Evolutionary-Mean shift algorithm for dynamic multimodal function optimization

Abstract

Recently, many dynamic optimization algorithms based on metaheuristic methods have been proposed. Although these schemes are highly efficient in determining a single global optimum, they fail in locating multiple optimal solutions. The central goal of dynamic multimodal optimization is to detect multiple optimal solutions for an optimization problem where its objective function is modified over time. Locating many optimal solutions (global and local) in a dynamic multimodal optimization problem is particularly crucial for several applications since the best solution could not always be the best implementable alternative due to various practical limitations. In spite of its importance, the problem of dynamic multimodal optimization through evolutionary principles has been scarcely considered in the literature. On the other hand, mean shift is a non-parametric and iterative process for detecting local maxima in a density function represented by a set of samples. Mean shift maintains interesting adaptive characteristics that allow it to find local maxima under dynamic environments. In this paper, the mean shift scheme is proposed to detect global and local optima in dynamic optimization problems. In the proposed method, the search strategy of the mean shift is modified to consider not only the density but also the fitness value of the candidate solutions. A competitive memory, along with a dynamic strategy, has also been added to accelerate the convergence process by using important information from previous environments. As a result, the proposed approach can effectively identify most of the global and local optima in dynamic environments. To demonstrate the performance of the proposed algorithm, a set of comparisons with other well-known dynamic optimization methods has been conducted. The study considers the benchmark generator of the CEC competition for dynamic optimization. The experimental results suggest a very competitive performance of the proposed scheme in terms of accuracy and robustness.