CONSTRAINT QUALIFICATIONS AND DUAL PROBLEMS FOR QUASI-DIFFERENTIABLE PROGRAMMING

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.

Surrogate dual method for multi-dimensional nonlinear knapsack problems

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.

THE DISCRETE ORLICZ-MINKOWSKI PROBLEM FOR p-CAPACITY

In this paper,we demonstrate the existence part of the discrete Orlicz-Minkowski problem for p-capacity when 1<p<2.

THE GENERALIZED(NONLINEAR)POISSON PROBLEM:A DUAL VARIATIONAL APPROACH

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.

Sufficiency and Wolfe Type Duality for Nonsmooth Multiobjective Programming Problems

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.

A Dual Approach for Solving Nonlinear Infinity-Norm Minimization Problems with Applications in Separable Cases

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.

Energy-Saving Distributed Flexible Job Shop Scheduling Optimization with Dual Resource Constraints Based on Integrated Q-Learning Multi-Objective Grey Wolf Optimizer

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.

Approximation Algorithms for the Priority Facility Location Problem with Penalties

develop a mentation This paper considers the priority facility primal-dual 3-approximation algorithm for procedure, the authors further improve the location problem with penalties： The authors this problem. Combining with the greedy aug- previous ratio 3 to 1.8526.

Solution to the quadratic assignment problem usingsemi-Lagrangian relaxation

The semi-Lagrangian relaxation （SLR）, a new exactmethod for combinatorial optimization problems with equality constraints,is applied to the quadratic assignment problem （QAP）.A dual ascent algorithm with finite convergence is developed forsolving the semi-Lagrangian dual problem associated to the QAP.We perform computational experiments on 30 moderately difficultQAP instances by using the mixed integer programming solvers,Cplex, and SLR＋Cplex, respectively. The numerical results notonly further illustrate that the SLR and the developed dual ascentalgorithm can be used to solve the QAP reasonably, but also disclosean interesting fact： comparing with solving the unreducedproblem, the reduced oracle problem cannot be always effectivelysolved by using Cplex in terms of the CPU time.

Research on Cell Manufacturing Facility Layout Problem Based on Improved NSGA-II

With the rapid development of the individualized demand market,the demand for manufacturing flexibility has increased over time.As a result,a cell manufacturing system suitable for many varieties and small batches has been produced.With the goal of minimizing the area and logistics handling volume,and considering the arrangement order of facilities and channel constraints,a mathematical model was established,and the problem was solved by improved NSGA-II.After non-dominated sorting,traditional NSGA-II will cross-operate the individuals with the best sorting to generate new individuals.Such a selection strategy is extremely easy to fall into the local optimal solution.The improved NSGA-II is to improve the original selection operation,which is to select the first half of the excellent individuals in the non-dominated sorting into the cross operation,and then select the last sorted ones of the remaining individuals into the cross operation,and combine the best and the worst ones into the cross operation.Finally,an example is given to simulate and improve the solution of NSGA-II and NSGA-II.The simulation results indicate that the improved NSGA-II population shows more obvious diversity,it is easier to jump out of the local optimal solution than NSGA-II,and the satisfactory layout scheme of manufacturing cells is obtained.Therefore,it is more effective to use improved NSGA-II to solve the problem of manufacturing cell layout.

Efficient Heuristic Based Methods for Two-Stage Transshipment Problem

In this article, we propose efficient methods for solving two stage transshipment problems. Transshipment problem is the special case of Minimum cost flow problem in which arc capacities are infinite. We start by proposing a novel problem formulation for a two stage transshipment problem. Later, special structure of our problem formulation is utilized to devise two dual based heuristics solutions with computational complexity of O (n2), and O (n3) respectively. These methods are motivated by the methods developed by Sharma and Saxena [1], Sinha and Sharma [2]. Our methods differ in the initialization and the subsequent variation of the dual variables associated with the transshipment nodes along the shortest path. Lastly, a method is proposed to extract a very good primal solution from the given dual solutions with a computational complexity of O (n2). Efficacy of these methods is demonstrated by our numerical analysis on 200 random problems.

Experimental Study of Methods of Scenario Lattice Construction for Stochastic Dual Dynamic Programming

The stochastic dual dynamic programming (SDDP) algorithm is becoming increasingly used. In this paper we present analysis of different methods of lattice construction for SDDP exemplifying a realistic variant of the newsvendor problem, incorporating storage of production. We model several days of work and compare the profits realized using different methods of the lattice construction and the corresponding computer time spent in lattice construction. Our case differs from the known one because we consider not only a multidimensional but also a multistage case with stage dependence. We construct scenario lattice for different Markov processes which play a crucial role in stochastic modeling. The novelty of our work is comparing different methods of scenario lattice construction. We considered a realistic variant of the newsvendor problem. The results presented in this article show that the Voronoi method slightly outperforms others, but the k-means method is much faster overall.

The Shephard Type Problems for General L_p-Centroid Bodies

In this paper, combining with the L_p-dual geominimal surface area and the general L_p-centroid bodies, we research the Shephard type problems for general L_p-centroid bodies.

