基于UNGO语言求解组合优化问题

LING09．0的主要功能是求解大型数学规划问题，但利用其求解组合问题尚未发现这方面的文献。本文从组合优化方面的一个经典问题——皇后问题入手，引入攻击函数。将该组合问题转化为一个线性规划问题，利用LINGO软件求解，取得了比较好的应用效果。但由于受到软件的限制。其求解规模还是受到一定的限制。     

证券投资组合模型及其应用

证券投资组合问题广泛存在于金融、风险投资等多个领域。文中分别在全部投资和选择性投资两种场合下重点研究了证券投资组合方案选择问题。对于全部投资而言,文中建立起了多目标规划模型并在求解过程中采用理想点法将其转化为线性规划模型,利用LINGO软件求解出最佳投资比例。对于后者,文中通过引入一个服从0-1分布的参数,将其化为一般情况求解。通过一个实例以说明上述方法的应用,并对模型进行了改进与推广。     

基于LINGO的优化问题动态规划法求解

介绍了LINGO优化软件的使用,指出LINGO在求解动态规划问题时可以不需要目标函数。基于LINGO分别对最短路问题和生产批量计划问题使用动态规划法进行了求解,给出了相应的LINGO求解代码,增强了学生对动态规划法的理解同时提高了使用优化软件编程解决问题的能力。     

基于LINGO的优化问题动态规划法求解

介绍了LINGO优化软件的使用,指出LINGO在求解动态规划问题时可以不需要目标函数。基于LINGO分别对最短路问题和生产批量计划问题使用动态规划法进行了求解,给出了相应的LINGO求解代码,增强了学生对动态规划法的理解同时提高了使用优化软件编程解决问题的能力。     

基于MGA的代工厂和仓库决策模型优化方法研究

针对单产品多层次生产外包环境下企业面对顾客需求随机导致运输成本过高的问题,采取允许代工厂和仓库可开关以及物流再分配方法,建立考虑代工厂的能力和最小加工批量、仓库转运能力以及货车运输能力的决策模型,设计加入STP（Shortest Travel Path）快速搜索策略的MGA（Modified Genetic Algorithm）进行求解。在变化工厂总数、仓库总数、顾客总数的不同维度下,将MGA与GA和LINGO分别进行对比。分析表明,MGA与LINGO求得的最优解之间差距均在10%以内,但求解时间明显优于LINGO求解时间,MGA在求解结果和时间方面均优于GA。     

一种求解二人序贯博弈均衡的新算法

虽然线性规划方法处理正规型零和博弈均衡问题有其独特的优点,但对零和序贯博弈均衡问题的求解却无能为力,而常用的逆向归纳法求解该类问题也有其固有的不足。鉴于上述原因,首先在序贯型博弈中定义了行动序列和实现概率等概念并给出相关定理。在此基础上,结合线性规划的思想,推出了求解二人零和序贯博弈均衡的新算法。该算法的目的是把序贯型博弈纳什均衡求解问题转化为线性规划问题,然后通过使用现成的线性规划软件（比如LINDO/LINGO软件）进行求解。该算法对解决该类问题提供了新的途径,具有一定的理论价值和实用价值。最后的算例对比分析说明了算法的可行性和有效性。     

中厚板热轧生产调度优化方法

中厚板热轧生产调度, 是一个有优先约束、等待时间和缓冲容量有限的单机调度问题. 用AON (Activity-on-node)网络对问题进行描述, 提出并证明了面向单机调度问题的AON网络平衡定理, 根据平衡定理, 建立了以轧机利用率最大为优化目标的非线性约束优化数学模型, 并利用优化软件LINGO进行求解. 计算实例表明, 所提出的数学优化方法, 与现有的启发式方法相比, 能够获得更好的优化目标, 所得到的生产调度方案, 生产节奏稳定, 更有利于组织生产.     

LINGO及其在化工过程优化中的应用

LINGO处理优化问题编程简单、收敛速度快、稳定性好、可靠性高.本文介绍了LINGO软件的编程特点和使用方法,选取了3个测试函数对LINGO优化性能进行测试,并应用模型语言结合化工中一些优化实例进行了应用探讨.测试结果表明LINGO具有良好的优化性能,值得在化工科研中推广和应用.     

管理运筹学在运输问题中的应用

运输问题是企业中经常发生的事情,如何使运输成本最小化,是每一个企业都会认真考虑的事情,可以说运输成本是影响企业成本的关键因素,降低运输成本,对减小企业物流成本、提高企业的综合实力具有重要意义。本文从企业运输途中运输成本的组成和影响因子分析,应用管理运筹学原理进行运输问题的分析、计算、处理,对企业运输环节的成本最小问题进行研究。利用LINGO软件进行求解,实现运输成本的最小化。     

基因组断点Median问题的算法研究

为有效解决生物信息学中的基因组断点median问题,针对4个以上环形基因组的一般情形,建立了该问题的图模型.鉴于基因组断点median问题自身的NP-困难性,从问题转化的角度,将其等价地化为图上的旅行商问题(TSP),找出二者之间最优解的关系,进而给出了其p-近似算法,其中p为用于求解TSP问题的近似算法的近似比.对算法的复杂度和近似比进行了分析,基于LINGO软件的算例表明了该算法的可行性和有效性.     

