A Multimodal Optimization Algorithm Inspired by the States of Matter

The main objective of multi-modal optimization is to find multiple global and local optima for a problem in only one execution. Detecting multiple solutions to a multi-modal optimization formulation is especially useful in engineering, since the best solution could not represent the best realizable due to various practical restrictions. The States of Matter Search (SMS) is a recently proposed stochastic optimization technique. Although SMS is highly effective in locating single global optimum, it fails in providing multiple solutions within a single execution. To overcome this inconvenience, a new multimodal optimization algorithm called the Multi-modal States of Matter Search (MSMS) in introduced. Under MSMS, the original SMS is enhanced with new multimodal characteristics by means of: (1) the definition of a memory mechanism to efficiently register promising local optima according to their fitness values and the distance to other probable high quality solutions; (2) the modification of the original SMS optimization strategy to accelerate the detection of new local minima; and (3) the inclusion of a depuration procedure at the end of each state to eliminate duplicated memory elements. The performance of the proposed approach is compared to several state-of-the-art multimodal optimization algorithms considering a benchmark suite of fourteen multimodal problems. The results confirm that the proposed method achieves the best balance over its counterparts regarding accuracy and computational cost.