Dynamic Multimodal Function Optimization: An Evolutionary-Mean Shift Approach

Numerous metaheuristic-based dynamic optimization algorithms have emerged recently. While these algorithms excel in locating a single global optimum, they fall short in identifying multiple optimal solutions. The primary objective of dynamic multimodal optimization is to identify several optimal solutions for a problem where the objective function changes over time. The discovery of multiple optimal solutions, both global and local, holds significant importance for numerous applications. The best implementable alternative may not always be the optimal solution due to practical limitations. Surprisingly, the literature has paid scant attention to the problem of dynamic multimodal optimization using evolutionary principles. Conversely, mean shift, a nonparametric iterative process, is capable of detecting local maxima in a density function represented by a sample set. Mean shift exhibits adaptive qualities that enable it to identify local maxima in dynamic environments. In this chapter, we present a mean shift approach to detect global and local optima in dynamic optimization problems. The presented method modifies the search strategy of mean shift by considering both density and fitness values of candidate solutions. To expedite the convergence process, a competitive memory and dynamic strategy are incorporated to leverage valuable information from previous environments. Consequently, the present approach effectively identifies a significant number of global and local optima in dynamic environments. To showcase its performance, we compare the present algorithm with well-known dynamic optimization methods using the CEC competition benchmark generator. Experimental results demonstrate the present scheme's high accuracy and robustness, positioning it as a highly competitive solution.