基于矩不确定模糊集的分布鲁棒风险-回报优化模型研究

本文研究随机变量分布不确定下的风险-回报优化模型。针对传统的风险-回报三类典型问题和分布不确定性背景,提出了更一般性条件下的分布鲁棒风险-回报优化新模型;基于矩不确定集合和优化对偶理论,化简复杂的新优化模型为常规结构的非线性优化问题。理论上证明了分布鲁棒风险-回报三类优化模型效率前沿的等价性。数值实验验证了理论分析的有效性。

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.

需求信息部分已知下生鲜品的低碳订购策略研究

为了研究需求信息缺失和低碳减排下的生鲜品企业运营决策问题,基于单周期随机库存系统,分别建立受碳限额与交易政策规制和无碳约束的分布式鲁棒优化模型,通过极大极小期望利润准则和最优化方法求解出两种情形下生鲜品的最优订购量,并运用数值算例检验需求随机因子的标准差系数和碳排放权交易价格对生鲜品订购量、利润和碳排放的影响。结果表明,存在唯一的最优库存因子使得生鲜品企业在最坏分布下的期望利润取得最大;与不受碳政策规制情形相比,生鲜品企业在碳限额与交易政策下能够实现高利润和低排放;需求信息缺失对生鲜品企业在碳限额与交易政策下期望利润的影响小于不受碳政策规制情形。

Semigroup of Weakly Continuous Operators Associated to a Generalized Schrödinger Equation

In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.

混合离散分布信息下的全局分布鲁棒问题

针对分布鲁棒问题的保守性,利用凸分析中的理论研究了一类混合离散分布信息下的全局分布鲁棒问题的等价形式.当只有概率分布是不确定变量时,得到了相应全局分布鲁棒优化问题的易计算的确定问题;当样本值与概率分布均不确定时,得到其全局分布鲁棒优化问题的等价确定形式.

Distributed Control for <i>n</i>×<i>n</i>Cooperative Systems Governed by Hyperbolic Operator of Infinite Order

In this study, a distributed optimal control problem for n × n cooperative hyperbolic systems with infinite order operators and Dirichlet conditions are considered. The existence and uniqueness of the state of these systems are proved. The necessary and sufficient conditions for optimality of distributed control with constraints are found, and the set of equations and inequalities that defining the optimal control of these systems is also obtained. Finally, some examples for the control problem without constraints are given.

Distributed Scheduling Problems in Intelligent Manufacturing Systems

Currently,manufacturing enterprises face increasingly fierce market competition due to the various demands of customers and the rapid development of economic globalization.Hence,they have to extend their production mode into distributed environments and establish multiple factories in various geographical locations.Nowadays,distributed manufacturing systems have been widely adopted in industrial production processes.In recent years,many studies have been done on the modeling and optimization of distributed scheduling problems.This work provides a literature review on distributed scheduling problems in intelligent manufacturing systems.By summarizing and evaluating existing studies on distributed scheduling problems,we analyze the achievements and current research status in this field and discuss ongoing studies.Insights regarding prior works are discussed to uncover future research directions,particularly swarm intelligence and evolutionary algorithms,which are used for managing distributed scheduling problems in manufacturing systems.This work focuses on journal papers discovered using Google Scholar.After reviewing the papers,in this work,we discuss the research trends of distributed scheduling problems and point out some directions for future studies.

Retrieval of aerosol size distribution using improved quantum-behaved particle swarm optimization on spectral extinction measurements

An improved quantum-behaved particle swarm optimization （IQPSO） algorithm is employed to deter- mine aerosol size distribution （ASD）. The direct problem is solved using the anomalous diffraction approximation and Lambert-Beer＇s Law. Compared with the standard particle swarm optimization algo- rithm, the stochastic particle size optimization algorithm and the original QPSO, our IQPSO has faster convergence speed and higher accuracy within a smaller number of generations. Optimization param- eters for the IQPSO were also evaluated; we recommend using four measurement wavelengths and S0 particles. Size distributions of various aerosol types were estimated using the IQPSO under dependent and independent models. Finally, experimental ASDs at different locations in Harbin were recovered using the IQPSO. All our results confirm that the IQpSO algorithm is an effective and reliable technique for estimatinz ASD.

