Ant colony optimization （ACO） is a new heuristic algo- rithm which has been proven a successful technique and applied to a number of combinatorial optimization problems. The traveling salesman problem （TSP） is amo...Ant colony optimization （ACO） is a new heuristic algo- rithm which has been proven a successful technique and applied to a number of combinatorial optimization problems. The traveling salesman problem （TSP） is among the most important combinato- rial problems. An ACO algorithm based on scout characteristic is proposed for solving the stagnation behavior and premature con- vergence problem of the basic ACO algorithm on TSP. The main idea is to partition artificial ants into two groups： scout ants and common ants. The common ants work according to the search manner of basic ant colony algorithm, but scout ants have some differences from common ants, they calculate each route＇s muta- tion probability of the current optimal solution using path evaluation model and search around the optimal solution according to the mutation probability. Simulation on TSP shows that the improved algorithm has high efficiency and robustness.展开更多
A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems....A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.展开更多
This paper considers a project scheduling problem with the objective of minimizing resource availability costs appealed to finish al activities before the deadline. There are finish-start type precedence relations amo...This paper considers a project scheduling problem with the objective of minimizing resource availability costs appealed to finish al activities before the deadline. There are finish-start type precedence relations among the activities which require some kinds of renewable resources. We predigest the process of sol-ving the resource availability cost problem （RACP） by using start time of each activity to code the schedule. Then, a novel heuris-tic algorithm is proposed to make the process of looking for the best solution efficiently. And then pseudo particle swarm optimiza-tion （PPSO） combined with PSO and path relinking procedure is presented to solve the RACP. Final y, comparative computational experiments are designed and the computational results show that the proposed method is very effective to solve RACP.展开更多
The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the pro...The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.展开更多
A novel hybrid algorithm named ABC-BBO, which integrates artificial bee colony(ABC) algorithm with biogeography-based optimization(BBO) algorithm, is proposed to solve constrained mechanical design problems. ABC-BBO c...A novel hybrid algorithm named ABC-BBO, which integrates artificial bee colony(ABC) algorithm with biogeography-based optimization(BBO) algorithm, is proposed to solve constrained mechanical design problems. ABC-BBO combined the exploration of ABC algorithm with the exploitation of BBO algorithm effectively, and hence it can generate the promising candidate individuals. The proposed hybrid algorithm speeds up the convergence and improves the algorithm's performance. Several benchmark test functions and mechanical design problems are applied to verifying the effects of these improvements and it is demonstrated that the performance of this proposed ABC-BBO is superior to or at least highly competitive with other population-based optimization approaches.展开更多
As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimizat...As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.展开更多
As a typical representative of the NP-complete problem, the traveling salesman problem(TSP) is widely utilized in computer networks, logistics distribution, and other fields. In this paper, a discrete lion swarm optim...As a typical representative of the NP-complete problem, the traveling salesman problem(TSP) is widely utilized in computer networks, logistics distribution, and other fields. In this paper, a discrete lion swarm optimization(DLSO) algorithm is proposed to solve the TSP. Firstly, we introduce discrete coding and order crossover operators in DLSO. Secondly, we use the complete 2-opt(C2-opt) algorithm to enhance the local search ability.Then in order to enhance the efficiency of the algorithm, a parallel discrete lion swarm optimization(PDLSO) algorithm is proposed.The PDLSO has multiple populations, and each sub-population independently runs the DLSO algorithm in parallel. We use the ring topology to transfer information between sub-populations. Experiments on some benchmarks TSP problems show that the DLSO algorithm has a better accuracy than other algorithms, and the PDLSO algorithm can effectively shorten the running time.展开更多
