Journal
IEEE TRANSACTIONS ON CYBERNETICS
Volume 46, Issue 12, Pages 2938-2952Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2015.2493239
Keywords
Constrained optimization problems (COPs); constraints; evolutionary algorithms (EAs); objective function
Categories
Funding
- National Basic Research Program 973 of China [2011CB013104]
- Innovation-driven Plan in Central South University [2015CXS012, 2015CX007]
- National Natural Science Foundation of China [61273314, 51175519, 61175064]
- RGC of Hong Kong [CityU: 11207714]
- Program for New Century Excellent Talents in University [NCET-13-0596]
- State Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing Institute of Technology
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When solving constrained optimization problems by evolutionary algorithms, an important issue is how to balance constraints and objective function. This paper presents a new method to address the above issue. In our method, after generating an offspring for each parent in the population by making use of differential evolution (DE), the well-known feasibility rule is used to compare the offspring and its parent. Since the feasibility rule prefers constraints to objective function, the objective function information has been exploited as follows: if the offspring cannot survive into the next generation and if the objective function value of the offspring is better than that of the parent, then the offspring is stored into a predefined archive. Subsequently, the individuals in the archive are used to replace some individuals in the population according to a replacement mechanism. Moreover, a mutation strategy is proposed to help the population jump out of a local optimum in the infeasible region. Note that, in the replacement mechanism and the mutation strategy, the comparison of individuals is based on objective function. In addition, the information of objective function has also been utilized to generate offspring in DE. By the above processes, this paper achieves an effective balance between constraints and objective function in constrained evolutionary optimization. The performance of our method has been tested on two sets of benchmark test functions, namely, 24 test functions at IEEE CEC2006 and 18 test functions with 10-D and 30-D at IEEE CEC2010. The experimental results have demonstrated that our method shows better or at least competitive performance against other state-of-the-art methods. Furthermore, the advantage of our method increases with the increase of the number of decision variables.
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