k-BBBC performs well on problems with up to 379 optima and 32 dimensions, outperforming other methods in accuracy and success rate on basic functions, but becomes computationally expensive and requires prior knowledge of the number of optima.
Multimodal optimization is often encountered in engineering problems, especially when different and alternative solutions are sought. Evolutionary algorithms can efficiently tackle multimodal optimization thanks to their features such as the concept of population, exploration/exploitation, and being suitable for parallel computation. This paper investigates whether a less-known optimizer, the Big Bang-Big Crunch (BBBC) algorithm, is suitable for multimodal optimization. We extended BBBC and propose k-BBBC, a clustering-based multi-modal optimizer. Additionally, we introduce two post-processing methods to (i) identify the local optima in a set of retrieved solutions (i.e., a population), and (ii) quantify the number of correctly retrieved optima against the expected ones (i.e., success rate). Our results show that k-BBBC performs well even with problems having a large number of optima (tested on $379$ optima) and high dimensionality (tested on $32$ decision variables), but it becomes computationally too expensive for problems with many local optima (i.e., in the CEC'2013 benchmark set). Compared to other multimodal optimization methods, it outperforms them in terms of accuracy (in both search and objective space) and success rate (number of correctly retrieved optima) when tested on basic multimodal functions, especially when elitism is applied; however, it requires knowing the number of optima of a problem, which makes its performance decrease when tested on niching competition test CEC'2013. Lastly, we validated our proposed post-processing methods by comparing their success rate to the actual one: results suggest that these methods can be used to evaluate the performance of a multimodal optimization algorithm by correctly identifying optima and providing an indication of success -- without the need to know where the optima are located in the search space.