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.

THE CHARACTERIZATION OF EFFICIENCY AND SADDLE POINT CRITERIA FOR MULTIOBJECTIVE OPTIMIZATION PROBLEM WITH VANISHING CONSTRAINTS

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.

The Optimal Conditions of the Linear Fractional Programming Problem with Constraint

在这篇文章，作者讨论线性部分编程问题的最佳的条件并且证明一个局部地可选的答案是一个全球性可选的答案，局部地最佳的答案能与限制状况在一个基本可行答案被达到。

SEQUENTIAL QUADRATIC PROGRAMMING METHODS FOR OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS

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.

A Note on the Guignard Constraint Qualification and the Guignard Regularity Condition in Vector Optimization

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.

A New Evolutionary Algorithm for Function Optimization

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.

Constrained Optimization Algorithm Based on Double Populations

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.

OPTIMAL CONTROL PROBLEM FOR PARABOLIC VARIATIONAL INEQUALITIES

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.

Iterative Solution of Mesh Constrained Optimal Control Problems with Two-Level Mesh Approximations of Parabolic State Equation

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.

面向复杂物流配送场景的车辆路径规划多任务辅助进化算法

在现代社会中,复杂物流配送场景的车辆路径规划问题(Vehicle routing problem,VRP)一般带有时间窗约束且需要提供同时取送货的服务.这种复杂物流配送场景的车辆路径规划问题是NP-难问题.当其规模逐渐增大时,一般的数学规划方法难以求解,通常使用启发式方法在限定时间内求得较优解.然而,传统的启发式方法从原大规模问题直接开始搜索,无法利用先前相关的优化知识,导致收敛速度较慢.因此,提出面向复杂物流配送场景的车辆路径规划多任务辅助进化算法(Multitask-based assisted evolutionary algorithm,MBEA),通过使用迁移优化方法加快算法收敛速度,其主要思想是通过构造多个简单且相似的子任务用于辅助优化原大规模问题.首先从原大规模问题中随机选择一部分客户订单用于构建多个不同的相似优化子任务,然后使用进化多任务(Evolutional multitasking,EMT)方法用于生成原大规模问题和优化子任务的候选解.由于优化子任务相对简单且与原大规模问题相似,其搜索得到的路径特征可以通过任务之间的知识迁移辅助优化原大规模问题,从而加快其求解速度.最后,提出的算法在京东物流公司快递取送货数据集上进行验证,其路径规划效果优于当前最新提出的路径规划算法.

具有紧时、高能耗特征的混合流水车间多目标调度优化问题

针对具有紧时、高能耗工序特征的混合流水车间调度问题,以优化产品暴露时间、最大完工时间和能源消耗为目标,建立混合流水车间调度模型,并提出一种改进的多目标粒子群算法进行有效求解。首先构建了基于ISDE指标的档案维护策略及局部邻域搜索策略,辅助算法跃出局部极值及减少生产阻塞。之后,提出一种基于模糊理论的决策分析方法选取最优调度方案。最后,通过仿真实验验证提出的多目标调度模型与算法的可行性和优越性。

考虑个体客户满意度的多车程生鲜品配送路径优化

随着生鲜电商的兴起,生鲜品的道路运输量越来越大,其配送任务越来越复杂,提升客户满意度是生鲜品配送的重要目标组成。文章以一个具有配送自主权的生鲜品供应商为研究对象,以整个计划周期内生鲜品配送的车辆运输成本最小及客户满意度最大为双目标,且客户满意度从顾客的个体视角考虑,构建双目标多车程带时间窗及考虑订单打包时间的车辆路径优化模型。基于ε-约束方法,设计了两阶段变邻域搜索(VNS)和模拟退火(SA)相结合的元启发式算法,基于车辆构造初始路线,并针对性地提出了3点改进措施,包括通过数学性质推导下界、减少求解过程中不必要的搜索空间以及规避求解过程中被支配解的后优化处理。最后,以Solomon标准算例为基础构造算例对所设计的算法进行了计算实验,其求解结果表明:其设计的算法具有有效性,并通过敏感性分析得出相关管理启示。

带隐藏约束昂贵黑箱问题的自适应代理优化方法

针对带隐藏约束的昂贵黑箱全局优化问题,提出采用自适应转换搜索策略的代理优化方法。在转换搜索子步中采用与已估值点个数相关的标准差在当前最优点附近通过随机扰动生成候选点,以更好地平衡局部搜索和全局搜索。为更好地近似真实黑箱目标函数,采用了自适应组合目标代理模型。在50个测试问题上进行了数值实验,计算结果说明了所提算法的有效性。

