用Excel求解网络优化问题

规划求解在各个行业都得到广泛的应用，并取得了显著的经济效益。各个领域中的大量问题都可以归结为线性规划问题。通过实例，分析了用Excel提供的“规划求解”功能解决网络优化中的主要问题，论证Excel对于需要大量进行处理数据研究中的实用性。使用Excel的“规划求解”工具可以很方便解决此类问题，为网络决策分析活动制定最优方案。     

Excel电子表格在数学规划中的应用

利用Excel的“规划求解”工具可以很好地解决包括线性规划和非线性规划在内的数学规划计算问题。本文以实际生产计划的规划问题为例介绍了在Excel中实现“规划求解”的具体步骤,建立数学规划模型的基本原则以及在表格中输入数据应注意的问题。     

Excel规划求解的两类应用

Excel规划求解在很多方面都有应用,但它的应用在一般的教材和Excel的帮助中都没有详细的介绍。本文介绍用Excel规划求解来解决线性规划和非线性回归这两类问题。这两类问题分别在经济、交通、通信和生物医学等领域都有广泛的应用。如果不用Excel的规划求解,解决线性规划和非线性回归问题是相当复杂的编程运算。应用了规划求解则可以直观而简捷地求得答案。本文对两类问题都提供案例,给出解决方案的步骤。     

解决鸡兔同笼问题又一法

看了21期《活用Excel，解决鸡兔同笼问题》一文后．深受启发。其实用Excel的“规划求解”功能来解决“鸡兔同笼”问题也十分方便，而且更加快捷。     

用Excel“规划求解”解决应用问题

Excel的“规划求解”有很强的功能,可以对有多个变量的线性和非线性规划问题进行求解,省去了人工编制程序和手工计算的麻烦。下面通过实例叙述“规划求解”的操作方法。     

单纯形法求解与Excel规划求解

利用单纯形法求解线性规划问题在产品品种问题、合理配料问题、开料问题等问题中有着极其广泛的应用,但整个计算过程非常繁杂,而且容易计算错误。对Excel规划求解的研究发现,利用Excel中的规划求解工具可以实现单纯形法求解线性规划的问题,大大提高了求解的速度和准确性。     

事半功倍把握利润 巧用模拟运算

“李宾是公司的市场总监，凭着多年在大公司的市场经验，现在干起工作来可以说已经是得心应手了。但还有一件事总是困扰着李宾，那就是制作每个季度的工作计划时，对于单项产品在不同操作成本时的盈利状况进行预计，准确地说应该是如何计算每季度公司产品的销售成本、销售数量和利润之间的关系。有李宾这样苦恼的人不在少数。他们总是为了每月、每季度的预算、报表所累，不得不花很多的时间来考察怎样才能恰到好处地掌握产品的盈利。这种问题其实很普遍，比如有“广告费用投放和利润收益关系”、“资金、人员投入与产出关系”等等，要想很好地解决这样的问题，其实可以利用Office中的Excel。在Excel中有很多关于计算和分析的手段和方法．其中“单变量求解”、“模拟预算表”和“规划求解”就可以解决各种因数据变化而影响其他数据结果的问题。今天我们就通过一个真实的案例来了解Excel中“模拟预算表”的应用。”     

解读“匈牙利法”——对《“匈牙利法”存在的问题及改进方法》一文的质疑

“匈牙利法”是目前为止被人们认为求解指派问题最简单有效的方法,但有些人对此算法认识不全面,产生了一些误解。文章详细解读了“匈牙利法”及其求解步骤,并通过两个实例详细演示了“匈牙利法”的具体求解过程,以助学习者更好地理解和运用“匈牙利法”来解决实际问题,同时也澄清了对“匈牙利法”的某些错误认识。为保证求解结果的正确性,利用Excel提供的“规划求解”模块对求解结果进行了验证。     

用EXCEL解方程和得出数学模型的最优化解

用 EXCEL解方程可以大大减轻手工求解的计算量 ,并可得到精确解。通过实例展示了 EXCEL求解数学方程的强大功能 ,描述了“规划求解”解多元方程或找到数学模型的最优解 ,其实“规划求解”远不止这些 ,它在求最高产量、最高收入、最合理的计划安排、工程问题等方面都有大量应用。     

