Penalty function is one of the most commonly used method in genetic algorithm (GA) to solve nonlinear constraint optimization problems. For traditional
penalty functions, it is always not easy to control penalty factors. In this paper we presenta new adaptive penalty function with simpler construction and prove its convergence.Then based on this adaptive penalty function we present a new genetic algorithm, which can make populations quickly access to feasible regions and improve local search capacity of genetic algorithms. Theoretical analysis and simulation results show that this algorithm has stronger stability and better convergence but needs less parameters than other ones.
CAI Hai-Luan
,
GUO Xue-Ping
. A new adaptive penalty function in the application of genetic algorithm[J]. Journal of East China Normal University(Natural Science), 2015
, 2015(6)
: 36
-45
.
DOI: 10.3969/j.issn.1000-5641.2015.06.006
[3]甘敏, 彭辉. 一种新的自适应惩罚函数算法求解约束优化问题~[J].信息与控制, 2009, 38(1): 24-28.
[4]王宜举, 修乃华. 非线性最优化理论与方法~[M]. 北京: 科学出版社, 2012:200-220.
[5]TESSEMA B, YEN G G. A self adptive penalty function based algorithm for constrained optimization [C]//Proceedings of the IEEE Congress on Evolutionary Computation. Piscataway, NJ, USA: IEEE, 2006:246-253.
[6]HOUCK C R, JOINES J A. On the use of non-staionary penalty functions to solve nonlinear constrained optimization problems with GA's[C]//Proceedings of the First IEEE Conference on Evolutionary Computation. Piscataway, NJ, USA: IEEE, 1994: 579-584.
[7]闫妍. 一种新的自适应遗传算法[D]. 哈尔滨: 哈尔滨工程大学, 2010.
[8]华东师范大学数学系. 数学分析(上)~[M]. 北京: 高等教育出版社, 2010:160-162.
[9]李广民, 刘三阳. 应用泛函分析原理~[M]. 西安: 西安电子科技大学出版社,2003: 88-95.
[10]RUDIN W. Real and Complex Analysis (3rd Edition) [M]. Beijing: China Machine Press, 2006: 103-108.
[11]HADI-ALOUNE A B, BEAN J C. A genetic algorithm for themultiple-choice integer program [J]. Operations Research, 1997,45(1): 92-101.
[12]RANARSSON T P, YAO X. Stochastic ranking for constrainedevolutionary optimization [J]. IEEE Transactions on Evolutionary Computation, 2000, 4(3): 284-294.
[13]FAMANI R, WRIGHT J A. Self-adaptive fitness formulation forconstrained optimization [J]. IEEE Transactions on EvolutionaryComputation, 2003(7): 445-455.
[14]HOMAIFAR A, QI C X, LAI S H. Constrained optimization via genetic algorithms [J]. Simulation, 1994, 62(4): 242-254.
[15]COELLO A C. Theoretical and numerical constraint-handling techniquesused with evolutionary algorithms: A survey of the art [J]. Computer Methods in Applied Mechanics and Engineering, 2002, 191: 1245-1289.