Superconvergence and L^(∞)-Error Estimates of the Lowest Order Mixed Methods for Distributed Optimal Control Problems Governed by Semilinear Elliptic Equations

In this paper, we investigate the superconvergence property and the L∞-errorestimates of mixed finite element methods for a semilinear elliptic control problem. Thestate and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions.We derive some superconvergence results for the control variable. Moreover, we derive L^(∞)-error estimates both for the control variable and the state variables. Finally, anumerical example is given to demonstrate the theoretical results.

Distributed Communication-Sliding Mirror-Descent Algorithm for Nonsmooth Resource Allocation Problem

This paper considers a distributed nonsmooth resource allocation problem of minimizing a global convex function formed by a sum of local nonsmooth convex functions with coupled constraints.A distributed communication-efficient mirror-descent algorithm,which can reduce communication rounds between agents over the network,is designed for the distributed resource allocation problem.By employing communication-sliding methods,agents can find aε-solution in O(1/ε)communication rounds while maintaining O(1/ε^(2))subgradient evaluations for nonsmooth convex functions.A numerical example is also given to illustrate the effectiveness of the proposed algorithm.

一类分布鲁棒优化问题的线性化方法及其应用

本文考虑一类特殊的极大极小化问题,即分布鲁棒优化问题.这类优化方法是不同于随机规划和鲁棒优化的一类方法,在这类问题中,不确定变量的概率分布往往是不能精确得知的,只知道概率分布所满足的一些条件,比如一次信息、二次信息以及支撑集合信息等.如此分布鲁棒优化问题便是寻求在所有满足条件的分布中找寻满足最坏可能分布的解.一般情况下,这类优化问题的求解都是NP难的.本文考虑一类简单的情形,即考虑不确定变量的概率分布只满足一次信息、支撑集合信息以及仿射一次信息,通过应用半无限规划问题的对偶性,本文指出这类分布鲁棒优化问题等价于线性规划问题,从而原分布鲁棒优化问题可以应用现成的求解线性规划的方法进行求解.为验证方法的有效性,本文将新方法应用于解决不确定条件下含有交易费用的利率管理问题.

Fuzzy Constraint-Based Agent Negotiation

Conflicts between two or more parties arise for various reasons andperspectives. Thus, resolution of con-flicts frequently relies on some form of negotiation. Thispaper presents a general problem-solving framework for modeling multi-issue multilateral negotiationusing fuzzy constraints. Agent negotiation is formulated as a distributed fuzzy constraintsatisfaction problem (DFCSP). Fuzzy constrains are thus used to naturally represent each agent''sdesires involving imprecision and human conceptualization, particularly when lexical imprecision andsubjective matters are concerned. On the other hand, based on fuzzy constraint-basedproblem-solving, our approach enables an agent not only to systematically relax fuzzy constraints togenerate a proposal, but also to employ fuzzy similarity to select the alternative that is subjectto its acceptability by the opponents. This task of problem-solving is to reach an agreement thatbenefits all agents with a high satisfaction degree of fuzzy constraints, and move towards the dealmore quickly since their search focuses only on the feasible solution space. An application tomultilateral negotiation of a travel planning is provided to demonstrate the usefulness andeffectiveness of our framework.

基于截断需求的分布鲁棒报童问题

在实际库存决策中,通常我们只能观察到销售量而非真实需求量,这导致了库存决策的截断需求问题——部分需求信息被库存水平所截断.本文在报童问题设置下首次提出使用条件分布鲁棒优化技术来处理截断需求信息.具体而言,基于历史销售数据,我们考虑了包含需求条件分布矩信息的分布不确定集,进一步提出将库存状态信息引入该分布不确定集,并导出了两类模型的闭式解:1)在基于均值-支撑集的分布不确定集下,支撑集的上下界决定了分布鲁棒报童模型的闭式解;2)在基于均值-方差-支撑集的分布不确定集下,期望、方差以及订货价与零售价共同决定了分布鲁棒报童模型的闭式解;3)随着订货价与零售价之比增大,分布鲁棒报童问题的最优订货数量降低.实验结果表明:当订货价与零售价之比处于某一范围时,截断需求信息可以提高分布鲁棒报童模型的期望收益,并且随着截断水平增加,提升收益率增加.