带冲突关系装箱问题的启发式求解算法

现实物流活动中大量存在的食品、药品和危险品等货物的分组包装问题属于带冲突关系的装箱问题(BPPC),其优化目标是在满足货物间冲突限制的前提下完成装箱操作,并最小化使用货箱的数量。本文从实际需求出发,基于货物之间的冲突关系、装箱顺序和货箱容量等约束建立相应的数学规划模型;随后设计了求解BPPC问题的启发式算法,算法通过迭代求解最大团结构实现货物间冲突关系的消去,根据当前货物最大团采用改进降序首次适应算法(FFD)完成货物装箱操作,并通过“洗牌”策略对已有装箱方案进行局部优化;最后,针对Iori算例数据,将以上算法与基于图着色的启发式算法进行比较分析,结果表明,本文算法是求解BPPC问题更为有效的方法。     

超尺寸物品装箱问题及其算法

本文探讨一类新装箱问题-超尺寸物品装箱问题。针对实际解决该问题的两涉法，我们提出了一个评价效率更高的目标函数，证明了在此目标函数下两步法的渐近最坏比不小于2，并给出了渐近量坏比与拆分次数的关系。最后本文提出了一种不同于两步法的新在线算法MA，证明了在新目标函数下其渐近最坏比不超过7/4。     

基于图着色模型的冲突装箱问题启发式算法

带有冲突关系装箱问题的优化目标是在满足货物冲突关系的前提下,使用数量最少的货箱完成货物装箱的目的。本文分析了冲突装箱问题的数学模型,提出了基于图着色模型的启发式算法进行求解。首先,使用冲突图来描述货物之间的冲突关系;其次,基于冲突图,采取图着色的方式将货物进行分组,并且组内的货物之间不存在冲突关系;最后,采取改进FFD算法对每组的货物进行装箱操作。实验表明,本文提出的启发式算法能够快速有效地找到问题的可行解,为此类装箱问题的求解提供了新思路。     

超尺寸物品装箱问题

本文给出一类新的装箱问题，超尺寸物品装箱问题。就实际解决该问题所普遍彩的两步法，证明了当采用经典目标函数并且拆分次数不超过2时，第二步采用FFDLR的渐进最坏比为3/2。进而针对超尺寸物品装箱问题的算法提出了一个评价效率更高的目标函数。证明了在此目标函数下，当不限制物品的最大尺寸时，第二步采用最优装法两步法的渐近最坏比为2。最后，给出渐近最坏与拆分次数的关系。     

在线约束单机排序问题的启发式算法

由于约束单机排序问题是经典装箱问题的一种推广并且同经典装箱问题有一些相同的特征。本文主要讨论了经典装箱问题的一些启发式算法在在线约束单机排序问题上的推广和最坏界估计。     

考虑货架存放期的经济批量排产问题的改良算法

经济批量排产问题是关于在单一设备上协调地、周期性地生产多种产品的问题.其解要求在生产准备与库存总成本最小的条件下,决定 I 种产品的生产序列.本文研究的经济批量排产问题考虑了产品货架存放期因素.指出了Dobson算法的不足,并提出了求解该问题的新算法(改进的装箱算法),新算法不仅以生产次数最大的产品为基础进行装箱,而且进一步以生产次数略低的产品为基础进行装箱.排产时,先按生产次数降序进行装箱,再按单次生产时间与生产准备时间之和降序装箱.计算结果显示,本算法结果更优.     

基于多目标进化算法的供水系统优化运行研究

将多目标进化算法与启发式算法相接合,对供水管网微观模型进行优化调度研究.目标函数为供水系统的运行费用和维护费用最小化,以及水压服务水平的最大化(保证安全供水),以各泵站各型号水泵的开启和调速泵的转数比为决策变量,进行二进制-实数混合编码,并采用新型的交叉算子.运用NSGA-Ⅱ、epsilon-MOEA、SPEA2三种多目标进化方法求解优化运行模型,并通过工程算例进行比较.应用表明,多目标进化算法能为供水系统的优化决策提供支持.     

汽车4S店维修车间的优化调度分析

调度研究的问题是将稀缺资源分配给在一定时间内的不同任务,它是一个决策过程,其目的是优化一个或多个目标。对实际问题的优化调度可以帮助企业提高资源利用率,减少客户等待时间,提升竞争力,对汽车4S维修服务站的优化调度问题进行研究,剖析这一实际应用问题的调度目标、机器环境、加工特征和约束等细节,提出了优化调度模型,设计了调度算法。然后,通过实例,简要分析了模型及算法的可行性.     