A new meta-heuristic method is proposed to enhance current meta-heuristic methods for global optimization and test scheduling for three-dimensional （3D） stacked system-on-chip （SoC） by hybridizing grey wolf optimi...A new meta-heuristic method is proposed to enhance current meta-heuristic methods for global optimization and test scheduling for three-dimensional （3D） stacked system-on-chip （SoC） by hybridizing grey wolf optimization with differential evo- lution （HGWO）. Because basic grey wolf optimization （GWO） is easy to fall into stagnation when it carries out the operation of at- tacking prey, and differential evolution （DE） is integrated into GWO to update the previous best position of grey wolf Alpha, Beta and Delta, in order to force GWO to jump out of the stagnation with DE＇s strong searching ability. The proposed algorithm can accele- rate the convergence speed of GWO and improve its performance. Twenty-three well-known benchmark functions and an NP hard problem of test scheduling for 3D SoC are employed to verify the performance of the proposed algorithm. Experimental results show the superior performance of the proposed algorithm for exploiting the optimum and it has advantages in terms of exploration.展开更多
Constrained optimization problems are very important as they are encountered in many science and engineering applications.As a novel evolutionary computation technique,cuckoo search(CS) algorithm has attracted much at...Constrained optimization problems are very important as they are encountered in many science and engineering applications.As a novel evolutionary computation technique,cuckoo search(CS) algorithm has attracted much attention and wide applications,owing to its easy implementation and quick convergence.A hybrid cuckoo pattern search algorithm(HCPS) with feasibility-based rule is proposed for solving constrained numerical and engineering design optimization problems.This algorithm can combine the stochastic exploration of the cuckoo search algorithm and the exploitation capability of the pattern search method.Simulation and comparisons based on several well-known benchmark test functions and structural design optimization problems demonstrate the effectiveness,efficiency and robustness of the proposed HCPS algorithm.展开更多
The route optimization problem for road networks was applied to pedestrian flow.Evacuation path networks with nodes and arcs considering the traffic capacities of facilities were built in metro hubs,and a path impedan...The route optimization problem for road networks was applied to pedestrian flow.Evacuation path networks with nodes and arcs considering the traffic capacities of facilities were built in metro hubs,and a path impedance function for metro hubs which used the relationships among circulation speed,density and flow rate for pedestrians was defined.Then,a route optimization model which minimizes the movement time of the last evacuee was constructed to optimize evacuation performance.Solutions to the proposed mathematical model were obtained through an iterative optimization process.The route optimization model was applied to Xidan Station of Beijing Metro Line 4 based on the actual situations,and the calculation results of the model were tested using buildingExodus microscopic evacuation simulation software.The simulation result shows that the proposed model shortens the evacuation time by 16.05%,3.15% and 2.78% compared with all or none method,equally split method and Logit model,respectively.Furthermore,when the population gets larger,evacuation efficiency in the proposed model has a greater advantage.展开更多
As far as the weight digraph is considered, based on the table instead of the weightdigraph, an optimal spanning tree method called the Table Operations Method (TOM) is proposed.And the optimality is proved and a nume...As far as the weight digraph is considered, based on the table instead of the weightdigraph, an optimal spanning tree method called the Table Operations Method (TOM) is proposed.And the optimality is proved and a numerical example is demonstrated.展开更多
A new efficient coupling relationship description method has been developed to provide an automated and visualized way to multidisciplinary design optimization (MDO) modeling and solving. The disciplinary relation mat...A new efficient coupling relationship description method has been developed to provide an automated and visualized way to multidisciplinary design optimization (MDO) modeling and solving. The disciplinary relation matrix (DRM) is proposed to describe the coupling relationship according to disciplinary input/output variables, and the MDO definition has been reformulated to adopt the new interfaces. Based on these, a universal MDO solving procedure is proposed to establish an automated and efficient way for MDO modeling and solving. Through a simple and convenient initial configuration, MDO problems can be solved using any of available MDO architectures with no further effort. Several examples are used to verify the proposed MDO modeling and solving process. Result shows that the DRM method has the ability to simplify and automate the MDO procedure, and the related MDO framework can evaluate the MDO problem automatically and efficiently.展开更多