Excel在经济规划与管理决策中的应用

在经济或管理问题中，有许多线性规划求解与解后分析，过去我们要么自已去编制求解程序，但只能解小型问题，要么采用引进的专门软件，本文中介绍Excel在经济规划与管理决策中的应用，Excel中的规划求解工具灵活方便，是人们的得力助手。     

面向复杂约束优化问题的进化算法综述

约束优化是多数实际工程应用优化问题的呈现方式.进化算法由于其高效的表现,近年来被广泛应用于约束优化问题求解.但约束条件使得问题解空间离散、缩小、改变,给进化算法求解约束优化问题带来极大挑战.在此背景下,融合约束处理技术的进化算法成为研究热点.此外,随着研究的深入,近年来约束处理技术在复杂工程应用问题优化中得到了广泛发展,例如多目标、高维、等式优化等.根据复杂性的缘由,将面向复杂约束优化问题的进化优化分为面向复杂目标的进化约束优化算法和面向复杂约束场景的进化算法两种类别进行综述,其中,重点探讨了实际工程应用的复杂性对约束处理技术的挑战和目前研究的最新进展,并最后总结了未来的研究趋势与挑战.     

Fuzzy programming for mixed-integer optimization problems

Mixed-integer optimization problems belong to the group of NP-hard combinatorial problems. Therefore, they are difficult to search for global optimal solutions. Mixed-integer optimization problems are always described by precise mathematical programming models. However, many practical mixed-integer optimization problems have inherited a more or less imprecise nature. Under these circumstances, if we take into account the flexibility of the constraints and the fuzziness of the objectives, the original mixed-integer optimization problems can be formulated as fuzzy mixed-integer optimization problems. Mixed-integer hybrid differential evolution (MIHDE) is an evolutionary search algorithm which has been successfully applied to many complex mixed-integer optimization problems. In this article, a fuzzy mixed-integer mathematical programming model is developed to formulate the fuzzy mixed-integer optimization problem. In addition the MIHDE is introduced to solve the fuzzy mixed-integer programming problem. Finally, the illustrative example shows that satisfactory results can be obtained by the proposed method. This demonstrates that MIHDE can effectively handle fuzzy mixed-integer optimization problems.     

An interactive simulation and analysis software for solving TSP using Ant Colony Optimization algorithms

Traveling salesman problem (TSP) is one of the extensively studied combinatorial optimization problems and tries to find the shortest route for salesperson which visits each given city precisely once. Ant colony optimization (ACO) algorithms have been used to solve many optimization problems in various fields of engineering. In this paper, a web-based simulation and analysis software (TSPAntSim) is developed for solving TSP using ACO algorithms with local search heuristics. Algorithms are tested on benchmark problems from TSPLIB and test results are presented. Importance of TSPAntSim providing also interactive visualization with real-time analysis support for researchers studying on optimization and people who have problems in form of TSP is discussed.     

基于深度强化学习的组合优化研究进展

组合优化问题广泛存在于国防、交通、工业、生活等各个领域, 几十年来, 传统运筹优化方法是解决组合优化问题的主要手段, 但随着实际应用中问题规模的不断扩大、求解实时性的要求越来越高, 传统运筹优化算法面临着很大的计算压力, 很难实现组合优化问题的在线求解. 近年来随着深度学习技术的迅猛发展, 深度强化学习在围棋、机器人等领域的瞩目成果显示了其强大的学习能力与序贯决策能力. 鉴于此, 近年来涌现出了多个利用深度强化学习方法解决组合优化问题的新方法, 具有求解速度快、模型泛化能力强的优势, 为组合优化问题的求解提供了一种全新的思路. 因此本文总结回顾近些年利用深度强化学习方法解决组合优化问题的相关理论方法与应用研究, 对其基本原理、相关方法、应用研究进行总结和综述, 并指出未来该方向亟待解决的若干问题.     

一类带约束动态多目标优化问题的进化算法

动态多目标约束优化问题是一类NP-Hard问题,定义了动态环境下进化种群中个体的序值和个体的约束度,结合这两个定义给出了一种选择算子.在一种环境变化判断算子下给出了求解环境变量取值于正整数集Z+的一类带约束动态多目标优化问题的进化算法.通过几个典型的Benchmark函数对算法的性能进行了测试,其结果表明新算法能够较好地求出带约束动态多目标优化问题在不同环境下质量较好、分布较均匀的Pareto最优解集.     