“双碳”目标下国土空间优化的挑战与应对

国土空间优化与调控始终是现代化建设面临的重大理论和实践问题。现有的国土空间规划研究多聚焦于对低碳空间治理思路、框架、工具的整体性把握,尚缺乏明确的碳约束目标及行动指南,亟待将“双碳”目标全面融入国土空间规划的目标体系、决策体系和保障体系,发挥规划在空间治理上的统筹引领作用。首先,国土空间优化光论“地”不谈“天”不行,也不能“就土论土、就地论地”;其次,低碳和“双碳”目标并不完全等同,要避免“双碳”研究中忽视国土,也要在研究国土问题中厘清“双碳”;再次,空间优化是个复杂动态过程,需要高度重视深度不确定性。因此,未来有必要建立国土空间抗解性识别分析范式和方法,开发应对深度不确定性的国土空间协同演化集成模型,构建国土空间多目标优化调控理论体系,并沿着科学认知、信息技术、智能规划、创新制度四个主轴展开深入研究和理论构建。

双重信息引导的蚁群算法求解绿色多舱车辆路径问题

针对当前实际运输中广泛存在的绿色多舱车辆路径问题(GMCVRP),文章提出一种双重信息引导的蚁群优化算法(DIACO)进行求解.首先,在DIACO的全局搜索阶段,重新构建传统蚁群优化算法(TACO)中的信息素浓度矩阵(PCM),使其同时包含客户块信息和客户序列信息,即建立具有双重信息的PCM(DIPCM),从而更全面学习和累积优质解的信息;采用3种启发式方法生成较高质量个体,用于初始化DIPCM,可快速引导算法朝向解空间中优质区域进行搜索.其次,在DIACO的局部搜索阶段,设计结合自适应策略的多种变邻域操作,用于对解空间的优质区域执行深入搜索.再次,提出信息素浓度平衡机制,以防止搜索陷入停滞.最后,使用不同规模的算例进行仿真测试和算法对比,结果验证了DIACO是求解GMCVRP的有效算法.

“双碳”与新工科背景下土木工程材料教学问题及改革对策研究

具备减碳思维的土木工程专业人才培养是实现我国“双碳”目标的关键。同时,创新能力是新工科土木工程人才培养的核心目标。目前将“双碳”与新工科相结合对土木工程专业人才培养的研究还有待进一步深入。该文提出当前土木工程材料课程教学中针对“双碳”和新工科的思考与做法,总结存在的问题。在改革对策方面,提出首先从架构层面探索“双碳”和新工科对土木工程专业人才培养的目标需求,对课程教学大纲提出调整建议;其次针对教材内容,提出以多学科交叉融合的知识体系和教学内容促进创新思维;最后是以提高新工科土木工程人才创新能力和培养“双碳”思维为目标,结合教学大纲和教学内容,开展多层次、全过程的创新实践以提升创新技能,提出教学实践过程的具体建议。

考虑双资源约束的分布式柔性作业车间调度

随着全球制造业的发展,分布式柔性作业车间调度问题(distributed flexible job shop scheduling problem, DFJSP)引起了学者们的关注.DFJSP的研究中常常忽略工人资源,作为生产的关键因素,有效利用工人资源可以提高生产率.研究了考虑双资源约束的分布式柔性作业车间调度问题(distributed flexible job shop scheduling problem with dual resource constraints, DFJSP-DRC),建立以最小化最大完工时间和总能耗为目标的数学模型,并提出一种改进的非支配排序遗传算法(improved non-dominated sorting genetic algorithm, INSGA-Ⅱ)去求解.在INSGA-Ⅱ中,通过混合初始化策略生成高质量的初始解,并设计了一种基于加工机器和工人公共空闲时间的主动解码策略来获得调度方案.为增强INSGA-Ⅱ的全局搜索能力,提出了改进的交叉变异策略和自适应交叉变异率.通过在45个算例与三种算法的比较,验证了INSGA-Ⅱ解决DFJSP-DRC的有效性.

带次模惩罚的部分命中集问题的近似算法

研究了带次模惩罚的部分命中集问题.给定一个超图H=(V,E),一个定义在V上的费用函数,一个定义在2~E上的次模惩罚函数,和一个非负整数k.问题的目标是找一个顶点子集S?V,使得S至少覆盖k条超边,且S的总费用加上未被S覆盖的超边集的惩罚费用之和最小.设计了一个基于原始-对偶的两阶段组合算法来解决该问题.当次模惩罚函数是正规化的且非减时,得到算法的近似因子为l+1,其中l是超边所含的顶点数的最大值.

求解非光滑鞍点问题的黄金比率原始对偶算法

该文提出了一类新的黄金比率原始对偶算法求解非光滑鞍点问题,该算法是完全可分裂的.在一定的假设下,证明了由算法迭代产生的序列收敛到问题的解,同时证明了O(1/N)遍历收敛率.数值实验表明该文提出的算法比Zhu,Liu和Tran-Ding文中的算法有更少的迭代步数和计算机耗时.

基于双流神经网络的个性化联邦学习方法

经典的联邦学习(FL)算法在数据高度异构的场景下难以取得较好的效果。个性化联邦学习(PFL)针对数据异构问题,提出新的解决方案,即为每个客户端“量身定做”专属模型,这样模型会拥有较好的性能;然而同时会引出难以将FL扩展到新客户端上的问题。针对PFL中的性能与扩展的难题展开研究,提出基于双流神经网络结构的联邦学习模型,简称FedDual。双流神经网络模型通过增加一个用于分析客户端个性化特征的编码器,既能拥有个性化模型的性能,又便于扩展到新客户端。实验结果表明,相较于经典联邦平均(FedAvg)算法,FedDual在MNIST和FashionMNIST等数据集上的准确率有明显提升,而在CIFAR10数据集上的准确率提升了10个百分点以上,且面对新客户端保持准确率不下降,实现了“即插即用”,解决了新客户端难以扩展的问题。