As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in mult...As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in multi-trip and multi-drop(VRP-mmD).The problem aims at making schedules for the trucks and drones such that the total travel time is minimized.This paper formulate the problem with a mixed integer program-ming model and propose a two-phase algorithm,i.e.,a parallel route construction heuristic(PRCH)for the first phase and an adaptive neighbor searching heuristic(ANSH)for the second phase.The PRCH generates an initial solution by con-currently assigning as many nodes as possible to the truck–drone pair to progressively reduce the waiting time at the rendezvous node in the first phase.Then the ANSH improves the initial solution by adaptively exploring the neighborhoods in the second phase.Numerical tests on some benchmark data are conducted to verify the performance of the algorithm.The results show that the proposed algorithm can found better solu-tions than some state-of-the-art methods for all instances.More-over,an extensive analysis highlights the stability of the pro-posed algorithm.展开更多
This paper proposed an enhanced NEH with full insertion moves to solve the permutation flow shop problem.The characteristics of the original NEH are investigated and analyzed,and it is concluded that the given method ...This paper proposed an enhanced NEH with full insertion moves to solve the permutation flow shop problem.The characteristics of the original NEH are investigated and analyzed,and it is concluded that the given method would be promising to find better solutions,while the cost would be increased.Fast makespan calculating method and eliminating non-promising permutation policy are introduced to reduce the evaluation effort.The former decreases the time complexity from O(n4m) to O(n3m),which is an acceptable cost for medium and small size instances considering the obtained solution quality.The results from computational experience show that the latter also can eliminate a lot of non-promising solutions.展开更多
This study deals with the Permutation Flow Shop Scheduling Problem （PFSP） based on the maximum completion time （makespan）. NEH （ the algorithm of Nawaz, Eascore and Ham） is the concluded most efficient construct...This study deals with the Permutation Flow Shop Scheduling Problem （PFSP） based on the maximum completion time （makespan）. NEH （ the algorithm of Nawaz, Eascore and Ham） is the concluded most efficient constructive method in solving this NP-hard problem. The principal features of its strengths are the initial arrangement of jobs and the job insertion phase. In some instances, ties will occur in both the initial permutation and the partial sequences. The problem of ties breaking may have a significant impact on the NEH performance, but evaluate all the ties will be non-polynomial in the worst case. Several kinds of methods are presented in the paper to break the ties in a quick time. Together with the basic one, all 22 methods are tested on the famous Taillard＇s benchmarks and the most suitable ties breaking policy is recommended.展开更多
For the car sequencing（CS） problem, the draw-backs of the ＂sliding windows＂ technique used in the objective function have not been rectified, and no high quality initial solution has been acquired to accelerate th...For the car sequencing（CS） problem, the draw-backs of the ＂sliding windows＂ technique used in the objective function have not been rectified, and no high quality initial solution has been acquired to accelerate the improvement of the solution quality. Firstly, the objective function is improved to solve the double and bias counting of violations broadly discussed. Then, a new method combining heuristic with constraint propagation is proposed which constructs initial solutions under a parallel framework. Based on constraint propagation, three filtering rules are designed to intersecting with three greedy functions, so the variable domain is narrowed in the process of the construction. The parallel framework is served to show its robustness in terms of the quality of the solution since it greatly increases the performance of obtaining the best solution. In the computational experiments, 109 instances of 3 sets from the CSPLib＇ s benchmarks are used to test the performance of the proposed method. Experiment results show that the proposed method outperforms others in acquiring the best-known results for 85 best-known results of 109 are obtained with only one construction. The proposed research provides an avenue to remedy the deficiencies of ＂sliding windows＂ technique and construct high quality initial solutions.展开更多
文摘As commercial drone delivery becomes increasingly popular,the extension of the vehicle routing problem with drones(VRPD)is emerging as an optimization problem of inter-ests.This paper studies a variant of VRPD in multi-trip and multi-drop(VRP-mmD).The problem aims at making schedules for the trucks and drones such that the total travel time is minimized.This paper formulate the problem with a mixed integer program-ming model and propose a two-phase algorithm,i.e.,a parallel route construction heuristic(PRCH)for the first phase and an adaptive neighbor searching heuristic(ANSH)for the second phase.The PRCH generates an initial solution by con-currently assigning as many nodes as possible to the truck–drone pair to progressively reduce the waiting time at the rendezvous node in the first phase.Then the ANSH improves the initial solution by adaptively exploring the neighborhoods in the second phase.Numerical tests on some benchmark data are conducted to verify the performance of the algorithm.The results show that the proposed algorithm can found better solu-tions than some state-of-the-art methods for all instances.More-over,an extensive analysis highlights the stability of the pro-posed algorithm.
基金New Century Excellent Talents in University (No.NCET04-0383)Science and Technology Phosphor Program of Shanghai (No.04QMH1405)
文摘This paper proposed an enhanced NEH with full insertion moves to solve the permutation flow shop problem.The characteristics of the original NEH are investigated and analyzed,and it is concluded that the given method would be promising to find better solutions,while the cost would be increased.Fast makespan calculating method and eliminating non-promising permutation policy are introduced to reduce the evaluation effort.The former decreases the time complexity from O(n4m) to O(n3m),which is an acceptable cost for medium and small size instances considering the obtained solution quality.The results from computational experience show that the latter also can eliminate a lot of non-promising solutions.
基金Programfor New Century Excellent Talents in University,China(NO.NCET04-0383)Science and Technology Phosphor Program of Shanghai,China(NO.04QMH1405)
文摘This study deals with the Permutation Flow Shop Scheduling Problem （PFSP） based on the maximum completion time （makespan）. NEH （ the algorithm of Nawaz, Eascore and Ham） is the concluded most efficient constructive method in solving this NP-hard problem. The principal features of its strengths are the initial arrangement of jobs and the job insertion phase. In some instances, ties will occur in both the initial permutation and the partial sequences. The problem of ties breaking may have a significant impact on the NEH performance, but evaluate all the ties will be non-polynomial in the worst case. Several kinds of methods are presented in the paper to break the ties in a quick time. Together with the basic one, all 22 methods are tested on the famous Taillard＇s benchmarks and the most suitable ties breaking policy is recommended.
基金Supported by National Natural Science Foundation of China(Grant Nos.51435009,71302085)Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ14E080002)K.C.Wong Magna Fund in Ningbo University
文摘For the car sequencing（CS） problem, the draw-backs of the ＂sliding windows＂ technique used in the objective function have not been rectified, and no high quality initial solution has been acquired to accelerate the improvement of the solution quality. Firstly, the objective function is improved to solve the double and bias counting of violations broadly discussed. Then, a new method combining heuristic with constraint propagation is proposed which constructs initial solutions under a parallel framework. Based on constraint propagation, three filtering rules are designed to intersecting with three greedy functions, so the variable domain is narrowed in the process of the construction. The parallel framework is served to show its robustness in terms of the quality of the solution since it greatly increases the performance of obtaining the best solution. In the computational experiments, 109 instances of 3 sets from the CSPLib＇ s benchmarks are used to test the performance of the proposed method. Experiment results show that the proposed method outperforms others in acquiring the best-known results for 85 best-known results of 109 are obtained with only one construction. The proposed research provides an avenue to remedy the deficiencies of ＂sliding windows＂ technique and construct high quality initial solutions.
