The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worke...The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.展开更多
In this article, we focus to study about modified objective function approach for multiobjective optimization problem with vanishing constraints. An equivalent η-approximated multiobjective optimization problem is co...In this article, we focus to study about modified objective function approach for multiobjective optimization problem with vanishing constraints. An equivalent η-approximated multiobjective optimization problem is constructed by a modification of the objective function in the original considered optimization problem. Furthermore, we discuss saddle point criteria for the aforesaid problem. Moreover, we present some examples to verify the established results.展开更多
A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which i...A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.展开更多
Some remarks are made on the use of the Abadie constraint qualification, the Guignard constraint qualifications and the Guignard regularity condition in obtaining weak and strong Kuhn-Tucker type optimality conditions...Some remarks are made on the use of the Abadie constraint qualification, the Guignard constraint qualifications and the Guignard regularity condition in obtaining weak and strong Kuhn-Tucker type optimality conditions in differentiable vector optimization problems.展开更多
We consider a linear-quadratical optimal control problem of a system governed by parabolic equation with distributed in right-hand side control and control and state constraints. We construct a mesh approximation of t...We consider a linear-quadratical optimal control problem of a system governed by parabolic equation with distributed in right-hand side control and control and state constraints. We construct a mesh approximation of this problem using different two-level approximations of the state equation, ADI and fractional steps approximations in time among others. Iterative solution methods are investigated for all constructed approximations of the optimal control problem. Their implementation can be carried out in parallel manner.展开更多
A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good...A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good performance. The computation results show that its generality, precision, robustness, simplicity and performance are all satisfactory.展开更多
An improved genetic algorithm(IGA) based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector w...An improved genetic algorithm(IGA) based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals' feature vector.Additionally,a local search(LS) process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.展开更多
In order to improve the distribution and convergence of constrained optimization algorithms,this paper proposes a constrained optimization algorithm based on double populations. Firstly the feasible solutions and infe...In order to improve the distribution and convergence of constrained optimization algorithms,this paper proposes a constrained optimization algorithm based on double populations. Firstly the feasible solutions and infeasible solutions are stored separately through two populations,which can avoid direct comparison between them. The usage of efficient information carried by the infeasible solutions will enlarge exploitation scope and strength diversity of populations. At the same time,adopting the presented concept of constraints domination to update the infeasible set may keep good variety of population and give consideration to convergence. Also the improved mutation operation is employed to further raise the diversity and convergence.The suggested algorithm is compared with 3 state- of- the- art constrained optimization algorithms on standard test problems g01- g13. Simulation results show that the presented algorithm has certain advantages than other algorithms because it can ensure good convergence accuracy while it has good robustness.展开更多
This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations. The maximum principle and some kind of approxima...This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations. The maximum principle and some kind of approximate controllability are studied.展开更多
The concept of vector optimization problems with equilibrium constraints (VOPEC) is introduced. By using the continuity results of the approximate solution set to the equilibrium problem, we obtain the same results of...The concept of vector optimization problems with equilibrium constraints (VOPEC) is introduced. By using the continuity results of the approximate solution set to the equilibrium problem, we obtain the same results of the marginal map and the approximate value in VOPEC (ε) for vector-valued mapping.展开更多
针对有服务顺序限制的带时间窗的多需求多目标车辆路径问题(multi-demand and multi-objective vehicle routing problem with time window,MDMOVRPTW),在考虑多种需求由不同车辆按顺序服务等约束条件的同时,构建了最小化配送成本和最...针对有服务顺序限制的带时间窗的多需求多目标车辆路径问题(multi-demand and multi-objective vehicle routing problem with time window,MDMOVRPTW),在考虑多种需求由不同车辆按顺序服务等约束条件的同时,构建了最小化配送成本和最大化客户满意度的多目标模型。根据模型的特点设计了改进的哈里斯鹰优化(improved Harris hawks optimization,IHHO)算法,随机地将种群中部分支配解作为父代解,用临时组合算子和4种交叉算子搜索新解。最后,算例测试结果表明,相较于传统的哈里斯鹰优化算法,IHHO算法的求解性能得到了有效改善,各操作算子中交叉算子2的求解效果最好。将IHHO算法用于实例中,求解结果得到了改善,充分验证了IHHO算法的有效性。展开更多
基金supported by the Natural Science Foundation of Anhui Province(Grant Number 2208085MG181)the Science Research Project of Higher Education Institutions in Anhui Province,Philosophy and Social Sciences(Grant Number 2023AH051063)the Open Fund of Key Laboratory of Anhui Higher Education Institutes(Grant Number CS2021-ZD01).
