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
A constrained multi-objective optimization model for the low-carbon vehicle routing problem(VRP)is established.A carbon emission measurement method considering various practical factors is introduced.It minimizes both...A constrained multi-objective optimization model for the low-carbon vehicle routing problem(VRP)is established.A carbon emission measurement method considering various practical factors is introduced.It minimizes both the total carbon emissions and the longest time consumed by the sub-tours,subject to the limited number of available vehicles.According to the characteristics of the model,a region enhanced discrete multi-objective fireworks algorithm is proposed.A partial mapping explosion operator,a hybrid mutation for adjusting the sub-tours,and an objective-driven extending search are designed,which aim to improve the convergence,diversity,and spread of the non-dominated solutions produced by the algorithm,respectively.Nine low-carbon VRP instances with different scales are used to verify the effectiveness of the new strategies.Furthermore,comparison results with four state-of-the-art algorithms indicate that the proposed algorithm has better performance of convergence and distribution on the low-carbon VRP.It provides a promising scalability to the problem size.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.
基金This work was supported by the Guangdong Provincial Key Laboratory(No.2020B121201001)the National Natural Science Foundation of China(NSFC)(Nos.61502239 and 62002148)+3 种基金Natural Science Foundation of Jiangsu Province of China(No.BK20150924)the Program for Guangdong Introducing Innovative and Enterpreneurial Teams(No.2017ZT07X386)Shenzhen Science and Technology Program(No.KQTD2016112514355531)Research Institute of Trustworthy Autonomous Systems(RITAS).
文摘A constrained multi-objective optimization model for the low-carbon vehicle routing problem(VRP)is established.A carbon emission measurement method considering various practical factors is introduced.It minimizes both the total carbon emissions and the longest time consumed by the sub-tours,subject to the limited number of available vehicles.According to the characteristics of the model,a region enhanced discrete multi-objective fireworks algorithm is proposed.A partial mapping explosion operator,a hybrid mutation for adjusting the sub-tours,and an objective-driven extending search are designed,which aim to improve the convergence,diversity,and spread of the non-dominated solutions produced by the algorithm,respectively.Nine low-carbon VRP instances with different scales are used to verify the effectiveness of the new strategies.Furthermore,comparison results with four state-of-the-art algorithms indicate that the proposed algorithm has better performance of convergence and distribution on the low-carbon VRP.It provides a promising scalability to the problem size.
