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.

最近，已经提出了许多基于元启发式方法的动态优化算法。尽管这些方案在确定单个全局最优解方面非常有效，但它们无法定位多个最优解。动态多模态优化的中心目标是检测优化问题的多个最优解，其中其目标函数随时间被修改。在动态多模态优化问题中定位多个最优解（全局和局部）对于多种应用尤其重要，因为由于各种实际限制，最佳解并不总是最佳的可实施替代方案。尽管它很重要，但文献中很少考虑通过进化原理进行动态多模态优化的问题。另一方面，均值偏移是一种非参数迭代过程，用于检测由一组样本表示的密度函数中的局部最大值。均值漂移保持了有趣的自适应特性，使其能够在动态环境下找到局部最大值。在本文中，提出了均值漂移方案来检测动态优化问题中的全局和局部最优。在所提出的方法中，修改了均值漂移的搜索策略，不仅考虑了密度，还考虑了候选解的适应度值。还添加了竞争性记忆以及动态策略，以通过使用来自先前环境的重要信息来加速收敛过程。因此，所提出的方法可以有效地识别动态环境中的大多数全局和局部最优。为了证明所提出算法的性能，与其他著名的动态优化方法进行了一组比较。该研究考虑了 CEC 竞赛的基准生成器进行动态优化。实验结果表明，所提出的方案在准确性和鲁棒性方面具有非常有竞争力的性能。