文摘The distributed flexible job shop scheduling problem(DFJSP)has attracted great attention with the growth of the global manufacturing industry.General DFJSP research only considers machine constraints and ignores worker constraints.As one critical factor of production,effective utilization of worker resources can increase productivity.Meanwhile,energy consumption is a growing concern due to the increasingly serious environmental issues.Therefore,the distributed flexible job shop scheduling problem with dual resource constraints(DFJSP-DRC)for minimizing makespan and total energy consumption is studied in this paper.To solve the problem,we present a multi-objective mathematical model for DFJSP-DRC and propose a Q-learning-based multi-objective grey wolf optimizer(Q-MOGWO).In Q-MOGWO,high-quality initial solutions are generated by a hybrid initialization strategy,and an improved active decoding strategy is designed to obtain the scheduling schemes.To further enhance the local search capability and expand the solution space,two wolf predation strategies and three critical factory neighborhood structures based on Q-learning are proposed.These strategies and structures enable Q-MOGWO to explore the solution space more efficiently and thus find better Pareto solutions.The effectiveness of Q-MOGWO in addressing DFJSP-DRC is verified through comparison with four algorithms using 45 instances.The results reveal that Q-MOGWO outperforms comparison algorithms in terms of solution quality.
基金financially supported by the CSIR,New Delhi,India through Grant no.:25(0266)/17/EMR-II
文摘In this article, we focus to study about modified objective function approach for multiobjective optimization problem with vanishing constraints. An equivalent η-approximated multiobjective optimization problem is constructed by a modification of the objective function in the original considered optimization problem. Furthermore, we discuss saddle point criteria for the aforesaid problem. Moreover, we present some examples to verify the established results.
文摘A kind of direct methods is presented for the solution of optimal control problems with state constraints. These methods are sequential quadratic programming methods. At every iteration a quadratic programming which is obtained by quadratic approximation to Lagrangian function and linear approximations to constraints is solved to get a search direction for a merit function. The merit function is formulated by augmenting the Lagrangian function with a penalty term. A line search is carried out along the search direction to determine a step length such that the merit function is decreased. The methods presented in this paper include continuous sequential quadratic programming methods and discreate sequential quadratic programming methods.
基金Supported by the Natural Science Foundation of Henan Province(0511012000 0511013600) Supported by the Science Foundation for Pure Research of Natural Science of the Education Department of Henan Province(200512950001)
文摘Some remarks are made on the use of the Abadie constraint qualification, the Guignard constraint qualifications and the Guignard regularity condition in obtaining weak and strong Kuhn-Tucker type optimality conditions in differentiable vector optimization problems.
文摘We consider a linear-quadratical optimal control problem of a system governed by parabolic equation with distributed in right-hand side control and control and state constraints. We construct a mesh approximation of this problem using different two-level approximations of the state equation, ADI and fractional steps approximations in time among others. Iterative solution methods are investigated for all constructed approximations of the optimal control problem. Their implementation can be carried out in parallel manner.
文摘A new algorithm based on genetic algorithm(GA) is developed for solving function optimization problems with inequality constraints. This algorithm has been used to a series of standard test problems and exhibited good performance. The computation results show that its generality, precision, robustness, simplicity and performance are all satisfactory.
基金supported by the National Natural Science Foundation of China (60632050)National Basic Research Program of Jiangsu Province University (08KJB520003)
文摘An improved genetic algorithm(IGA) based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals' feature vector.Additionally,a local search(LS) process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms.
文摘In order to improve the distribution and convergence of constrained optimization algorithms,this paper proposes a constrained optimization algorithm based on double populations. Firstly the feasible solutions and infeasible solutions are stored separately through two populations,which can avoid direct comparison between them. The usage of efficient information carried by the infeasible solutions will enlarge exploitation scope and strength diversity of populations. At the same time,adopting the presented concept of constraints domination to update the infeasible set may keep good variety of population and give consideration to convergence. Also the improved mutation operation is employed to further raise the diversity and convergence.The suggested algorithm is compared with 3 state- of- the- art constrained optimization algorithms on standard test problems g01- g13. Simulation results show that the presented algorithm has certain advantages than other algorithms because it can ensure good convergence accuracy while it has good robustness.
基金This work was partially supported by the NutionalNatural Science Foundation of China
文摘This paper deals with the optimal control problems of systems governed by a parabolic variational inequality coupled with a semilinear parabolic differential equations. The maximum principle and some kind of approximate controllability are studied.
文摘The concept of vector optimization problems with equilibrium constraints (VOPEC) is introduced. By using the continuity results of the approximate solution set to the equilibrium problem, we obtain the same results of the marginal map and the approximate value in VOPEC (ε) for vector-valued mapping.
文摘针对有服务顺序限制的带时间窗的多需求多目标车辆路径问题(multi-demand and multi-objective vehicle routing problem with time window,MDMOVRPTW),在考虑多种需求由不同车辆按顺序服务等约束条件的同时,构建了最小化配送成本和最大化客户满意度的多目标模型。根据模型的特点设计了改进的哈里斯鹰优化(improved Harris hawks optimization,IHHO)算法,随机地将种群中部分支配解作为父代解,用临时组合算子和4种交叉算子搜索新解。最后,算例测试结果表明,相较于传统的哈里斯鹰优化算法,IHHO算法的求解性能得到了有效改善,各操作算子中交叉算子2的求解效果最好。将IHHO算法用于实例中,求解结果得到了改善,充分验证了IHHO算法的有效性。