Multi-Modal Optimization with k-Cluster Big Bang-Big Crunch Algorithm

Multi-modal optimization is often encountered in engineering problems, especially when different and alternative solutions are sought. Evolutionary algorithms can efficiently tackle multi-modal optimization thanks to their features such as the concept of population, exploration/exploitation, and being suitable for parallel computation. This paper introduces a multi-modal optimization version of the Big Bang-Big Crunch algorithm based on clustering, namely, k-BBBC. This algorithm guarantees a complete convergence of the entire population, retrieving on average the 99\% of local optima for a specific problem. 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). When compared to other multi-modal optimization methods, it outperforms them in terms of accuracy (in both search and objective space) and success rate (number of correctly retrieved optima) -- especially when elitism is applied. 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 multi-modal 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.