Genetic Algorithm to Solve Optimization Problem with Equality Constrains

Abstract

Abstract: Aiming at difficultly solving optimization with equality constraint in genetic algorithm, based on independence analysis of design variables, a descending dimension method was used to deal with equality constraint. In this way, not only equality constraints can be strictly satisfied during optimization, but also there are only inequality constrains in optimization. Furthermore, referring to the multiobjective idea, individuals was ranked through violation degree and violation times simultaneously, which is more in accord with practice. Finally, three numerical examples were used to examine the proposed method, satisfying results were achieved, which indicates the method is valid and feasible.

Key words: genetic algorithm, equality constraint, descending dimension, rank, optimization

CLC Number:

TP18

HU Kuan-1, 2 , CHANG Xin-Long-1, SONG Bi-Feng-2, ZHANG Lin-3, LONG Bing-1, YU Yan-Feng-1. Genetic Algorithm to Solve Optimization Problem with Equality Constrains[J]. Journal of Shanghai Jiaotong University, 2011, 45(07): 966-969.

References

［1］Gen M, Cheng R W. Genetic algorithms and engineering design［M］. New York: WileyInterscience, 2000.

［2］Huang F, Wang L, He Q. An effective coevolutionary differential evolution for constrained optimization［J］. Applied Mathematics and Computation, 2007, 186(1):340356.

［3］Yu J X, Yao X, Choi C, et al. Materialized view selection as constrained evolutionary optimization［J］. IEEE Trans on Systems, Man, and Cybernetics, 2003,33(4):458467.

［4］Takahama T, Sakai S. Constrained optimization by applying the α constrained method to the nonlinear simplex method with mutations［J］. IEEE Trans on Evolutionary Computation, 2005,9(5):437451.

［5］MezuraMontes E, Coello Coello C A. A simple multimembered evolution strategy to solve constrained optimization problems［J］. IEEE Trans on Evolutionary Computation, 2005, 9(1):117.

［6］林丹, 李敏强. 基于遗传算法求解约束优化问题的一种算法［J］. 软件学报, 2001,12(4):628632.

LIN Dan, LI Mingqiang. A GAbased method for solving constrained optimization problems［J］. Journal of Software, 2001,12(4): 628632.

［7］Zhou Y R, Li Y X, Wang Y, et al. A Pareto strength evolutionary algorithm for constrained optimization［J］. Journal of Software, 2003,14(7):12431249.

［8］Deb K. An efficient constraint handling method for genetic algorithms［J］. Computation Methods in Applied Mechanics and Engineering,2000,86(2):311338.［9］沈琦, 李泽民. 具有线性等式约束非线性规划问题的一种新算法［J］. 重庆大学学报，2006, 29(7):98101.

SHEN Qi, LI Zemin. Algorithm for the nonlinear programming with linear equality constraints［J］. Journal of Chongqing University, 2006, 29(7): 98101.

［10］杨懿, 张守贵.具有线性不等式约束非线性规划问题的降维算法［J］. 重庆大学学报, 2007, 30(10):4245.

YANG Yi, ZHANG Shougui. Descending dimension algorithm of nolinear programming problem with linear inequality constraints［J］. Journal of Chongqing University, 2007, 30(10): 4245.

［11］张长林, 余建星. 非线性约束最优化问题的多目标模拟退火算法［J］. 复旦学报, 2003, 42(1):9397.

ZHANG Changlin, YU Jianxing. The multiobject simulated annealing algorithm［J］. Journal of Fudan University, 2003, 42(1): 9397.