Human behavior-based optimization: a novel metaheuristic approach to solve complex optimization problems

Optimization techniques, specially evolutionary algorithms, have been widely used for solving various scientific and engineering optimization problems because of their flexibility and simplicity. In this paper, a novel metaheuristic optimization method, namely human behavior-based optimization (HBBO), is presented. Despite many of the optimization algorithms that use nature as the principal source of inspiration, HBBO uses the human behavior as the main source of inspiration. In this paper, first some human behaviors that are needed to understand the algorithm are discussed and after that it is shown that how it can be used for solving the practical optimization problems. HBBO is capable of solving many types of optimization problems such as high-dimensional multimodal functions, which have multiple local minima, and unimodal functions. In order to demonstrate the performance of HBBO, the proposed algorithm has been tested on a set of well-known benchmark functions and compared with other optimization algorithms. The results have been shown that this algorithm outperforms other optimization algorithms in terms of algorithm reliability, result accuracy and convergence speed.

     

Logspace Optimization Problems and Their Approximability Properties

Logspace optimization problems are the logspace analogues of the well-studied polynomial-time optimization problems. Similarly to them, logspace optimization problems can have vastly different approximation properties even though their underlying decision problems have the same computational complexity. Natural problems - including the shortest path problems for directed graphs, undirected graphs, tournaments, and forests - exhibit such a varying complexity. In order to study the approximability of logspace optimization problems in a systematic way, polynomial-time approximation classes and polynomial-time reductions between optimization problems are transferred to logarithmic space. It is proved that natural problems are complete for different logspace approximation classes. This is used to show that under the assumption L ≠ NL some logspace optimization problems cannot be approximated with a constant ratio; some can be approximated with a constant ratio, but do not permit a logspace approximation scheme; and some have a logspace approximation scheme, but optimal solutions cannot be computed in logarithmic space.     

Variable neighborhood search for the Vertex Separation Problem

The Vertex Separation Problem belongs to a family of optimization problems in which the objective is to find the best separator of vertices or edges in a generic graph. This optimization problem is strongly related to other well-known graph problems; such as the Path-Width, the Node Search Number or the Interval Thickness, among others. All of these optimization problems are NP-hard and have practical applications in VLSI (Very Large Scale Integration), computer language compiler design or graph drawing. Up to know, they have been generally tackled with exact approaches, presenting polynomial-time algorithms to obtain the optimal solution for specific types of graphs. However, in spite of their practical applications, these problems have been ignored from a heuristic perspective, as far as we know. In this paper we propose a pure 0-1 optimization model and a metaheuristic algorithm based on the variable neighborhood search methodology for the Vertex Separation Problem on general graphs. Computational results show that small instances can be optimally solved with this optimization model and the proposed metaheuristic is able to find high-quality solutions with a moderate computing time for large-scale instances.     

Bat Algorithm: A Survey of the State-of-the-Art

The area of metaheuristic optimization algorithms has been attracting researchers for many years. These algorithms have built in capability to explore a large region of the solution space, are computationally robust, efficient and can avoid premature convergence. They have been extensively tested and applied on many hard optimization problems where conventional computing techniques perform unsatisfactorily. They are capable of solving general N-dimensional, linear, nonlinear and complex global optimization problems. One of the latest entrants in this field is the Bat algorithm which is based on the echolocation behaviour of bats. It has been proven to have good convergence properties on different benchmark functions and seems promising for dealing with optimization problems. The aim of this paper is to provide a survey of the state of the art on Bat algorithm. A concise effort has been made so that the readers get a rapid insight into some of the applications upon which bat algorithm has been applied till date in specialized fields of science and engineering. Some of the variants of the bat algorithm as reported in the literature have also been discussed.     

On the computational complexity of combinatorial flexibility problems

The concept of flexibility – originated in the context of heat exchanger networks design – is associated with a substructure which allows the same optimal value on the substructure (for example an optimal flow) as in the whole structure, for all the costs in a given range of costs. In this work, we extend the concept of flexibility to general combinatorial optimization problems, and prove several computational complexity results in this new framework. Under some monotonicity conditions, we prove that a combinatorial optimization problem can be polynomially reduced to its associated flexibility problem. However, the minimum cut, maximum weighted matching and shortest path problems have NP-complete associated flexibility problems. In order to obtain polynomial flexibility problems, we have to restrict ourselves to combinatorial optimization problems on matroids.