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An adaptive genetic algorithm for solving bilevel linear programming problem
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作者 王广民 王先甲 +1 位作者 万仲平 贾世会 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第12期1605-1612,共8页
Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this pr... Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes maybe infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references. 展开更多
关键词 bilevel linear programming genetic algorithm fitness value adaptive operator probabilities crossover and mutation
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Bilevel linear programming model of charging for effluent based on price control
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作者 李煜华 李磊 +1 位作者 胡运权 邵海宏 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2007年第2期292-296,共5页
For the optimum price problem of charging for effluent, this paper analyzes the optimal Pigovian Tax and the serious information asymmetry problem existing in the application process of optimal Pigovian Tax, which is ... For the optimum price problem of charging for effluent, this paper analyzes the optimal Pigovian Tax and the serious information asymmetry problem existing in the application process of optimal Pigovian Tax, which is predominant in theory. Then the bilevel system optimizing decision-making theory is applied to give bilevel linear programming decision-making model of charging for effluent, in which the government (environmental protection agency) acts as the upper level decision-making unit and the polluting enterprises act as the lower level decision-making unit. To some extent, the model avoids the serious information asymmetry between the government and the polluting enterprises on charging for effluent. 展开更多
关键词 charging for effluent Pigovian Tax price control bilevel linear programming information asymmetry
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Solution for integer linear bilevel programming problems using orthogonal genetic algorithm 被引量:9
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作者 Hong Li Li Zhang Yongchang Jiao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第3期443-451,共9页
An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorith... An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm. 展开更多
关键词 integer linear bilevel programming problem integer optimization genetic algorithm orthogonal experiment design
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Global convergent algorithm for the bilevel linear fractional-linear programming based on modified convex simplex method 被引量:2
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作者 Guangmin Wang Bing Jiang +1 位作者 Kejun Zhu Zhongping Wan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第2期239-243,共5页
A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equ... A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm. 展开更多
关键词 bilevel linear fractional-linear programming convex simplex method dual problem.
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Discrete differential evolution algorithm for integer linear bilevel programming problems 被引量:1
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作者 Hong Li Li Zhang Yongchang Jiao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2016年第4期912-919,共8页
A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forc... A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods. 展开更多
关键词 discrete linear bilevel programming problem discrete differential evolution constraint handling method branch and bound algorithm
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An Algorithm to Solve Linear Bilevel Programs 被引量:6
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作者 LIU Xiaomin WANG Rishuang(Dept. of Math. Beijing University of Aero.& Astro.,Beijing,100083,P.R.China)WANG Shouyang WANG Qian (Institute of Systems Science,Chinese Academy of Sciences. Beijing,100081, P.R. China) 《Systems Science and Systems Engineering》 CSCD 1995年第2期158-167,共10页
Linear bilevel programming deals with optimization problems in which the constraint region is implicitly determined by another optimization problem. This paper presents a new algorithm for solving linear bilevel progr... Linear bilevel programming deals with optimization problems in which the constraint region is implicitly determined by another optimization problem. This paper presents a new algorithm for solving linear bilevel programs. A numerical example is given to illustrate this method. 展开更多
关键词 linear bilevel programming algorithm. convergence.
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