范数下无容量限制设施选址逆问题的求解方法

一个优化问题的逆问题是这样一类问题,在给定该优化问题的一个可行解时,通过最小化目标函数中参数的改变量(在某个范数下)使得该可行解成为改变参数后的该优化问题的最优解。对于本是NP-难问题的无容量限制设施选址问题,证明了其逆问题仍是NP-难的。研究了使用经典的行生成算法对无容量限制设施选址的逆问题进行计算,并给出了求得逆问题上下界的启发式方法。两种方法分别基于对子问题的线性松弛求解给出上界和利用邻域搜索以及设置迭代循环次数的方式给出下界。数值结果表明线性松弛法得到的上界与最优值差距较小,但求解效率提升不大;而启发式方法得到的下界与最优值差距极小,极大地提高了求解该逆问题的效率。     

有时间窗装卸问题的多策略分组编码遗传算法

根据有时间窗装卸问题(PDPTW)的数学模型,设计了多策略分组编码遗传算法,将禁忌思想用于产生可行解的启发式插入算法之中,对计算实例进行了求解,结果表明,此算法可以有效求得有时间窗装卸问题的近似最优解.     

带时间窗分车运输同时收发车辆路径问题及其启发式算法

本文结合汽车零部件第三方物流的实际背景,提出了带时间窗的可分车运输同时收发车辆路径问题(简称SVRPSPDTW),并给出了问题的数学模型,同时提出两个求解该问题的启发式算法,最后进行了数值试验.由于没有可以利用的算例,本文在Solomn测试基准库的基础上构建了针对新问题的算例.计算结果表明,所有算例计算时间均不超过1秒,且算法1无论是从车辆的使用数还是从车辆行驶的路径总长度上都明显优于算法2,从而说明算法1是寻找SVRPSPDTW问题初始可行解的较为有效的算法.     

求解旅行商问题的基于类Kruskal的混合粒子群算法

本文针对求解旅行商问题的标准粒子群算法所存在的早熟和低效的问题,提出一种基于Greedy Heuristic的初始解与粒子群相结合的混合粒子群算法(SKHPSO)。该算法通过本文给出的类Kruskal算法作为Greedy Heuristic的具体实现手段,产生一个较优的初始可行解,作为粒子群中的一员,然后再用改进的混合粒子群算法进行启发式搜索。SKHPSO的局部搜索借鉴了Lin-Kernighan邻域搜索,而全局搜索结合了遗传算法中的交叉及置换操作。应用该算法对TSPLIB中的典型算例进行了算法测试分析,结果表明:SKHPSO可明显提高求解的质量和效率。     

置换流水车间调度问题的中心引力优化算法求解

目前求解置换流水车间调度问题的智能优化算法都是随机型优化方法,存在的一个问题是解的稳定性较差。针对该问题,本文给出一种确定型智能优化算法——中心引力优化算法的求解方法。为处理基本中心引力优化算法对初始解选择要求高的问题,利用低偏差序列生成初始解,提高初始解质量;利用加速度和位置迭代方程更新解的状态;利用两位置交换排序法进行局部搜索,提高算法的优化性能。采用置换流水车间调度问题标准测试算例进行数值实验,并和基本中心引力优化算法、NEH启发式算法、微粒群优化算法和萤火虫算法进行比较。结果表明该算法不仅具有更好的解的稳定性,而且具有更高的计算精度,为置换流水车间调度问题的求解提供了一种可行有效的方法。     

遗传算法与蚂蚁算法的融合在带时间窗的车辆路径问题中的应用

对带时间窗的车辆路径问题(VRPTW)的求解分为两个过程,先由遗传算法求解出初步的可行解,由此生成信息素初始分布,而后采用蚂蚁算法找出问题的最优解或近似最优解.通过具体算例,从数值计算上探索了遗传算法和蚂蚁算法融合后的优化能力,获得了满意的效果.     

求解零等待流水车间调度问题的改进蝙蝠算法

针对零等待流水车间调度问题特性,设计了一种蝙蝠算法进行求解.算法模拟蝙蝠捕食搜索行为进行寻优,利用基于最小位置值规则的随机键编码方式来表示问题解,采用基于NEH方法的局部搜索策略和随机交换、插入、逆序操作的变邻域搜索策略来提高局部优化性能,进一步根据Metropolis概率准则接受劣解来避免早熟.通过典型算例对所提算法进行仿真测试并与粒子群算法和RAJ启发式算法进行对比,结果表明所设计算法求解零等待流水车间调度问题的有效性和优越性,是求解流水车间生产调度问题的一种有效工具.     

