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
Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s f...Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.展开更多
International freedom of the air(traffic rights)is a key resource for airlines to carry out international air transport business.An efficient and reasonable traffic right resource allocation within a country between a...International freedom of the air(traffic rights)is a key resource for airlines to carry out international air transport business.An efficient and reasonable traffic right resource allocation within a country between airlines can affect the quality of a country’s participation in international air transport.In this paper,a multi-objective mixed-integer programming model for traffic rights resource allocation is developed to minimize passenger travel mileages and maximize the number of traffic rights resources allocated to hub airports and competitive carriers.A hybrid heuristic algorithm combining the genetic algorithm and the variable neighborhood search is devised to solve the model.The results show that the optimal allocation scheme aligns with the principle of fairness,indicating that the proposed model can play a certain guiding role in and provide an innovative perspective on traffic rights resource allocation in various countries.展开更多
目的针对冷链运输中的生鲜打包及装载优化问题,提出一种允许货物以体积恒定为前提进行尺寸变化的包装装载方案,以最大化集装箱的空间利用率。方法基于上述问题,构建非线性混合整数规划模型,为了方便CPLEX或LINGO等求解器对该非线性混合...目的针对冷链运输中的生鲜打包及装载优化问题,提出一种允许货物以体积恒定为前提进行尺寸变化的包装装载方案,以最大化集装箱的空间利用率。方法基于上述问题,构建非线性混合整数规划模型,为了方便CPLEX或LINGO等求解器对该非线性混合整数规划模型进行求解,采用一种分段线性化方法,将该非线性模型进行线性化处理。由于所研究问题具有NP-hard属性,无论是CPLEX还是LINGO都无法有效求解大规模算例,因此设计一种有效结合遗传算法与深度、底部、左部方向优先装载(Deepest bottom left with fill,DBLF)的算法。结果大小规模算例实验验证结果表明,混合遗传算法能够在合理时间内获得最优解或近似最优解。结论所提出的可变尺寸包装方案有效提高了装载率,有益于客户和物流公司。展开更多
基金supported by the Fundamental Research Funds for the Central Universities(K50511700004)the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)
文摘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.
基金supported by the National Natural Science Fundation of China (60374063)
文摘Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.
基金supported by the National Natural Science Foundation of Chinathe Civil Aviation Administration of China (U2333206).
文摘International freedom of the air(traffic rights)is a key resource for airlines to carry out international air transport business.An efficient and reasonable traffic right resource allocation within a country between airlines can affect the quality of a country’s participation in international air transport.In this paper,a multi-objective mixed-integer programming model for traffic rights resource allocation is developed to minimize passenger travel mileages and maximize the number of traffic rights resources allocated to hub airports and competitive carriers.A hybrid heuristic algorithm combining the genetic algorithm and the variable neighborhood search is devised to solve the model.The results show that the optimal allocation scheme aligns with the principle of fairness,indicating that the proposed model can play a certain guiding role in and provide an innovative perspective on traffic rights resource allocation in various countries.
文摘目的针对冷链运输中的生鲜打包及装载优化问题,提出一种允许货物以体积恒定为前提进行尺寸变化的包装装载方案,以最大化集装箱的空间利用率。方法基于上述问题,构建非线性混合整数规划模型,为了方便CPLEX或LINGO等求解器对该非线性混合整数规划模型进行求解,采用一种分段线性化方法,将该非线性模型进行线性化处理。由于所研究问题具有NP-hard属性,无论是CPLEX还是LINGO都无法有效求解大规模算例,因此设计一种有效结合遗传算法与深度、底部、左部方向优先装载(Deepest bottom left with fill,DBLF)的算法。结果大小规模算例实验验证结果表明,混合遗传算法能够在合理时间内获得最优解或近似最优解。结论所提出的可变尺寸包装方案有效提高了装载率,有益于客户和物流公司。