This paper establishes a mathematical model of the reliability optimization design for the safe-arming system of an air-faced missile, and presents a solving method for the model. The computational results provide a v...This paper establishes a mathematical model of the reliability optimization design for the safe-arming system of an air-faced missile, and presents a solving method for the model. The computational results provide a valuable reference for the reliability design for the safe-arming system of an air-faced missile.展开更多
The vehicle routing problem (VRP) can be described as the problem of designing the optimal delivery or collection routes from one or several depots to a number of geographically scattered customers, subject to load co...The vehicle routing problem (VRP) can be described as the problem of designing the optimal delivery or collection routes from one or several depots to a number of geographically scattered customers, subject to load constraints. The routing decision involves determining which of the demand s will be satisfied by each vehicle and what route each vehicle will follow in s erving its assigned demand in order to minimize total delivery cost. In this pap er, a methodology for the design of VRP by integrating optimization and simulate d annealing (SA) approach is presented hierarchically. To express the problem of vehicle routing, a new mathematical formulation is first conducted. The objecti ve function involves both the delivery cost and the vehicle acquisition cost wit h load constraints. A heuristic is then proposed to solve this problem by using SA procedure in conjunction with any solution procedure of travelling salesman p roblem (TSP). The initial configuration is arranged as one vehicle route ser ving one customer. The SA searching procedure is then developed to combine custo mer to any one of the vehicle routes existed in the system if the capacity and c ost are attractive. An important concept of this proposed heuristic is that it attempts to minimize total number of vehicle required in the system on the b asis of the fixed cost and the variable cost view points. In addition, this appr oach can be easily adapted to accommodate many additional problem complexities.展开更多
针对消防设施选址问题,构建考虑时效性、市民等待救援的焦急心理和建设成本的三目标消防设施选址模型,以实现更科学的消防设施布局。鉴于该问题的NP难特性,提出基于算子学习的多目标深度强化学习模型(multi-objective deep reinforcemen...针对消防设施选址问题,构建考虑时效性、市民等待救援的焦急心理和建设成本的三目标消防设施选址模型,以实现更科学的消防设施布局。鉴于该问题的NP难特性,提出基于算子学习的多目标深度强化学习模型(multi-objective deep reinforcement learning,MDRL)。设计多种优化算子作为强化学习的动作空间,训练策略网络以选择最佳优化算子来改进解决方案。针对多目标问题,设计基于优势差异的方法(MDRL-AD)和基于支配性评估的方法(MDRL-DE)。采用四种规模的测试算例及实际案例进行数值实验,将MDRL和改进的NSGA-Ⅱ、MOPSO、L2I算法进行比较,并利用Hypervolume指标、Spacing指标、Ω指标、IGD指标对算法性能进行评估。实验结果表明,MDRL-AD方法更适用于求解小规模算例,MDRL-DE方法则在求解大规模和超大规模算例时相比其他算法优势明显。MDRL在非劣解集的收敛性和均匀性方面明显优于其他对比算法,为消防设施布局规划提供了一种有竞争力的解决方案。展开更多
在经典车辆路径问题(vehicle routing problem,VRP)的基础上增加了客户要求访问的时间窗约束,以车辆行驶路径最短和使用车辆数最小为目标,建立了不确定车辆数的多约束车辆路径问题(multi-constraint vehicle routing problem with varia...在经典车辆路径问题(vehicle routing problem,VRP)的基础上增加了客户要求访问的时间窗约束,以车辆行驶路径最短和使用车辆数最小为目标,建立了不确定车辆数的多约束车辆路径问题(multi-constraint vehicle routing problem with variable fleets,MVRP-VF)的数学模型。引入遗传算法的交叉操作以及大规模邻域搜索算法中的破坏算子和修复算子,重新定义了基本灰狼优化算法(grey wolf optimizer,GWO)的操作算子,优化了GWO的寻优机制,从而设计出用于求解MVRP-VF问题的混合灰狼优化算法(hybrid grey wolf optimizer,HGWO)。通过仿真实验与其他参考文献中的算法求解结果进行比较,验证了HGWO求解该类问题的有效性与可行性。展开更多
基金supported by the National Natural Science Foundation of China(60573159)
文摘Ant colony optimization （ACO） is a new heuristic algo- rithm which has been proven a successful technique and applied to a number of combinatorial optimization problems. The traveling salesman problem （TSP） is among the most important combinato- rial problems. An ACO algorithm based on scout characteristic is proposed for solving the stagnation behavior and premature con- vergence problem of the basic ACO algorithm on TSP. The main idea is to partition artificial ants into two groups： scout ants and common ants. The common ants work according to the search manner of basic ant colony algorithm, but scout ants have some differences from common ants, they calculate each route＇s muta- tion probability of the current optimal solution using path evaluation model and search around the optimal solution according to the mutation probability. Simulation on TSP shows that the improved algorithm has high efficiency and robustness.
