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 ...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-Ⅱis prevented from premature convergence and refine the performance of NSGA-Ⅱat each step.In the distribution problem of a distribution center in Michigan,US,the GNSGA-Ⅱis compared with NSGA-Ⅱ.As a result,the GNSGA-Ⅱis 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
The need to transport goods across countries and islands has resulted in a high demand for commercial vessels.Owing to such trends,shipyards must efficiently produce ships to reduce production costs.Layout and materia...The need to transport goods across countries and islands has resulted in a high demand for commercial vessels.Owing to such trends,shipyards must efficiently produce ships to reduce production costs.Layout and material flow are among the crucial aspects determining the efficiency of the production at a shipyard.This paper presents the initial design optimization of a shipyard layout using Nondominated Sorting Algorithm-Ⅱ(NSGA-Ⅱ)to find the optimal configuration of workstations in a shipyard layout.The proposed method focuses on simultaneously minimizing two material handling costs,namely work-based material handling and duration-based material handling.NSGA-Ⅱ determines the order of workstations in the shipyard layout.The semiflexible bay structure is then used in the workstation placement process from the sequence formed in NSGA-Ⅱ into a complete design.Considering that this study is a case of multiobjective optimization,the performance for both objectives at each iteration is presented in a 3D graph.Results indicate that after 500 iterations,the optimal configuration yields a work-based MHC of 163670.0 WBM-units and a duration-based MHC of 34750 DBM-units.Starting from a random solution,the efficiency of NSGA-Ⅱ demonstrates significant improvements,achieving a 50.19%reduction in work-based MHC and a 48.58%reduction in duration-based MHC.展开更多
Modern automated generation control(AGC)is increasingly complex,requiring precise frequency control for stability and operational accuracy.Traditional PID controller optimisation methods often struggle to handle nonli...Modern automated generation control(AGC)is increasingly complex,requiring precise frequency control for stability and operational accuracy.Traditional PID controller optimisation methods often struggle to handle nonlinearities and meet robustness requirements across diverse operational scenarios.This paper introduces an enhanced strategy using a multi-objective optimisation framework and a modified non-dominated sorting genetic algorithm Ⅱ(SNSGA).The proposed model optimises the PID controller by minimising key performance metrics:integration time squared error(ITSE),integration time absolute error(ITAE),and rate of change of deviation(J).This approach balances convergence rate,overshoot,and oscillation dynamics effectively.A fuzzy-based method is employed to select the most suitable solution from the Pareto set.The comparative analysis demonstrates that the SNSGA-based approach offers superior tuning capabilities over traditional NSGA-Ⅱ and other advanced control methods.In a two-area thermal power system without reheat,the SNSGA significantly reduces settling times for frequency deviations:2.94s for Δf_(1) and 4.98s for Δf_(2),marking improvements of 31.6%and 13.4%over NSGA-Ⅱ,respectively.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-Ⅱis prevented from premature convergence and refine the performance of NSGA-Ⅱat each step.In the distribution problem of a distribution center in Michigan,US,the GNSGA-Ⅱis compared with NSGA-Ⅱ.As a result,the GNSGA-Ⅱis 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.
基金Supported by Direktorat Riset dan Pengembangan(Directorate of Research and Development)Universitas Indonesia(NKB-690/UN2.RST/HKP.05.00/2022).
文摘The need to transport goods across countries and islands has resulted in a high demand for commercial vessels.Owing to such trends,shipyards must efficiently produce ships to reduce production costs.Layout and material flow are among the crucial aspects determining the efficiency of the production at a shipyard.This paper presents the initial design optimization of a shipyard layout using Nondominated Sorting Algorithm-Ⅱ(NSGA-Ⅱ)to find the optimal configuration of workstations in a shipyard layout.The proposed method focuses on simultaneously minimizing two material handling costs,namely work-based material handling and duration-based material handling.NSGA-Ⅱ determines the order of workstations in the shipyard layout.The semiflexible bay structure is then used in the workstation placement process from the sequence formed in NSGA-Ⅱ into a complete design.Considering that this study is a case of multiobjective optimization,the performance for both objectives at each iteration is presented in a 3D graph.Results indicate that after 500 iterations,the optimal configuration yields a work-based MHC of 163670.0 WBM-units and a duration-based MHC of 34750 DBM-units.Starting from a random solution,the efficiency of NSGA-Ⅱ demonstrates significant improvements,achieving a 50.19%reduction in work-based MHC and a 48.58%reduction in duration-based MHC.
基金supported in part by the Science and Technology Innovation Program of Hunan Province under Grant 2022RC4028in part by the National Natural Science Foundation of China under Grant 62473204+3 种基金in part by the Chunhui Program Collaborative Scientific Research Project under Grant 202202004in part by the Natural Science Foundation of Nanjing University of Posts and Telecommunications under Grants NY221082,NY222144,and NY223075in part by the Huali Program for Excellent Talents in Nanjing University of Posts and Telecommunicationsin part by the Postgraduate Research and Practice Innovation Program of Jiangsu Province under Grant KYCX24_1215.
文摘Modern automated generation control(AGC)is increasingly complex,requiring precise frequency control for stability and operational accuracy.Traditional PID controller optimisation methods often struggle to handle nonlinearities and meet robustness requirements across diverse operational scenarios.This paper introduces an enhanced strategy using a multi-objective optimisation framework and a modified non-dominated sorting genetic algorithm Ⅱ(SNSGA).The proposed model optimises the PID controller by minimising key performance metrics:integration time squared error(ITSE),integration time absolute error(ITAE),and rate of change of deviation(J).This approach balances convergence rate,overshoot,and oscillation dynamics effectively.A fuzzy-based method is employed to select the most suitable solution from the Pareto set.The comparative analysis demonstrates that the SNSGA-based approach offers superior tuning capabilities over traditional NSGA-Ⅱ and other advanced control methods.In a two-area thermal power system without reheat,the SNSGA significantly reduces settling times for frequency deviations:2.94s for Δf_(1) and 4.98s for Δf_(2),marking improvements of 31.6%and 13.4%over NSGA-Ⅱ,respectively.
