基于单形正交实验设计的差分演化算法

doi:10.11772/j.issn.1001-9081.2016.01.0143

计算机应用 ›› 2016, Vol. 36 ›› Issue (1): 143-149.DOI: 10.11772/j.issn.1001-9081.2016.01.0143

基于单形正交实验设计的差分演化算法

李康顺^1,2, 左磊¹, 李伟^1,2

1. 华南农业大学数学与信息学院, 广州 510642;
2. 江西理工大学信息工程学院, 江西赣州 341000

收稿日期:2015-07-14 修回日期:2015-09-21 出版日期:2016-01-10 发布日期:2016-01-09
通讯作者: 左磊(1992-),男,江西南昌人,硕士研究生,主要研究方向:演化计算
作者简介:李康顺(1962-),男,江西兴国人,教授,博士生导师,博士,CCF会员,主要研究方向:演化计算、图像视觉;李伟(1980-),男,江西瑞金人,副教授,博士研究生,CCF会员,主要研究方向:进化计算、进化算法、机器学习。
基金资助:
国家自然科学基金资助项目(61573157);广东省自然科学基金资助项目(2014A030313454,2015A030313408)。

Novel differential evolution algorithm based on simplex-orthogonal experimental design

LI Kangshun^1,2, ZUO Lei¹, LI Wei^1,2

1. College of Mathematics and Informatics, South China Agricultural University, Guangzhou Guangdong 510642, China;
2. School of Information Engineering, Jiangxi University of Science and Technology, Ganzhou Jiangxi 341000, China

Received:2015-07-14 Revised:2015-09-21 Online:2016-01-10 Published:2016-01-09
Supported by:
This work is partially supported by the National Natural Science Foundation of China (61573157), the Natural Science Foundation of Guangdong Province (2014A030313454, 2015A030313408).

摘要/Abstract

摘要： 为了克服传统差分演化(DE)算法在求解约束优化问题时出现的收敛性慢和容易陷入早熟等缺陷,提出一种新的基于单形正交实验设计的差分演化(SO-DE)算法。该算法设计了一种结合单形交叉和正交实验设计的混合交叉算子来提高差分演化算法的搜索能力;同时采用了一种改进的个体优劣比较准则对种群个体进行比较和选择。这种新的混合交叉算子利用多个父代个体进行单形交叉产生多个子代个体,从两者中选择优秀个体进行正交实验设计得到下一代种群个体。改进的个体优劣比较准则对不同状态下的种群采用不同的处理方案,其目的在于能够有效地权衡目标函数值和约束违反量之间的关系,从而选择优秀个体进入下一代种群。通过对13个标准测试函数和2个工程设计问题进行仿真实验,实验结果表明SO-DE算法求解的精度和标准方差都要优于HEAA算法和COEA/OED算法。SO-DE算法具有更高的精度以及更好的稳定性。

关键词: 差分演化算法, 比较准则, 单形交叉, 正交实验设计, 约束优化

Abstract: Focusing on the defects, such as slow convergence and premature phenomenon, in solving constrained optimization problems by the traditional Differential Evolution (DE) algorithm, a novel DE based on Simplex-Orthogonal experimental design (SO-DE) algorithm was proposed. The algorithm designed a new hybrid crossover operator that combined simplex crossover and orthogonal experimental design to improve the search ability of DE algorithm, and the improved comparison criteria was used to compare and select the individuals of population. Several parent individuals were used to produce multiple offspring individuals by simplex crossover in the new hybrid crossover operator, then the multiple excellent individuals, which were selected from two set by orthogonal experimental design, were copied in the next generation. Different treatment schemes were used for different stages of population in the improved comparison criterion, which aimed to effectively weigh the relationship between the value of the objective function and the degree of constraint violation, thus better individuals were chosen into the next generation. Simulation experiments were conducted on 13 standard test functions and 2 engineering design problems. The SO-DE algorithm is much better than HEAA (Hybrid Evolutionary Algorithm and Adaptive constraint-handling technique) and COEA/ODE (a novel Constrained Optimization Evolutionary Algorithm based on Orthogonal Experimental Design) in terms of the accuracy and standard variance of final solution. The experimental results demonstrate that the SO-DE algorithm has better accuracy and stability.

Key words: Differential Evolution (DE) algorithm, comparison criterion, simplex crossover, orthogonal experimental design, constrained optimization

中图分类号:

TP181

李康顺, 左磊, 李伟. 基于单形正交实验设计的差分演化算法[J]. 计算机应用, 2016, 36(1): 143-149.

LI Kangshun, ZUO Lei, LI Wei. Novel differential evolution algorithm based on simplex-orthogonal experimental design[J]. Journal of Computer Applications, 2016, 36(1): 143-149.

