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 paper,we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite,and where there are an i...In this paper,we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite,and where there are an infinite number of results that can be observed by the principal.This principal-agent problem has an infinite number of incentive-compatibility constraints,and we transform it into an optimization problem with an infinite number of constraints called a semi-infinite programming problem.We then propose an exterior penalty function method to find the optimal solution to this semi-infinite programming and illustrate the convergence of this algorithm.By analyzing the optimal solution obtained by the proposed penalty function method,we can obtain the optimal incentive mechanism for the principal-agent problem with an infinite number of incentive-compatibility constraints under moral hazard.展开更多
In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of ...In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of the functions at a given feasible point. The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case. As in classical case so called constraint qualifications have to be imposed on the constraint functions to guarantee that for a given local minimizer of the original problem the nullvector is an optimal solution of the corresponding 'quasilinearized' problem. In this paper, constraint qualifications for inequality constrained quasi differentiable programming problems of type min {f(x)|g(x)≤0} are considered, where f and g are qusidifferentiable functions in the sense of Demyanov. Various constraint qualifications for this problem are presented and a new one is proposed. The relations among these conditions are investigated. Moreover, a Wolf dual problem for this problem is introduced, and the corresponding dual theorems are given.展开更多
Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of prob...Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of problems. Multiply constrained problem was relaxed to a singly constrained problem by using the surrogate technique. To compute tighter bounds of the primal problem, the cutting plane method was used to solve the surrogate dual problem, where the surrogate relaxation problem was solved by the 0-1 linearization method. The domain cut technique was employed to eliminate the duality gap and thus to guarantee the convergence of tile algorithm. Numerical results were reported for large-scale multi-dimensional nonlinear knapsack problems.展开更多
A series of problems in mechanics and physics are governed by the ordinary Poisson equation which demands linearity,isotropy,and material homo- geneity.In this paper a generalization with respect to nonlinearity,aniso...A series of problems in mechanics and physics are governed by the ordinary Poisson equation which demands linearity,isotropy,and material homo- geneity.In this paper a generalization with respect to nonlinearity,anisotropy,and inhomogeneity is made.Starting from the canonical basic equations in the primal and dual formulation respectively we derive systematically the corresponding generalized variational principles;under certain conditions they can be extended to so called complementary extremum principles allowing for global bounds.For simplicity a restriction to two dimensional problems is made,including twice-connected domains.展开更多
In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concept of invex of order??type II for nondifferentiable locally Lipschitz functions using the tools of Clark...In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concept of invex of order??type II for nondifferentiable locally Lipschitz functions using the tools of Clarke subdifferential. The new functions are used to derive the sufficient optimality condition for a class of nonsmooth multiobjective programming problems. Utilizing the sufficient optimality conditions, weak and strong duality theorems are established for Wolfe type duality model.展开更多
The optimization investment policy decision of SCM-Supply Chain Management-implementation has been analysed under symmetric and asymmetric information conditions. For both conditions, SCM implementation options’ deci...The optimization investment policy decision of SCM-Supply Chain Management-implementation has been analysed under symmetric and asymmetric information conditions. For both conditions, SCM implementation options’ decision optimizing models have been developed. In these models, both clients and vendors try to pursue their own benefits. Based upon the principal-agent theory, the models show to what extent a principal (a client) needs to pay more to an agent (a vendor) in a context of asymmetric information. For the client, it is important to understand the extra costs to be able to adopt effective strategies to stimulate a vendor to perform an optimal implementation of a SCM system. The results of a simulation experiment regarding SCM implementation options illustrate and verify the theoretical findings and confirm the general notion that the less informed party is obliged to pay information rent to the better-informed party.展开更多
In this paper,we consider nonlinear infinity-norm minimization problems.We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed li...In this paper,we consider nonlinear infinity-norm minimization problems.We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed linear and nonlinear infinity- norm minimization problems.Numerical results are presented.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supported by National Natural Science Foundation of China(72031009 and 71871171)the National Social Science Foundation of China(20&ZD058).
