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School of Computer Science, China University of Geosciences, Wuhan 430074, Hubei, People’s Republic of China [email protected], [email protected] 2 School of Information Engineering, Shijiazhuang University of Economics, Shijiazhuang 050031, Hebei, People’s Republic of China

Abstract. This paper proposes a dynamic constrained many-objective optimization method for solving constrained optimization problems. We first convert a constrained optimization problem (COP) into an equivalent dynamic constrained many-objective optimization problem (DCMOP), then present many-objective optimization evolutionary algorithm with dynamic constraint handling mechanism, called MaDC, to solve the DCMOP, thus the COP is addressed. MaDC uses DE as the search engine, and reference-point-based nondominated sorting approach to select individuals to construct next population. The effectiveness of MaDC has been verified by comparing with peer algorithms. Keywords: Constrained optimization problem · Many-objective optimization · Dynamic constraint · DE · Reference points

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Introduction

In science and engineering disciplines, it is common to encounter a large number of constrained optimization problems (COPs). During the past decades, researchers have widely used evolutionary algorithms (EAs) to deal with COPs [1–3], and made considerable achievements. In recent years, with the development of the multi-objective and adaptive evolutionary theories and methodologies, more and more works are managed to add these fruits to solving constrained problems. Coello first used dominance-based selection strategy to deal with constraints [4]. In [5] Coello and Mezura proposed a new version of the Niched-Pareto Genetic Algorithm (NPGA). This approach uses dominance-based selection scheme to assign fitness function value, and adopts an additional parameter called Sr to control the diversity of the population. Venkatraman and Yen [6] proposed genetic algorithm-based two-phase framework for solving COPs. In the first phase the objective function is completely disregarded, and only the constraints of the problem are focused on. In the second phase, the objective c Springer Science+Business Media Singapore 2016  K. Li et al. (Eds.): ISICA 2015, CCIS 575, pp. 64–73, 2016. DOI: 10.1007/978-981-10-0356-1 7

Combining Dynamic Constrained Many-Objective Optimization

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function and satisfaction of the constraints are treated as two objectives to be simultaneously optimized. Hsieh [7] proposed an algorithm based on wellknown multi-objective evolutionary algorithm, NSGA-II. The procedure, used as a hybrid constraint handling mechanism, combines -comparison method of multi-objective optimization and penalty method of constraints-handling. Yong Wang [8] presented hybrid constrained optimization EA (HCOEA), which effectively combines multi-objective optimization with global and local search models. In global model, Pareto-dominance-based tournament selection among parent and offspring and similarity measuring by Euclidean distance among individuals are used to promote