基金Projects(50275150,61173052) supported by the National Natural Science Foundation of ChinaProject(14FJ3112) supported by the Planned Science and Technology of Hunan Province,ChinaProject(14B033) supported by Scientific Research Fund Education Department of Hunan Province,China
文摘A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.
基金supported by the National Natural Science Foundation of China(7120116671201170)
文摘This paper considers a project scheduling problem with the objective of minimizing resource availability costs appealed to finish al activities before the deadline. There are finish-start type precedence relations among the activities which require some kinds of renewable resources. We predigest the process of sol-ving the resource availability cost problem （RACP） by using start time of each activity to code the schedule. Then, a novel heuris-tic algorithm is proposed to make the process of looking for the best solution efficiently. And then pseudo particle swarm optimiza-tion （PPSO） combined with PSO and path relinking procedure is presented to solve the RACP. Final y, comparative computational experiments are designed and the computational results show that the proposed method is very effective to solve RACP.
文摘The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.
基金Projects(61463009,11264005,11361014)supported by the National Natural Science Foundation of ChinaProject([2013]2082)supported by the Science Technology Foundation of Guizhou Province,China
文摘A novel hybrid algorithm named ABC-BBO, which integrates artificial bee colony(ABC) algorithm with biogeography-based optimization(BBO) algorithm, is proposed to solve constrained mechanical design problems. ABC-BBO combined the exploration of ABC algorithm with the exploitation of BBO algorithm effectively, and hence it can generate the promising candidate individuals. The proposed hybrid algorithm speeds up the convergence and improves the algorithm's performance. Several benchmark test functions and mechanical design problems are applied to verifying the effects of these improvements and it is demonstrated that the performance of this proposed ABC-BBO is superior to or at least highly competitive with other population-based optimization approaches.
基金supported by the National Natural Science Foundation of China(60873099)the Fundamental Research Funds for the Central Universities(2011QNA29)
文摘As a new-style stochastic algorithm, the electromagnetism-like mechanism（EM） method gains more and more attention from many researchers in recent years. A novel model based on EM（NMEM） for multiobjective optimization problems is proposed, which regards the charge of all particles as the constraints in the current population and the measure of the uniformity of non-dominated solutions as the objective function. The charge of the particle is evaluated based on the dominated concept, and its magnitude determines the direction of a force between two particles. Numerical studies are carried out on six complex test functions and the experimental results demonstrate that the proposed NMEM algorithm is a very robust method for solving the multiobjective optimization problems.
