Incorporating Fitness Inheritance and k-Nearest Neighbors for Evolutionary Dynamic Optimization

Many real-world problems encounter varying environments while searching for the optimal solutions. Problems of these kinds are known as dynamic optimization problems. Evolutionary algorithms (EAs) have shown their high capability of solving dynamic optimization problems. The large number of fitness evaluations, however, limits the utility of EAs in dynamic optimization with expensive fitness evaluation. This study proposes a fitness inheritance method based on $k$-nearest neighbors (kNN) to reduce the number of fitness evaluations. This fitness inheritance method is applied to the covariance matrix adaptation evolution strategy (CMAES), a state-of-the-art evolutionary algorithm for complex numerical optimization problems, to save fitness evaluations and improve search efficiency. This study further presents a convergence checking operator to maintain a reasonable accuracy of fitness inheritance by reinitializing the population and multivariate normal distribution model timely. Experimental results verify the effectiveness and efficiency of the proposed method on six benchmark problems of dynamic optimization.