基于P_(EV)准则的D-UMOP求解方法及应用研究
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摘要
针对目标函数相关的不确定多目标规划问题提出了一种在期望-方差准则下的求解方法.首先,给出了不确定多目标规划的等价模型,基于期望-方差准则和帕累托有效解的定义,利用线性加权或理想点法将原问题转化为不确定单目标规划问题,再利用该准则将不确定单目标规划问题转化为确定型单目标规划问题;其次,通过相关理论推导证明了在该准则下转化后的问题求得的最优解是原不确定问题的帕累托有效解;最后,结合不确定多目标规划模型在航路网络容量评估中的应用,设计了一个具有代表性的数值算例以说明本文方法的有效性,考虑算例的特点,用遗传-粒子群算法进行了求解.
A novel approach under the expected-variance value principle was proposed for dependent-uncertain multi-objective programming problem.Firstly,an equivalent model for uncertain multi-objective programming was proposed and according to the concepts of Pareto efficient solution and expected-variance value principle the original uncertain multi-objective problem was converted into an uncertain single objective programming problem by linear weighted method or ideal point method,and then it was transformed into a deterministic single objective programming problem under the expected-variance value principle.Secondly,four lemmas and two theorems were proved to illustrate that the optimal solution of the deterministic single objective programming problem was a Pareto efficient solution of the original uncertain problem.Finally,a numerical example based on air route network capacity evaluation was presented to illustrate the effectiveness of the proposed approach,and genetic-particle swarm optimization algorithm was adopted to solve it.
A novel approach under the expected-variance value principle was proposed for dependent-uncertain multi-objective programming problem.Firstly,an equivalent model for uncertain multi-objective programming was proposed and according to the concepts of Pareto efficient solution and expected-variance value principle the original uncertain multi-objective problem was converted into an uncertain single objective programming problem by linear weighted method or ideal point method,and then it was transformed into a deterministic single objective programming problem under the expected-variance value principle.Secondly,four lemmas and two theorems were proved to illustrate that the optimal solution of the deterministic single objective programming problem was a Pareto efficient solution of the original uncertain problem.Finally,a numerical example based on air route network capacity evaluation was presented to illustrate the effectiveness of the proposed approach,and genetic-particle swarm optimization algorithm was adopted to solve it.
引文
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[22]刘琼,刘炜琪,张超勇.基于GA-PSO的多目标混流装配线排序问题[J].华中科技大学学报:自然科学版,2011,39(10):1-5.
[2]Padhan S K,Nahak C.Higher-order symmetric duality in multi-objective programming problems under higherorder invexity[J].Applied Mathematics and Computation,2011,218(5):1705-1712.
[3]Kou Y N,Zheng J H,Li Z G.Many-objective optimization for coordinated operation of integrated electricity and gas network[J].Journal of Modern Power Systems and Clean Energy,2017,5(3):350-363.
[4]Pavan K Y V,Bhimasingu R.Renewable energy based micro-grid system sizing and energy management for green buildings[J].Journal of Modern Power Systems and Clean Energy,2015,3(1):1-13.
[5]Stancu-Minasian I M.Stochastic programming with multiple objective functions[M].Dordrecht:D Reidel Publishing Company,1984.
[6]Wang Zutong,Guo Jiansheng,Zheng Mingfa,et al.Anew approach for uncertain multi-objective programming problem based on PE principle[J].Journal of Industrial and Management Optimization,2015,11(1):13-26.
[7]Xie Guihua,Zhang Jiasheng,Liu Ronggui.Application of matrix-based system reliability method in complex slopes[J].Journal of Central South University,2013,20(3):812-820.
[8]廖梦琛,孙鹏,张杰勇,等.基于云遗传算法的不确定性环境下平台资源调度适应性优化算法[J].空军工程大学学报:自然科学版,2017,18(4):86-92.
[9]Liu Baoding.Why is there a need for uncertainty theory[J].Journal of Uncertain Systems,2012,6(1):3-10.
[10]王族统.基于不确定理论的多目标规划方法及其应用研究[D].西安:空军工程大学装备管理与安全工程学院,2015.
[11]Liu Baoding,Chen Xiaowei.Uncertain multi-objective programming and uncertain goal programming[J].Journal of Uncertainty Analysis&Applications,2015,3(1):1-8.
[12]Zhao Jialiang,Qiu Xiaolei,Ma Jing,et al.Multi-objective optimization method of micro-grid based on fuzzy clustering analysis and model recognition[J].Power System Technology.2016,40(8):2316-2323.
[13]Zadeh L A.Fuzzy sets as a basis for a theory of possibility[J].Fuzzy Sets and Systems,1978,1(1):3-28.
[14]王晓军,杨海峰,邱志平,等.基于测量数据的不确定性结构分析的模糊理论[J].北京航空航天大学学报,2010,36(8):887-891.
[15]Wang Zutong,Guo Jiansheng,Zheng Mingfa,et al.Uncertain multi-objective travelling salesman problem[J].European Journal of Operational Research,2015,241(2):478-479.
[16]Liu Baoding,Yao Kai.Uncertain multilevel programming:algorithm and applications[J].Computers&Industrial Engineering,2015,89:235-240.
[17]Liu Baoding.Uncertainty theory[M].Berlin:SpringerVerlag,2016.
[18]Liu Baoding.Uncertain set theory and uncertain inference rule with application to uncertain control[J].Journal of Uncertain Systems,2010,4(2):83-98.
[19]Liu Baoding.Membership functions and operational law of uncertain sets[J].Fuzzy Optimization&Decision Making,2012,11(4):387-410.
[20]孟祥飞,王瑛,亓尧,等.基于PEV准则的I-UMOP问题求解方法研究[J].系统工程与电子技术,2018,40(2):50-57.
[21]郑煜坤,王瑛,亓尧,等.区域航路网络容量评估模型研究[J].空军工程大学学报:自然科学版,2018,19(5):21-26.
[22]刘琼,刘炜琪,张超勇.基于GA-PSO的多目标混流装配线排序问题[J].华中科技大学学报:自然科学版,2011,39(10):1-5.
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