Landscape-based Evolutionary Algorithms for Dynamic Optimization Problems

Abstract

In real-world structured optimization problems, specific objective functions, decision variables, constraints, data and/or parameters may vary over time. These problems are generally recognized as dynamic optimization problems (DOPs). Evolutionary computation (EC) is a stochastic global search approach that has been successfully used to find optimal or near-optimal solutions for a wide range of optimization problems. EC is conceptually simple and imposes no specific mathematical properties requirement, thus showing competitive performance in dealing with static optimization problems. However, EC encounters challenges in dynamic problems on adaptability and efficiency. For the employment of EC in DOPs, two key points should be considered: the nature of optimization problems to be solved and the class of algorithms to be designed, where the crucial element of the former is landscape analysis and the latter frequently leads to the type of the algorithm. A new approach named Landscape Influenced Dynamic Optimization Algorithm (LIDOA) is proposed to incorporate landscape analysis information into the search process, where a landscape-based strategy is integrated with appropriately designed evolutionary algorithms. In LIDOA, the knowledge learned in each landscape is archived and re-utilized in the new environment. Several classical evolutionary algorithms, including genetic algorithm (GA), self-adaptive differential evolution algorithm (jDE) and covariance matrix adaptation evolution strategy (CMA-ES), are employed to examine the efficiency of LIDOA, and four landscape measures are considered. Experimental results showed the overall advantage of LIDOA. LIDOA with a single landscape measure is then expanded to multiple landscape measures. Three multi-measure methods are designed that are able to achieve good performance on evolutionary algorithms with appropriately integrated multiple landscape measures. According to the experimental results, LIDOA with multi-measure methods also improves the performance of GA, jDE and CMA-ES. The second key point in employing multiple evolutionary algorithms in DOPs is also studied. Three multi-algorithm methods are investigated based on jDE and GA, where an information sharing strategy and a self-adjusted parameter strategy are designed. Experimental results show that with an appropriate integration mechanism, all three multi-algorithm methods can obtain better performance over a single algorithm. Two key parameters in multi-algorithm methods are discussed. The similarity check strategy with multi-measure is also integrated with three multi-algorithm methods, and experimental results demonstrate the efficacy of both multi-algorithm methods and multi-measure strategies. Furthermore, to show the applicability of the concept in other algorithms, it is tested on quantum-inspired evolutionary algorithms. The performance of LIDOA with quantum-inspired evolutionary algorithms shows that LIDOA and quantum operators are beneficial for jDE, GA and CMA-ES, though their contributions vary. Finally, the proposed algorithms are applied to two practical problems (parameter estimation for frequency-modulated (FM) sound waves and spread spectrum radar polyphase code design). With appropriately selected landscape measure(s), LIDOA is able to improve the performance on both problems. When the complexity of the two applicable problems increases, the proposed hybrid framework with a multi-algorithm and multi-measure method is more reliable