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
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
Multi-criteria decision-making(MCDM)is essential for handling complex decision problems under uncertainty,especially in fields such as criminal justice,healthcare,and environmental management.Traditional fuzzy MCDM te...Multi-criteria decision-making(MCDM)is essential for handling complex decision problems under uncertainty,especially in fields such as criminal justice,healthcare,and environmental management.Traditional fuzzy MCDM techniques have failed to deal with problems where uncertainty or vagueness is involved.To address this issue,we propose a novel framework that integrates group and overlap functions with Aczel-Alsina(AA)operational laws in the intuitionistic fuzzy set(IFS)environment.Overlap functions capture the degree to which two inputs share common features and are used to find how closely two values or criteria match in uncertain environments,while the Group functions are used to combine different expert opinions into a single collective result.This study introduces four new aggregation operators:Group Overlap function-based intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Weighted Averaging(GOF-IFAAWA)operator,intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Weighted Geometric(GOF-IFAAWG),intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)OrderedWeighted Averaging(GOF-IFAAOWA),and intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Ordered Weighted Geometric(GOF-IFAAOWG),which are rigorously defined and mathematically analyzed and offer improved flexibility in managing overlapping,uncertain,and hesitant information.The properties of these operators are discussed in detail.Further,the effectiveness,validity,activeness,and ability to capture the uncertain information,the developed operators are applied to the AI-based Criminal Justice Policy Selection problem.At last,the comparison analysis between prior and proposed studies has been displayed,and then followed by the conclusion of the result.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.
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.
基金supported by“1 Decembrie 1918”University of Alba Iulia,510009 Alba Iuliasupported in part by the HEC-NRPU project,under the grant No.14566.
文摘Multi-criteria decision-making(MCDM)is essential for handling complex decision problems under uncertainty,especially in fields such as criminal justice,healthcare,and environmental management.Traditional fuzzy MCDM techniques have failed to deal with problems where uncertainty or vagueness is involved.To address this issue,we propose a novel framework that integrates group and overlap functions with Aczel-Alsina(AA)operational laws in the intuitionistic fuzzy set(IFS)environment.Overlap functions capture the degree to which two inputs share common features and are used to find how closely two values or criteria match in uncertain environments,while the Group functions are used to combine different expert opinions into a single collective result.This study introduces four new aggregation operators:Group Overlap function-based intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Weighted Averaging(GOF-IFAAWA)operator,intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Weighted Geometric(GOF-IFAAWG),intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)OrderedWeighted Averaging(GOF-IFAAOWA),and intuitionistic fuzzy Aczel-Alsina(GOF-IFAA)Ordered Weighted Geometric(GOF-IFAAOWG),which are rigorously defined and mathematically analyzed and offer improved flexibility in managing overlapping,uncertain,and hesitant information.The properties of these operators are discussed in detail.Further,the effectiveness,validity,activeness,and ability to capture the uncertain information,the developed operators are applied to the AI-based Criminal Justice Policy Selection problem.At last,the comparison analysis between prior and proposed studies has been displayed,and then followed by the conclusion of the result.