一个双目标单机调度问题及其几个多项式可解情形

研究了一个双目标单机调度问题及其几个多项式可解的情形。问题的主目标是延误工件数最小,在此条件下,最小化各工件加权提前期的总和,由于该问题是NP一难的,故研究求解它的一个启发式算法及问题的几个多项式可解的特殊情形。     

约束装箱问题的混合遗传算法求解

本将最佳适应法和遗传算法相结合，提出了一种新的启发式混合遗传算法对具有时间约束的装箱问题进行求解，给出了具体的算法步骤，试算结果表明基于启发式算法的混合遗传算法适合于求解各种约束条件下的大规模装箱问题。     

Valid inequalities and facets of the capacitated plant location problem

Recently, several successful applications of strong cutting plane methods to combinatorial optimization problems have renewed interest in cutting plane methods, and polyhedral characterizations, of integer programming problems. In this paper, we investigate the polyhedral structure of the capacitated plant location problem. Our purpose is to identify facets and valid inequalities for a wide range of capacitated fixed charge problems that contain this prototype problem as a substructure.The first part of the paper introduces a family of facets for a version of the capacitated plant location problem with a constant capacity for all plants. These facet inequalities depend on the capacity and thus differ fundamentally from the valid inequalities for the uncapacited version of the problem.We also introduce a second formulation for a model with indivisible customer demand and show that it is equivalent to a vertex packing problem on a derived graph. We identify facets and valid inequalities for this version of the problem by applying known results for the vertex packing polytope.This research was partially supported by Grant # ECS-8316224 from the National Science Foundation's Program in Systems Theory and Operations Research.     

Fast Fourier optimization

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the fast Fourier transform (fft) is a recursive algorithm that can dramatically improve the efficiency for computing the discrete Fourier transform. However, because it is recursive, it is difficult to embed into a linear optimization problem. In this paper, we explain the main idea behind the fast Fourier transform and show how to adapt it in such a manner as to make it encodable as constraints in an optimization problem. We demonstrate a real-world problem from the field of high-contrast imaging. On this problem, dramatic improvements are translated to an ability to solve problems with a much finer grid of discretized points. As we shall show, in general, the “fast Fourier” version of the optimization constraints produces a larger but sparser constraint matrix and therefore one can think of the fast Fourier transform as a method of sparsifying the constraints in an optimization problem, which is usually a good thing.     

Random sampling and greedy sparsification for matroid optimization problems

Random sampling is a powerful tool for gathering information about a group by considering only a small part of it. We discuss some broadly applicable paradigms for using random sampling in combinatorial optimization, and demonstrate the effectiveness of these paradigms for two optimization problems on matroids: finding an optimum matroid basis and packing disjoint matroid bases. Application of these ideas to the graphic matroid led to fast algorithms for minimum spanning trees and minimum cuts. An optimum matroid basis is typically found by agreedy algorithm that grows an independent set into an optimum basis one element at a time. This continuous change in the independent set can make it hard to perform the independence tests needed by the greedy algorithm. We simplify matters by using sampling to reduce the problem of finding an optimum matroid basis to the problem of verifying that a givenfixed basis is optimum, showing that the two problems can be solved in roughly the same time. Another application of sampling is to packing matroid bases, also known as matroid partitioning. Sampling reduces the number of bases that must be packed. We combine sampling with a greedy packing strategy that reduces the size of the matroid. Together, these techniques give accelerated packing algorithms. We give particular attention to the problem of packing spanning trees in graphs, which has applications in network reliability analysis. Our results can be seen as generalizing certain results from random graph theory. The techniques have also been effective for other packing problems. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.Some of this work done at Stanford University, supported by National Science Foundation and Hertz Foundation Graduate Fellowships, and NSF Young Investigator Award CCR-9357849, with matching funds from IBM, Schlumberger Foundation, Shell Foundation and Xerox Corporation. Also supported by NSF award 962-4239.     

A family of genetic algorithms for the pallet loading problem

This paper is concerned with a family of genetic algorithms for the pallet loading problem. Our algorithms differ from previous applications of genetic algorithms to two-dimensional packing problems in that our coding contains all the information needed to produce the packing it represents, rather than relying on a packing algorithm to decode each individual solution. We experiment with traditional one-dimensional string representations, and a two-dimensional matrix representation which preserves the notion of closeness between positions on the pallet. Two new crossover operators are introduced for the two-dimensional case. Our definition of solution space includes both feasible and infeasible solutions and we suggest a number of different fitness functions which penalise infeasibility in different ways and a repair operator which allows our populations to maintain feasibility. The results of experiments designed to test the effectiveness of these features are presented.     