Developing model-based software to optimise wheat storage and transportation: A real-world application

This paper investigates a real-world case of a logistical management problem. We determine the optimal amounts of wheat to be transported from each producing province to each consuming province per month across the year. The problem was formulated as a linear integer programming (LIP) model, which could then be solved using LINGO optimisation software. As the LIP model needs to be run each month, a genetic algorithm (GA) was developed to solve the real-size problems in a reasonable time period. The solutions obtained by LINGO are compared with those obtained from the GA and the results show that the developed GA is efficient in terms of computational time and the quality of the solutions obtained.     

基于TSP的图的路包装问题的算法研究

图的路包装问题是一类有着重要应用背景的最优化问题,然而它在计算复杂度上是NP-困难的。受Hassin和Rubinstein的思想启发,在max-TSP问题的基础上给出了完全图的路包装问题的近似算法,分析了算法的复杂度和近似比;基于LINGO软件的算例表明了算法的可行性和有效性。     

Solving the ship inventory routing and scheduling problem with undedicated compartments

This paper presents a ship inventory routing and scheduling problem with undedicated compartments (sIRPSP-UC). The objective of the problem is to find a minimum cost solution while satisfying a number of technical and physical constraints within a given planning horizon. In this problem, we identify four sub-problems that need to be decided simultaneously: route selections, ship selection, loading, and unloading activity procedures. To solve this problem, first, we developed a mixed integer linear programming model. We then developed a one-step greedy heuristic, and then based on this heuristic, we propose a set of heuristics. Each heuristic has a combination of rules for each sub-problem. A number of problem instances are used to compare the solutions of the two approaches. We applied selected good combinations of rules to solve each problem using the heuristic approach. The results show that 8 out 12 of the considered problem instances have no gap with MILP solution solved using LINGO. We also find that the average gap is 1.96%. In contrast when we consistently use the same combination for all iterations, there are no dominant combinations of heuristics that can find good solutions for all the problem instances.     

A genetic algorithm based heuristic to the multi-period fixed charge distribution problem

This paper proposes a genetic algorithm (GA) based heuristic to the multi-period fixed charge distribution problem associated with backorder and inventories. The objective is to determine the size of the shipments, backorder and inventories at each period, so that, the total cost incurred during the entire period towards transportation, backorder and inventories is minimum. The model is formulated as pure integer nonlinear programming and 0-1 mixed integer linear programming problems, and proposes a GA based heuristic to provide solution to the above problem. The proposed GA based heuristic is evaluated by comparing their solutions with lower bound, LINGO solver and approximate solutions. The comparisons reveal that the GA generates better solutions than the approximate solutions, and is capable of providing solutions equal to LINGO solutions and closer to the lower bound value of the problems.     

Fuzzy Bayesian system reliability assessment based on prior two‐parameter exponential distribution under different loss functions

The fuzzy Bayesian system reliability assessment based on prior two‐parameter exponential distribution under squared error symmetric loss function and precautionary asymmetric loss function is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed as fuzzy random variables with fuzzy prior distributions. Because the goal of the paper is to obtain fuzzy Bayes point estimators of system reliability assessment, prior distributions of location‐scale family has been changed to scale family with change variable. On the other hand, also the computational procedures to evaluate the membership degree of any given Bayes point estimate of system reliability have been provided. In order to achieve this purpose, we transform the original problem into a non‐linear programming problem. This non‐linear programming problem is then divided into four sub‐problems for the purpose of simplifying computation. Finally, the sub‐problems can be solved by using any commercial optimizers, e.g. GAMS or LINGO. Copyright © 2010 John Wiley & Sons, Ltd.     

Josephus问题分析与探讨

Josephus问题是一个经典的递归问题。本文从问题的编程解决入手，提出静态数组、环链表、递归等3种解题方案。本文还对问题作进一步分析，考虑解的稳定点,最后提出一个优化方案，将问题的解决归约到一个较小的规模。     

Modeling and solving a capacitated stochastic location-allocation problem using sub-sources

We study a capacitated multi-facility location-allocation problem in which the customers have stochastic demands based on Bernoulli distribution function. We consider the capacitated sub-sources of facilities to satisfy demands of customers. In the discrete stochastic problem, the goal is to find optimal locations of facilities among candidate locations and optimal allocations of existing customers to operating facilities so that the total sum of fixed costs of operating facilities, allocation cost of the customers, expected values of servicing and outsourcing costs is minimized. The model is formulated as a mixed-integer nonlinear programming problem. Since finding an optimal solution may require an excessive amount of time depending on nonlinear constraints, we transform the nonlinear constraints of the problem to linear ones to arrive at a simple formulation of the model. Numerical results show that the LINGO 9.0 software is capable of solving small size problems. For medium and large-size problems, we propose two meta-heuristic algorithms, namely a genetic algorithm and a discrete version of colonial competitive algorithm. Computational results show that the proposed algorithms efficiently obtain effective solutions.     

多种群伪正态分布估计算法

为了提高基于正态分布模型的分布估计算法子代候选解的质量,防止早熟收敛,文中提出多种群伪正态分布估计算法.首先,采用佳点集方法进行种群初始化,将种群分为3个子群.然后,采用样本重心取代样本均值的方式,获得伪正态分布模型.最后,融合种群与子群伪正态分布模型,得到子群进化的概率模型.23个基准函数的对比测试表明,文中算法在求解质量和收敛速度上较优.针对多约束条件下的并行装配优化问题,提出工序池、员工池、罚函数等措施,将具有工序约束和人员约束的离散组合优化问题转化为无约束的多种群伪正态分布估计优化问题.工程应用结果表明,只需要将候选解的无限集合修正为有限集合,文中算法可方便地用于离散组合优化问题的快速求解.