Vehicle routing problem in distribution （VRPD） is a widely used type of vehicle routing problem （VRP）, which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when mode...Vehicle routing problem in distribution （VRPD） is a widely used type of vehicle routing problem （VRP）, which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm （GA）, non-dominated sorting in genetic algorithm-Ⅱ （NSGA-Ⅱ） also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ （GNSGA-Ⅱ） is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-Ⅱ is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-Ⅱ, premature convergence is better avoided and search efficiency has been improved sharply.展开更多
This paper uses the Butterfly Optimization Algorithm(BOA)with dominated sorting and crowding distance mechanisms to solve multi-objective optimization problems.There is also an improvement to the original version of B...This paper uses the Butterfly Optimization Algorithm(BOA)with dominated sorting and crowding distance mechanisms to solve multi-objective optimization problems.There is also an improvement to the original version of BOA to alleviate its drawbacks before extending it into a multi-objective version.Due to better coverage and a well-distributed Pareto front,non-dominant rankings are applied to the modified BOA using the crowding distance strategy.Seven benchmark functions and eight real-world problems have been used to test the performance of multi-objective non-dominated advanced BOA(MONSBOA),including unconstrained,constrained,and real-world design multiple-objective,highly nonlinear constraint problems.Various performance metrics,such as Generational Distance(GD),Inverted Generational Distance(IGD),Maximum Spread(MS),and Spacing(S),have been used for performance comparison.It is demonstrated that the new MONSBOA algorithm is better than the compared algorithms in more than 80%occasions in solving problems with a variety of linear,nonlinear,continuous,and discrete characteristics based on the Pareto front when compared quantitatively.From all the analysis,it may be concluded that the suggested MONSBOA is capable of producing high-quality Pareto fronts with very competitive results with rapid convergence.展开更多
In this paper,a novel location inventory routing(LIR)model is proposed to solve cold chain logistics network problem under uncertain demand environment. The goal of the developed model is to optimize costs of location...In this paper,a novel location inventory routing(LIR)model is proposed to solve cold chain logistics network problem under uncertain demand environment. The goal of the developed model is to optimize costs of location,inventory and transportation.Due to the complex of LIR problem( LIRP), a multi-objective genetic algorithm(GA), non-dominated sorting in genetic algorithm Ⅱ( NSGA-Ⅱ) has been introduced. Its performance is tested over a real case for the proposed problems. Results indicate that NSGA-Ⅱ provides a competitive performance than GA,which demonstrates that the proposed model and multi-objective GA are considerably efficient to solve the problem.展开更多
A precedence order is defined based on the release dates of jobs＇ direct successors. Using the defined precedence order and Heap Sort, a new polynomial algorithm is provided which aims to solve the parallel schedulin...A precedence order is defined based on the release dates of jobs＇ direct successors. Using the defined precedence order and Heap Sort, a new polynomial algorithm is provided which aims to solve the parallel scheduling problem P｜pj = 1, r j, outtree｜ ∑Cj Cj. The new algorithm is shown to be more compact and easier to implement.展开更多
电网停电计划的排期结果关系到电网安全稳定运行和检修工作的开展,是电网运行方式业务的重要组成。目前,已有计划排期方法缺乏对计划间存在冲突这一场景的考虑,且算法效率较低,难以满足停电计划排期的实际需求。为此,该文以工作量不均...电网停电计划的排期结果关系到电网安全稳定运行和检修工作的开展,是电网运行方式业务的重要组成。目前,已有计划排期方法缺乏对计划间存在冲突这一场景的考虑,且算法效率较低,难以满足停电计划排期的实际需求。为此,该文以工作量不均衡度、停电计划时间调整量、停电经济成本为目标,涵盖计划关联关系判别和优先级排序等过程,建立了考虑冲突的电网停电计划优化求解模型。在此基础上,通过对NSGA II算法(the second generation of non-dominated sorting genetic algorithm,NSGAII)进行性能改进,提出了基于约束的自适应NSGAII算法(constraint-basedadaptive NSGAII,CA-NSGAII),并将其用于模型求解。最后,在IEEE-300输电系统模型中模拟了月停电计划排期过程,验证了该文所提模型与实际情况更为贴近,所提求解算法更加准确高效。展开更多
基金supported by National Natural Science Foundation of China (No.60474059)Hi-tech Research and Development Program of China (863 Program,No.2006AA04Z160).