Packing problems and project scheduling models: an integrating perspective

This paper considers two problem classes, namely packing and project scheduling problems that are important to researchers as well as practitioners. The two problem categories are described, and a classification is given for the different kinds of packing problems and project scheduling concepts. While both problem classes are different with respect to their fields of application, similarities of their mathematical structures are examined. It is shown that all packing problems considered here are special cases of models for project scheduling. The aim is to indicate which project scheduling models can be used to capture the different types of packing problems. Finally, some implications for research on optimisation algorithms for these two problem classes are discussed, and the applicability of the results of this work in practice are pointed out.     

A tutorial in irregular shape packing problems

Cutting and packing problems have been a core area of research for many decades. Irregular shape packing is one of the most recent variants to be widely researched and its history extends over 40 years. The evolution of solution approaches to this problem can be attributed to increased computer power and advances in geometric techniques as well as more sophisticated and insightful algorithm design. In this paper we will focus on the latter. Our aim is not to give a chronological account or an exhaustive review, but to draw on the literature to describe and evaluate the core approaches. Irregular packing is combinatorial and as a result solution methods are heuristic, save a few notable exceptions. We will explore different ways of representing the problem and mechanisms for moving between solutions. We will also propose where we see the future challenges for researchers in this area.     

Packing strong subgraph in digraphs

In this paper, we study two types of strong subgraph packing problems in digraphs, including internally disjoint strong subgraph packing problem and arc-disjoint strong subgraph packing problem. These problems can be viewed as generalizations of the famous Steiner tree packing problem and are closely related to the strong arc decomposition problem. We first prove the NP-completeness for the internally disjoint strong subgraph packing problem restricted to symmetric digraphs and Eulerian digraphs. Then we get inapproximability results for the arc-disjoint strong subgraph packing problem and the internally disjoint strong subgraph packing problem. Finally we study the arc-disjoint strong subgraph packing problem restricted to digraph compositions and obtain some algorithmic results by utilizing the structural properties.     

Comparison of bundle and classical column generation

When a column generation approach is applied to decomposable mixed integer programming problems, it is standard to formulate and solve the master problem as a linear program. Seen in the dual space, this results in the algorithm known in the nonlinear programming community as the cutting-plane algorithm of Kelley and Cheney-Goldstein. However, more stable methods with better theoretical convergence rates are known and have been used as alternatives to this standard. One of them is the bundle method; our aim is to illustrate its differences with Kelley’s method. In the process we review alternative stabilization techniques used in column generation, comparing them from both primal and dual points of view. Numerical comparisons are presented for five applications: cutting stock (which includes bin packing), vertex coloring, capacitated vehicle routing, multi-item lot sizing, and traveling salesman. We also give a sketchy comparison with the volume algorithm. This research has been supported by Inria New Investigation Grant “Convex Optimization and Dantzig-Wolfe Decomposition”.     

Weak convergence in applied probability

Weak convergence of probability measures on function spaces has been active area of research in recent years. While the theory has a somewhat abstract base, it is extremely useful in a wide variety of problems and we believe has much to offer to applied probability. Our aim in this survey paper is to discuss those aspects of the theory which are relevant to work in applied probability. After an introduction to the foundations of weak convergence, we shall discuss partial sum, point, Markov and extremal processes. These processes form the building blocks for many of the important models of applied probability.     

A hybrid grouping genetic algorithm for bin packing

The grouping genetic algorithm (GGA) is a genetic algorithm heavily modified to suit the structure of grouping problems. Those are the problems where the aim is to find a good partition of a set or to group together the members of the set. The bin packing problem (BPP) is a well known NP-hard grouping problem: items of various sizes have to be grouped inside bins of fixed capacity. On the other hand, the reduction method of Martello and Toth, based on their dominance criterion, constitutes one of the best OR techniques for optimization of the BPP to date.In this article, we first describe the GGA paradigm as compared to the classic Holland-style GA and the ordering GA. We then show how the bin packing GGA can be enhanced with a local optimization inspired by the dominance criterion. An extensive experimental comparison shows that the combination yields an algorithm superior to either of its components.