参考文献

[1] LEE K S, GEE Z M. A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice [J]. Computer methods in applied mechanics and engineering, 2005, 194(36/37/38): 3902-3933.
[2] GOLDBERG D E. Genetic algorithms in search, optimization and machine learning [M]. Boston: Addison-Wesley Publishing Company, 1989: 1-14.
[3] STORM R, PRICE K. Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces [J]. Journal of global optimization, 1997, 11(4): 341-359.
[4] KENNEDY J, EBERHART R. Particle swarm optimization [C]// Proceedings of the 1995 IEEE International Conference on Neural Networks. Piscataway, NJ: IEEE, 1995: 1942-1948.
[5] BREST J, GREINER S, BOSKOVIC B, et al. Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems [J]. IEEE transactions on evolutionary computation, 2007, 10(6): 646-657.
[6] WANG Y, CAI Z, ZHOU Y, et al. Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint-handling technique [J]. Structural and multidisciplinary optimization, 2009, 37(4): 395-413.
[7] LIU H, CAI Z, WANG Y. Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization [J]. Applied soft computing, 2010, 10(2): 629-640.
[8] 董宁,王宇平.求解约束优化问题的偏好多目标进化算法[J].西安电子科技大学学报,2014,41(1):98-104.(DONG N, WANG Y P. Multi-objective evolutionary algorithm based on preference for constrained optimization problems [J]. Journal of Xidian university, 2014, 41(1): 98-104.)
[9] 蔡自兴,江中央,王勇,等.一种新的基于正交实验设计的约束优化进化算法[J].计算机学报,2010,33(5):855-864.(CAI Z X, JIANG Z Y, WANG Y, et al. A novel constrained optimization evolutionary algorithm based on orthogonal experimental design [J]. Chinese journal of computers, 2010, 33(5): 855-864.)
[10] JIA G, WANG Y, CAI Z, et al. An improved (μ+λ)-constrained differential evolution for constrained optimization [J]. Information sciences, 2013, 222: 302-322.
[11] MEZURA-MONTES E, MIRANDA-VARELA M, GOMEZ-RA-MON R. Differential evolution in constrained numerical optimization: an empirical study [J]. Information sciences, 2010, 180(22): 4223-4262.
[12] NERI F, TIRRONEN V. Recent advances in differential evolution: a survey and experimental analysis [J]. Artificial intelligence review, 2010, 33(1/2): 61-106.
[13] 龚文引,刘小波,蔡之华.一种基于正交设计的快速差分演化算法及其应用研究[J].小型微型计算机系统,2007,28(7):1297-1301.(GONG W Y, LIU X B, CAI Z H. Research on a fast differential evolution based on orthogonal design and its application [J]. Journal of Chinese computer systems, 2007, 28(7): 1297-1301.)
[14] 郭振宇,程博,叶敏,等.一种并行混沌差异演化算法[J].西安交通大学学报,2007,41(3):299-302.(GUO Z Y, CHENG B, YE M, et al. Parallel chaos differential evolution algorithm [J]. Journal of Xi'an jiaotong university, 2007, 41(3): 299-302.)
[15] TSUTSUI S, YAMAMURA M, HIGUCHI T. Multi-parent recombination with simplex crossover in real coded genetic algorithms [C]// Proceedings of the Genetic and Evolutionary Computation Conference. San Francisco, CA: Morgan Kaufmann Publishers, 1999: 657-664.
[16] LIANG J J, RUNARSSON T P, MEZURA-MONTES E, et al. Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization [R]. Singapore: Nanyang Technological University, 2006.
[17] ESKANDAR H, SAFOLLAH A, BAHREININEJAD A, et al. Water cycle algorithm—a novel metaheuristic optimization method for solving constrained engineering optimization problems [J]. Computers & structures, 2012, 110/111: 151-166.
[18] WANG Y, CAI Z, GUO G, et al. Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems [J]. IEEE transactions on systems, man, and cybernetics, part B: cybernetics, 2007, 37(3): 560-575.
[19] WANG Y, CAI Z, ZHOU Y, et al. An adaptive tradeoff model for constrained evolutionary optimization [J]. IEEE transactions on evolutionary computation, 2008, 12(1): 80-92.
[20] MEZURA-MONTS E, CETINA-DOMINGUEZ O. Empirical analysis of a modified artificial bee colony for constrained numerical optimization [J]. Applied mathematics and computation, 2012, 218(22): 10943-10973.
[21] FARMANI R, WRIGHT J A. Self-adaptive fitness formulation for constrained optimization [J]. IEEE transactions on evolutionary computation, 2003, 7(5): 445-455.
[22] HUANG F, WANG L, HE Q. An effective co-evolutionary differ-ential evolution for constrained optimization [J]. Applied mathematics and computation, 2007, 186(1): 340-356.

基于单形正交实验设计的差分演化算法

Novel differential evolution algorithm based on simplex-orthogonal experimental design

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