基金supported by the National Natural Science Foundation of China(61771293)the Key Project of Shangdong Province(2019JZZY010111)。
文摘As a typical representative of the NP-complete problem, the traveling salesman problem(TSP) is widely utilized in computer networks, logistics distribution, and other fields. In this paper, a discrete lion swarm optimization(DLSO) algorithm is proposed to solve the TSP. Firstly, we introduce discrete coding and order crossover operators in DLSO. Secondly, we use the complete 2-opt(C2-opt) algorithm to enhance the local search ability.Then in order to enhance the efficiency of the algorithm, a parallel discrete lion swarm optimization(PDLSO) algorithm is proposed.The PDLSO has multiple populations, and each sub-population independently runs the DLSO algorithm in parallel. We use the ring topology to transfer information between sub-populations. Experiments on some benchmarks TSP problems show that the DLSO algorithm has a better accuracy than other algorithms, and the PDLSO algorithm can effectively shorten the running time.
基金supported by the National Natural Science Foundation of China(6076600161105004)+1 种基金the Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ14110)the Program for Innovative Research Team of Guilin University of Electronic Technology(IRTGUET)
文摘A new meta-heuristic method is proposed to enhance current meta-heuristic methods for global optimization and test scheduling for three-dimensional （3D） stacked system-on-chip （SoC） by hybridizing grey wolf optimization with differential evo- lution （HGWO）. Because basic grey wolf optimization （GWO） is easy to fall into stagnation when it carries out the operation of at- tacking prey, and differential evolution （DE） is integrated into GWO to update the previous best position of grey wolf Alpha, Beta and Delta, in order to force GWO to jump out of the stagnation with DE＇s strong searching ability. The proposed algorithm can accele- rate the convergence speed of GWO and improve its performance. Twenty-three well-known benchmark functions and an NP hard problem of test scheduling for 3D SoC are employed to verify the performance of the proposed algorithm. Experimental results show the superior performance of the proposed algorithm for exploiting the optimum and it has advantages in terms of exploration.
基金Projects([2013]2082,[2009]2061)supported by the Science Technology Foundation of Guizhou Province,ChinaProject([2013]140)supported by the Excellent Science Technology Innovation Talents in Universities of Guizhou Province,ChinaProject(2008040)supported by the Natural Science Research in Education Department of Guizhou Province,China
文摘Constrained optimization problems are very important as they are encountered in many science and engineering applications.As a novel evolutionary computation technique,cuckoo search(CS) algorithm has attracted much attention and wide applications,owing to its easy implementation and quick convergence.A hybrid cuckoo pattern search algorithm(HCPS) with feasibility-based rule is proposed for solving constrained numerical and engineering design optimization problems.This algorithm can combine the stochastic exploration of the cuckoo search algorithm and the exploitation capability of the pattern search method.Simulation and comparisons based on several well-known benchmark test functions and structural design optimization problems demonstrate the effectiveness,efficiency and robustness of the proposed HCPS algorithm.
基金Project(51078086)supported by the National Natural Science Foundation of China
文摘The route optimization problem for road networks was applied to pedestrian flow.Evacuation path networks with nodes and arcs considering the traffic capacities of facilities were built in metro hubs,and a path impedance function for metro hubs which used the relationships among circulation speed,density and flow rate for pedestrians was defined.Then,a route optimization model which minimizes the movement time of the last evacuee was constructed to optimize evacuation performance.Solutions to the proposed mathematical model were obtained through an iterative optimization process.The route optimization model was applied to Xidan Station of Beijing Metro Line 4 based on the actual situations,and the calculation results of the model were tested using buildingExodus microscopic evacuation simulation software.The simulation result shows that the proposed model shortens the evacuation time by 16.05%,3.15% and 2.78% compared with all or none method,equally split method and Logit model,respectively.Furthermore,when the population gets larger,evacuation efficiency in the proposed model has a greater advantage.
文摘As far as the weight digraph is considered, based on the table instead of the weightdigraph, an optimal spanning tree method called the Table Operations Method (TOM) is proposed.And the optimality is proved and a numerical example is demonstrated.
