一种新的自适应惩罚函数在遗传算法中的应用

摘要: 惩罚函数是遗传算法中解决非线性约束最优化问题最常用的方法之一.但传统的惩罚函数运用到遗传算法中往往难以控制惩罚因子, 因此本文引进了一种结构简单、通用性强的新自适应惩罚函数, 并证明了其收敛性.随后构建了基于新自适应惩罚函数的遗传算法, 使得种群能快速进入可行域,并且提高了遗传算法的局部搜索能力.理论分析及仿真结果表明该算法具有参数少、稳定性强、收敛快等优点.
- 约束最优化 /
- 惩罚函数 /
- 遗传算法 /
- 自适应惩罚函数
Abstract: 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.

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[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.

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