[1]	WANG Hong, QI Yankun, HE Yong, YANG Guojun. Multi-Stage Opportunistic Maintenance Decision-Making for Electric Multiple Unit Systems with Bi-Objective Optimization [J]. Journal of Shanghai Jiao Tong University, 2022, 56(9): 1276-1284.
[2]	FU Yang, DING Zhiyin, MI Yang. Frequency Control Strategy for Interconnected Power Systems with Time Delay Considering Optimal Energy Storage Regulation [J]. Journal of Shanghai Jiao Tong University, 2022, 56(9): 1128-1138.
[3]	HUANG Yuhao, HAN Chao, ZHAO Minghui, DU Qiankun, WANG Shigang. Multi-Objective Optimization Strategy of Trajectory Planning for Unmanned Aerial Vehicles Considering Constraints of Safe Flight Corridors [J]. Journal of Shanghai Jiao Tong University, 2022, 56(8): 1024-1033.
[4]	LI Dechang, YANG Hualong, DUAN Jingru. A Joint Optimization of Vessel Scheduling and Refueling Strategy for Container Liner Shipping with Cooperative Agreements [J]. Journal of Shanghai Jiao Tong University, 2022, 56(7): 953-964.
[5]	YAN Qing, LU Jiansha, JIANG Weiguang, SHAO Yiping, TANG Hongtao, LI Yingde. Path Optimization of Stacker in Compact Storage System with Dual-Port Layout [J]. Journal of Shanghai Jiao Tong University, 2022, 56(7): 858-867.
[6]	OUYANG Xuyu, CHANG Haichao, LIU Zuyuan, FENG Baiwei, ZHAN Chengsheng, CHENG Xide. Application of Adaptive Sampling Method in Hull Form Optimization [J]. Journal of Shanghai Jiao Tong University, 2022, 56(7): 937-943.
[7]	FU Lia (傅莉), LONG Xia∗ (龙洗), HE Wenbinb (何文斌). Air Combat Assignment Problem Based on Bayesian Optimization Algorithm [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(6): 799-805.
[8]	LI Shiqi (李世其), LI Xiao∗ (李肖), HAN Ke (韩可), XIONG Youjun (熊友军), XIE Zheng (谢铮), CHEN Jinliang (陈金亮). Path Planning and Optimization of Humanoid Manipulator in Cartesian Space [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(5): 614-620.
[9]	HUANG Yinghao1,2 (黄颖浩), WU Yi3 (吴怡), YAO Lixiu2 (姚莉秀), CAI Yunze1,2∗ (蔡云泽). A Class of Distributed Variable Structure Multiple Model Algorithm Based on Posterior Information of Information Matrix [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(5): 671-679.
[10]	ZHOU Tianyan, FENG Xiaoen, FAN Yunfeng, DONG Shiyin, LI Yuqing, JIN Huizhong. Optimization Model of Ground Air Defense Force Deployment to Avoid Excessive Air Defense Firepower [J]. Air & Space Defense, 2022, 5(4): 19-23.
[11]	WANG Xiaojian, HONG Jun, CHEN Jinghua, LI Hongguang. Weight Reduction Study of Box Structure Based on Parametric Modeling and Response Surface Optimization [J]. Air & Space Defense, 2022, 5(4): 60-66.
[12]	LIU Jiea (刘洁), ZHANG Baojib∗ (张宝吉). Multiobjective Optimization of Hull Form Based on Global Optimization Algorithm [J]. J Shanghai Jiaotong Univ Sci, 2022, 27(3): 346-355.
[13]	ZENG Bo, MU Hongwei, DONG Houqi, ZENG Ming. Optimization of Active Distribution Network Operation Considering Decarbonization Endowment from 5G Base Stations [J]. Journal of Shanghai Jiao Tong University, 2022, 56(3): 279-292.
[14]	MA Zhoujun, WANG Yong, WANG Jie, CHEN Shaoyu. A Dual Cooperative Optimization for Optimal Redundancy Quantity of MMC Submodules of Flexible Controller [J]. Journal of Shanghai Jiao Tong University, 2022, 56(3): 325-332.
[15]	WANG Ning, FU Yunpeng, LI Ting, LI Tie, YI Ping. Optimization of Control Scheme for Large Flow Seawater Cooling System Based on FloMaster-Simulink Co-Simulation [J]. Journal of Shanghai Jiao Tong University, 2022, 56(3): 379-385.