基金supported by the National Natural Science Foundation of China(51505385)Shanghai Aerospace Science and Technology Innovation Foundation(SAST2015010)the Defense Basic Research Program(JCKY2016204B102)
文摘A new efficient coupling relationship description method has been developed to provide an automated and visualized way to multidisciplinary design optimization (MDO) modeling and solving. The disciplinary relation matrix (DRM) is proposed to describe the coupling relationship according to disciplinary input/output variables, and the MDO definition has been reformulated to adopt the new interfaces. Based on these, a universal MDO solving procedure is proposed to establish an automated and efficient way for MDO modeling and solving. Through a simple and convenient initial configuration, MDO problems can be solved using any of available MDO architectures with no further effort. Several examples are used to verify the proposed MDO modeling and solving process. Result shows that the DRM method has the ability to simplify and automate the MDO procedure, and the related MDO framework can evaluate the MDO problem automatically and efficiently.
文摘This paper establishes a mathematical model of the reliability optimization design for the safe-arming system of an air-faced missile, and presents a solving method for the model. The computational results provide a valuable reference for the reliability design for the safe-arming system of an air-faced missile.
文摘The vehicle routing problem (VRP) can be described as the problem of designing the optimal delivery or collection routes from one or several depots to a number of geographically scattered customers, subject to load constraints. The routing decision involves determining which of the demand s will be satisfied by each vehicle and what route each vehicle will follow in s erving its assigned demand in order to minimize total delivery cost. In this pap er, a methodology for the design of VRP by integrating optimization and simulate d annealing (SA) approach is presented hierarchically. To express the problem of vehicle routing, a new mathematical formulation is first conducted. The objecti ve function involves both the delivery cost and the vehicle acquisition cost wit h load constraints. A heuristic is then proposed to solve this problem by using SA procedure in conjunction with any solution procedure of travelling salesman p roblem (TSP). The initial configuration is arranged as one vehicle route ser ving one customer. The SA searching procedure is then developed to combine custo mer to any one of the vehicle routes existed in the system if the capacity and c ost are attractive. An important concept of this proposed heuristic is that it attempts to minimize total number of vehicle required in the system on the b asis of the fixed cost and the variable cost view points. In addition, this appr oach can be easily adapted to accommodate many additional problem complexities.
文摘针对消防设施选址问题,构建考虑时效性、市民等待救援的焦急心理和建设成本的三目标消防设施选址模型,以实现更科学的消防设施布局。鉴于该问题的NP难特性,提出基于算子学习的多目标深度强化学习模型(multi-objective deep reinforcement learning,MDRL)。设计多种优化算子作为强化学习的动作空间,训练策略网络以选择最佳优化算子来改进解决方案。针对多目标问题,设计基于优势差异的方法(MDRL-AD)和基于支配性评估的方法(MDRL-DE)。采用四种规模的测试算例及实际案例进行数值实验,将MDRL和改进的NSGA-Ⅱ、MOPSO、L2I算法进行比较,并利用Hypervolume指标、Spacing指标、Ω指标、IGD指标对算法性能进行评估。实验结果表明,MDRL-AD方法更适用于求解小规模算例,MDRL-DE方法则在求解大规模和超大规模算例时相比其他算法优势明显。MDRL在非劣解集的收敛性和均匀性方面明显优于其他对比算法,为消防设施布局规划提供了一种有竞争力的解决方案。
文摘在经典车辆路径问题(vehicle routing problem,VRP)的基础上增加了客户要求访问的时间窗约束,以车辆行驶路径最短和使用车辆数最小为目标,建立了不确定车辆数的多约束车辆路径问题(multi-constraint vehicle routing problem with variable fleets,MVRP-VF)的数学模型。引入遗传算法的交叉操作以及大规模邻域搜索算法中的破坏算子和修复算子,重新定义了基本灰狼优化算法(grey wolf optimizer,GWO)的操作算子,优化了GWO的寻优机制,从而设计出用于求解MVRP-VF问题的混合灰狼优化算法(hybrid grey wolf optimizer,HGWO)。通过仿真实验与其他参考文献中的算法求解结果进行比较,验证了HGWO求解该类问题的有效性与可行性。