基于离散粒子群算法的管道保温结构优化研究

针对目前管道保温结构优化算法不稳定、结果优化程度不高的问题,建立以经济效益为目标函数,以满足国家散热损失标准等条件为约束函数的离散型数学模型。以BPSO算法为基础改变其位置更新规则,防止种群进化失效;采用自适应权重增加粒子的全局和局部搜索能力;充分利用模拟退火算法的思想避免出现早熟现象。应用改进的算法分别对普通蒸汽管道和核电站的蒸汽管道进行系统仿真实验。结果表明,该算法能够在满足国家散热损失标准等条件下取得最优解,可以为管道保温结构提供合理的优化方案。

求解有服务顺序限制的MDMOVRPTW的IHHO算法

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。

云资源调度的回答集程序描述性求解

针对求解难度为NP完全的基础设施即服务(IaaS)模式云资源调度问题,本文提出一种基于回答集程序(ASP)的描述性优化求解方法,并对其正确性进行分析。首先,把满足虚拟机CPU使用的情况下关闭尽可能多的主机做为减少云平台能耗的方法,将云资源调度问题形式化表述;其次,结合形式化描述以及减少云平台能耗的策略,将云资源调度问题用ASP编码为描述性(优化)问题,并分析其正确性;最后,在公开的PlanetLab数据集上进行实验,结果显示,ASP方法可在保障服务质量的同时减少集群能耗,最高可节能13%以上。这表明ASP方法在云资源调度问题上是有效的,从而提供一种易理解、易修改并能充分利用ASP最新工具成果的有效云资源调度新方法。

基于学习-推理的约束求解方法研究进展

机器学习与自动推理的融合是当前人工智能研究的新趋势.约束满足问题是人工智能研究的经典问题,现实世界中大量的调度、规划和配置等问题均可以建模为约束满足问题,高效的求解算法一直是研究热点.近年来涌现出众多将机器学习应用于约束满足问题求解的新方法,这些基于“学习-推理”的新方法为约束满足问题求解开辟了新方向并展示出巨大发展潜力,方法的突出优点是适应性强、可在线优化并具有更强的可扩展性.将当前的“学习-推理”方法分为基于消息传递神经网络、基于序列到序列和基于最优化等3类进行综述,详细分析各类方法的特点和在不同的问题集上求解效果,尤其对每类方法所涵盖的相关工作进行多角度的对比分析.最后,对基于“学习-推理”的约束求解方法进行总结和展望.

和优化问题的松弛型Farkas引理

利用共轭函数的上图性质,并引入2类新的约束规范条件,建立了和优化问题的松弛型Farkas引理.

基于双阶段搜索的约束进化多任务优化算法

高效地平衡算法的多样性、收敛性和可行性是求解约束多目标优化问题(CMOP)的关键;然而,复杂约束的出现给该类问题的求解带来了更大的挑战。因此,提出一种基于双阶段搜索的约束进化多任务优化算法(TEMA),通过完成两个协同进化的任务实现多样性、收敛性和可行性之间的平衡。首先,进化过程由探索和利用两个阶段组成,分别致力于加强算法在目标空间的广泛探索能力和高效搜索能力;其次,设计一种动态约束处理策略以平衡种群中可行解的比例,从而增强算法在可行区域的探索能力;再次,提出一种回退搜索策略,利用无约束Pareto前沿所包含的信息指导算法向约束Pareto前沿快速收敛;最后,在两个基准测试集中的23个问题上进行对比实验。实验结果表明,TEMA分别在14个和13个测试问题上取得最优反世代距离(IGD)值和超体积(HV)值,体现出明显优势。

基于非线性自适应比例因子的雪豹优化算法

针对雪豹优化算法在求解复杂优化问题时,存在全局勘探能力不足、寻优精度低等问题,提出一种改进的雪豹优化算法。首先,基于分段Logistic混沌映射初始化从而提高初始种群多样性;其次,引入非线性比例因子用于平衡算法的全局勘探能力和局部开发能力;然后,提出了一种差分变异策略,在第一次种群更新位置后,使用5个随机个体提高全局搜索能力和算法收敛能力,在第二次种群更新位置后,使用3个随机个体保证在求解过程的中后期也具有一定的全局勘探能力,尽可能避免陷入局部最优。通过在IEEE CEC2022基准函数测试集上测试,并与其他算法进行比较,结果表明所提出的算法在种群质量、求解精度以及算法稳定性上均有较大提升。最后将所提出的算法应用于工程优化,计算结果进一步证实了算法的强优化能力。