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语言求解组合优化问题

LINGO9.0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.     

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。     

基于动态规划和遗传算法的混合算法研究

动态规划法和遗传算法是目前在水电站厂内经济运行中广泛应用的两种优化算法，文章提出了一种基于动态规划法和遗传算法的混合优化算法来分别解决大规模机组组合问题中空间最优化和时间最优化的计算机求解问题。避免了遗传算法计算速度缓慢的问题，又避免了动态规划法的“维数灾”问题。最后使用清江隔河岩水电站的4台机组的运行数据进行了仿真研究，并和完全使用动态规划法的结果进行了比较，获得了良好的效果，说明该混合优化算法对于厂内经济运行是一种可行的算法。     

基于动态规划法求解动态o-1背包问题

随机时变背包问题(RTVKP)是一种动态组合优化问题,也是一种典型的NP-hard问题。由于RTVKP问题中物品的价值、重量和背包载重均是动态变化的,导致问题的求解非常困难。在动态规划法基础上,提出了一种求解背包载重随机变化的RTVKP问题的确定性算法,分析了其复杂度和成功求解需要满足的条件。对两个大规模实例的计算表明,该算法是求解RTVKP问题的一种高效算法。     

基于动态规划算法的最值问题分析

动态规划法是一种重要的求最优解的计算机程序设计算法,在各类软件设计大赛等各类程序设计大赛中广泛运用。文章通过设计合适的状态转移方程,分别使用两种算法对最值问题进行求解,并通过对求解过程及求解时间效率的对比实验验证了动态规划方法的高效性。     

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.     

基于0/1背包问题的算法探究

0／1背包问题是计算机科学中的一个经典问题。动态规划法，递归法，回溯法是求解该问题的三种典型方法，使用这三种方法求解0／1背包问题，并对各算法进行了理论分析。用不同规模的0／1背包问题对三种算法进行测试，比较它们的运行时间，发现测试结果与其理论分析结果相符．最后指出就求解不同规模的0／1背包问题而言各算法的优劣。     

利用动态规划算法解决购物单问题

购物单问题是0-1背包问题的一种应用,解决购物单问题已有贪婪法,动态规划法,蚁群算法,回溯法等.动态规划算法是求解决策过程最优化的方法,通常用于求解具有某种最优性质的问题.根据动态规划原理解决购物单问题,说明了动态规划算法解决实际生活问题的高效性.     

用动态规划法求解延时/面积最小化工艺映射

本文提出了一个求解延时／面积最小化工艺映射动态规划法．它首先基干线性延时模型，给出了用动态规划法求解延时最小化工艺映射的步骤；然后从树型网络的面积计算公式入手，用动态规划法近似计算面积最小化工艺映射；最后用“线性加权和法”把延时／面积最小化工艺映射转变为单目标最优化问题求解．     

A dynamic programming approach to GA-based heuristic for multi-period CF problems

In this paper we have introduced a multi-period cell formation (CF) model which is more computationally challenging than the most comprehensive CF models in the literature. A dynamic programming (DP) based approach coupled with GA-based heuristic is proposed to solve the multi-period problem. Since, the introduced dynamic programming is general and can be applied to any GA-based heuristic with full rejuvenation cycles to solve the multi-period part of the model, we focused only on the DP approach in this paper but have explained the interface with the GA-based heuristic. Illustrative example has been provided that clarifies the application of DP-heuristic. The performance of the DP-heuristic has been evaluated against LINGO and multi period GA-based heuristic.     

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.     

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.     

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。     

No special schemes are needed for solving software reliabilityoptimization models

This paper resolves four previous software reliability optimization models published in this journal (Berman and Ashrafi, 1993). It is shown that a recent optimization software, LINGO, makes it unnecessary to develop special branch and bound or dynamic programming schemes to solve nonlinear reliability optimization models with binary decision variables     

Algorithms for solving the single-sink fixed-charge transportation problem

The single-sink fixed-charge transportation problem is an important subproblem of the fixed-charge transportation problem. Just a few methods have been proposed in the literature to solve this problem. In this paper, solution approaches based on dynamic programming and implicit enumeration are revisited. It is shown how the problem size as well as the search space of a recently published dynamic programming method can be reduced by exploiting reduced cost information. Additionally, a further implicit enumeration approach relying on solution concepts for the binary knapsack problem is introduced. The performance of the various solution methods is compared in a series of computational experiments.     

用AOP的横切机制解决面向对象设计中的耦合问题

传统的面向对象思想无法有效解决由于系统对横切点的关注造成的实现代码散乱耦合问题。面向方面思想是为解决这一途径的技术,本文对面向方面思想中的静态横切机制和动态横切机制作了比较详细的分析说明,探讨了如何利用它们来解决这一问题。     

A gamma type-2 defuzzification method for solving a solid transportation problem considering carbon emission

This paper intends to develop a multi-objective solid transportation problem considering carbon emission, where the parameters are of gamma type-2 fuzzy in nature. This paper proposed the defuzzification process for gamma type-2 fuzzy variable using critical value (CV ) and nearest interval approximation method. A chance constraint programming problem is generated using the CV based reduction method to convert the fuzzy problem to its equivalent crisp form. Applying the \(\alpha \)-cut based interval approximation method, a deterministic problem is developed. Some real life data are used to minimize the cost and carbon emission. LINGO standard optimization solver has been used to solve the multi-objective problem using weighted sum method and intuitionistic fuzzy programming technique. The Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) algorithm are implemented to generate efficient optimal solution by converting the multi-objective problem to a single objective problem using penalty cost for carbon emission. After solving the problem, analysis on some particular cases has been presented. The sensitivity analysis has been shown to different credibility levels of cost, emission, source, demand, conveyance to find total cost, emission and transported amount in each level. A comparison study on the performance of three algorithms (LINGO, GA and PSO) is presented. At the end, some graphs have been plotted which shows the effect of emission with different emission parameters.     

0/1背包问题

本文对“0/1背包问题”采用贪婪算法、动态规划、回溯法、分枝限界四种不同方法进行求解和算法分析,并通过各种算法的实现,研究了0/1背包问题的实质。