文摘Vehicle routing problem in distribution （VRPD） is a widely used type of vehicle routing problem （VRP）, which has been proved as NP-Hard, and it is usually modeled as single objective optimization problem when modeling. For multi-objective optimization model, most researches consider two objectives. A multi-objective mathematical model for VRP is proposed, which considers the number of vehicles used, the length of route and the time arrived at each client. Genetic algorithm is one of the most widely used algorithms to solve VRP. As a type of genetic algorithm （GA）, non-dominated sorting in genetic algorithm-Ⅱ （NSGA-Ⅱ） also suffers from premature convergence and enclosure competition. In order to avoid these kinds of shortage, a greedy NSGA-Ⅱ （GNSGA-Ⅱ） is proposed for VRP problem. Greedy algorithm is implemented in generating the initial population, cross-over and mutation. All these procedures ensure that NSGA-Ⅱ is prevented from premature convergence and refine the performance of NSGA-Ⅱ at each step. In the distribution problem of a distribution center in Michigan, US, the GNSGA-Ⅱ is compared with NSGA-Ⅱ. As a result, the GNSGA-Ⅱ is the most efficient one and can get the most optimized solution to VRP problem. Also, in GNSGA-Ⅱ, premature convergence is better avoided and search efficiency has been improved sharply.
文摘This paper uses the Butterfly Optimization Algorithm(BOA)with dominated sorting and crowding distance mechanisms to solve multi-objective optimization problems.There is also an improvement to the original version of BOA to alleviate its drawbacks before extending it into a multi-objective version.Due to better coverage and a well-distributed Pareto front,non-dominant rankings are applied to the modified BOA using the crowding distance strategy.Seven benchmark functions and eight real-world problems have been used to test the performance of multi-objective non-dominated advanced BOA(MONSBOA),including unconstrained,constrained,and real-world design multiple-objective,highly nonlinear constraint problems.Various performance metrics,such as Generational Distance(GD),Inverted Generational Distance(IGD),Maximum Spread(MS),and Spacing(S),have been used for performance comparison.It is demonstrated that the new MONSBOA algorithm is better than the compared algorithms in more than 80%occasions in solving problems with a variety of linear,nonlinear,continuous,and discrete characteristics based on the Pareto front when compared quantitatively.From all the analysis,it may be concluded that the suggested MONSBOA is capable of producing high-quality Pareto fronts with very competitive results with rapid convergence.
基金Natural Science Foundation of Shanghai,China(No.15ZR1401600)the Fundamental Research Funds for the Central Universities,China(No.CUSF-DH-D-2015096)
文摘In this paper,a novel location inventory routing(LIR)model is proposed to solve cold chain logistics network problem under uncertain demand environment. The goal of the developed model is to optimize costs of location,inventory and transportation.Due to the complex of LIR problem( LIRP), a multi-objective genetic algorithm(GA), non-dominated sorting in genetic algorithm Ⅱ( NSGA-Ⅱ) has been introduced. Its performance is tested over a real case for the proposed problems. Results indicate that NSGA-Ⅱ provides a competitive performance than GA,which demonstrates that the proposed model and multi-objective GA are considerably efficient to solve the problem.
基金This work was supported by the National Natural Science Foundation of China(No.60474023)Science and Technology Key Project Fund of theMinistry of Education(No.03184)the Major State Basic Research Development Program of China(No.2002CB312200).
文摘A precedence order is defined based on the release dates of jobs＇ direct successors. Using the defined precedence order and Heap Sort, a new polynomial algorithm is provided which aims to solve the parallel scheduling problem P｜pj = 1, r j, outtree｜ ∑Cj Cj. The new algorithm is shown to be more compact and easier to implement.
文摘电网停电计划的排期结果关系到电网安全稳定运行和检修工作的开展,是电网运行方式业务的重要组成。目前,已有计划排期方法缺乏对计划间存在冲突这一场景的考虑,且算法效率较低,难以满足停电计划排期的实际需求。为此,该文以工作量不均衡度、停电计划时间调整量、停电经济成本为目标,涵盖计划关联关系判别和优先级排序等过程,建立了考虑冲突的电网停电计划优化求解模型。在此基础上,通过对NSGA II算法(the second generation of non-dominated sorting genetic algorithm,NSGAII)进行性能改进,提出了基于约束的自适应NSGAII算法(constraint-basedadaptive NSGAII,CA-NSGAII),并将其用于模型求解。最后,在IEEE-300输电系统模型中模拟了月停电计划排期过程,验证了该文所提模型与实际情况更为贴近,所提求解算法更加准确高效。
