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
Purpose Round beam,i.e.,with equal horizontal and vertical emittance,is preferable than a horizontally flat one for some beamline applications in Diffraction-limited storage rings(DLSRs),for the purposes of reducing t...Purpose Round beam,i.e.,with equal horizontal and vertical emittance,is preferable than a horizontally flat one for some beamline applications in Diffraction-limited storage rings(DLSRs),for the purposes of reducing the number of photons getting discarded and better phase space match between photon and electron beam.Conventional methods of obtaining round beam inescapably results in a reduction of dynamic aperture(DA).In order to recover the DA as much as possible for improving the injection efficiency,the DA optimization by using Non-dominated sorting genetic algorithm-Ⅱ(NSGA-Ⅱ)to generate round beam,particularly to one of the designed lattice of the High Energy Photon Source(HEPS)storage ring,are presented.Method According to the general unconstrained model of NSGA-Ⅱ,we modified the standard model by using parallel computing to optimize round beam lattices with errors,especially for a strong coupling,such as solenoid scheme.Results and conclusion The results of numerical tracking verify the correction of the theory framework of solenoids with fringe fields and demonstrates the feasibility on the HEPS storage ring with errors to operate in round beam mode after optimizing DA.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supported by the Guangdong Joint fund for basic and applied basic research(Guangdong-dongguan,Grant Number 2019B1515120069,2019).
文摘Purpose Round beam,i.e.,with equal horizontal and vertical emittance,is preferable than a horizontally flat one for some beamline applications in Diffraction-limited storage rings(DLSRs),for the purposes of reducing the number of photons getting discarded and better phase space match between photon and electron beam.Conventional methods of obtaining round beam inescapably results in a reduction of dynamic aperture(DA).In order to recover the DA as much as possible for improving the injection efficiency,the DA optimization by using Non-dominated sorting genetic algorithm-Ⅱ(NSGA-Ⅱ)to generate round beam,particularly to one of the designed lattice of the High Energy Photon Source(HEPS)storage ring,are presented.Method According to the general unconstrained model of NSGA-Ⅱ,we modified the standard model by using parallel computing to optimize round beam lattices with errors,especially for a strong coupling,such as solenoid scheme.Results and conclusion The results of numerical tracking verify the correction of the theory framework of solenoids with fringe fields and demonstrates the feasibility on the HEPS storage ring with errors to operate in round beam mode after optimizing DA.