文摘In this paper,we propose an iterative algorithm to find the optimal incentive mechanism for the principal-agent problem under moral hazard where the number of agent action profiles is infinite,and where there are an infinite number of results that can be observed by the principal.This principal-agent problem has an infinite number of incentive-compatibility constraints,and we transform it into an optimization problem with an infinite number of constraints called a semi-infinite programming problem.We then propose an exterior penalty function method to find the optimal solution to this semi-infinite programming and illustrate the convergence of this algorithm.By analyzing the optimal solution obtained by the proposed penalty function method,we can obtain the optimal incentive mechanism for the principal-agent problem with an infinite number of incentive-compatibility constraints under moral hazard.
文摘In classical nonlinear programming, it is a general method of developing optimality conditions that a nonlinear programming problem is linearized as a linear programming problem by using first order approximations of the functions at a given feasible point. The linearized procedure for differentiable nonlinear programming problems can be naturally generalized to the quasi differential case. As in classical case so called constraint qualifications have to be imposed on the constraint functions to guarantee that for a given local minimizer of the original problem the nullvector is an optimal solution of the corresponding 'quasilinearized' problem. In this paper, constraint qualifications for inequality constrained quasi differentiable programming problems of type min {f(x)|g(x)≤0} are considered, where f and g are qusidifferentiable functions in the sense of Demyanov. Various constraint qualifications for this problem are presented and a new one is proposed. The relations among these conditions are investigated. Moreover, a Wolf dual problem for this problem is introduced, and the corresponding dual theorems are given.
基金partially supported by the National Natural Science Foundation of China （Grant Nos.10271073, 10571116）
文摘Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of problems. Multiply constrained problem was relaxed to a singly constrained problem by using the surrogate technique. To compute tighter bounds of the primal problem, the cutting plane method was used to solve the surrogate dual problem, where the surrogate relaxation problem was solved by the 0-1 linearization method. The domain cut technique was employed to eliminate the duality gap and thus to guarantee the convergence of tile algorithm. Numerical results were reported for large-scale multi-dimensional nonlinear knapsack problems.
文摘A series of problems in mechanics and physics are governed by the ordinary Poisson equation which demands linearity,isotropy,and material homo- geneity.In this paper a generalization with respect to nonlinearity,anisotropy,and inhomogeneity is made.Starting from the canonical basic equations in the primal and dual formulation respectively we derive systematically the corresponding generalized variational principles;under certain conditions they can be extended to so called complementary extremum principles allowing for global bounds.For simplicity a restriction to two dimensional problems is made,including twice-connected domains.
文摘In this paper, a class of nonsmooth multiobjective programming problems is considered. We introduce the new concept of invex of order??type II for nondifferentiable locally Lipschitz functions using the tools of Clarke subdifferential. The new functions are used to derive the sufficient optimality condition for a class of nonsmooth multiobjective programming problems. Utilizing the sufficient optimality conditions, weak and strong duality theorems are established for Wolfe type duality model.
文摘The optimization investment policy decision of SCM-Supply Chain Management-implementation has been analysed under symmetric and asymmetric information conditions. For both conditions, SCM implementation options’ decision optimizing models have been developed. In these models, both clients and vendors try to pursue their own benefits. Based upon the principal-agent theory, the models show to what extent a principal (a client) needs to pay more to an agent (a vendor) in a context of asymmetric information. For the client, it is important to understand the extra costs to be able to adopt effective strategies to stimulate a vendor to perform an optimal implementation of a SCM system. The results of a simulation experiment regarding SCM implementation options illustrate and verify the theoretical findings and confirm the general notion that the less informed party is obliged to pay information rent to the better-informed party.
文摘In this paper,we consider nonlinear infinity-norm minimization problems.We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed linear and nonlinear infinity- norm minimization problems.Numerical results are presented.