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。     

带时间窗取送货问题的混合算法

为解决带时间窗的取送货问题,建立了集合划分模型,设计列生成算法与启发式规则相结合的CGA混合算法进行求解。首先,放松约束构建主问题及受限主问题,运用单纯形法与分支定界进行求解;其次,建立时空网络以构建子问题,基于修正的Dijkstra's算法,设计包含算法A、B1、B2的求解算法;最后,通过启发式算法解决节点重复覆盖问题。为验证算法有效性,进一步构建了OPT近似最优解算法;并基于CGA提出三种求解策略C1、C2、C3,做单因素方差分析,采用算例分析算法的性能。实验结果表明,对于客户点数量小于30的小规模算例,CGA与OPT所得结果相近,但CGA求解效率更显著;针对客户点数量为600的大规模算例,CGA至多在20分钟内求得结果,可见本文算法的精度和效率较高。而针对不同类型及规模的客户点的单因素方差分析结果显示,C1、C2、C3在“平均行驶距离成本”、“平均车辆数”、“平均求解时间”三个维度上差异性显著,经营者可根据实际需求进行策略选择。     

基于资源受限广义指派问题的分解启发式算法

资源受限广义指派问题(RGAP)是NP-难的,对RGAP问题给出一个分解启发式算法.通过分解目标函数及约束条件,把原问题分解成子问题的集合,并设计分解启发式算法找到该问题的满意解.最后,通过算例说明算法的有效性.     

Heuristics for the 0–1 multidimensional knapsack problem

Two heuristics for the 0–1 multidimensional knapsack problem (MKP) are presented. The first one uses surrogate relaxation, and the relaxed problem is solved via a modified dynamic-programming algorithm. The heuristics provides a feasible solution for (MKP). The second one combines a limited-branch-and-cut-procedure with the previous approach, and tries to improve the bound obtained by exploring some nodes that have been rejected by the modified dynamic-programming algorithm. Computational experiences show that our approaches give better results than the existing heuristics, and thus permit one to obtain a smaller gap between the solution provided and an optimal solution.     

改进的混合算法求解车间作业调度问题

车间作业调度问题是个典型的NP-hard问题,为了更有效的解决车间作业调度问题,提出了一种改进的混合算法(IGASA).算法设计了一种基于当前最优解的免疫算子,算子对当前最优个体中选取运行时间最少的一台机器上的工件顺序当作疫苗,并用车间调度问题的图论模型解释了此算子的合理性.最后通过大量实验证明改进的混合算法的性能的优越性,从而证明设计的免疫算子是有意义的.     

Heuristic methods for the sectoring arc routing problem

The sectoring arc routing problem (SARP) is introduced to model activities associated with the streets of large urban areas, like municipal waste collection. The aim is to partition the street network into a given number of sectors and to build a set of vehicle trips in each sector, to minimize the total duration of the trips. Two two-phase heuristics and one best insertion method are proposed. In the two-phase methods, phase 1 constructs the sectors using two possible heuristics, while phase 2 solves a mixed capacitated arc routing problem (MCARP) to compute the trips in each sector. The best insertion method determines sectors and trips simultaneously. In addition to solution cost, some evaluation criteria such as imbalance, diameter and dispersion measures are used to compare algorithms. Numerical results on large instances with up to 401 nodes and 1056 links (arcs or edges) are reported and analysed.     

Worst case analysis of Max-Regret,Greedy and other heuristics for Multidimensional Assignment and Traveling Salesman Problems

Optimization heuristics are often compared with each other to determine which one performs best by means of worst-case performance ratio reflecting the quality of returned solution in the worst case. The domination number is a complement parameter indicating the quality of the heuristic in hand by determining how many feasible solutions are dominated by the heuristic solution. We prove that the Max-Regret heuristic introduced by Balas and Saltzman (Oper. Res. 39:150–161, 1991) finds the unique worst possible solution for some instances of the s-dimensional (s≥3) assignment and asymmetric traveling salesman problems of each possible size. We show that the Triple Interchange heuristic (for s=3) also introduced by Balas and Saltzman and two new heuristics (Part and Recursive Opt Matching) have factorial domination numbers for the s-dimensional (s≥3) assignment problem.     

A repeated matching heuristic for the single-source capacitated facility location problem

Facility location models form an important class of integer programming problems, with application in many areas such as the distribution and transportation industries. An important class of solution methods for these problems are so-called Lagrangean heuristics which have been shown to produce high quality solutions and which are at the same time robust. The general facility location problem can be divided into a number of special problems depending on the properties assumed. In the capacitated location problem each facility has a specific capacity on the service it provides. We describe a new solution approach for the capacitated facility location problem when each customer is served by a single facility. The approach is based on a repeated matching algorithm which essentially solves a series of matching problems until certain convergence criteria are satisfied. The method generates feasible solutions in each iteration in contrast to Lagrangean heuristics where problem dependent heuristics must be used to construct a feasible solution. Numerical results show that the approach produces solutions which are of similar and often better than those produced using the best Lagrangean heuristics.     

Using Genetic Algorithms and Heuristics for Job Shop Scheduling with Sequence-Dependent Setup Times

In this work a new heuristic solution technique for the Resource-Constrained Project Scheduling Problem (RCPSP) is proposed. This technique is a hybrid multi-pass method that combines random sampling procedures with a backward–forward method. The impact of each component of the algorithm is evaluated through a step-wise computational analysis which in addition permits the value of their parameters to be specified. Furthermore, the performance of the new technique is evaluated against the best currently available heuristics using a well known set of instances. The results obtained point out that the new technique greatly outperforms both the heuristics and metaheuristics currently available for the RCPSP being thus competitive with the best heuristic solution techniques for this problem.     

Optimizing simulated annealing schedules with genetic programming

Combinatorial optimization problems are encountered in many areas of science and engineering. Most of these problems are too difficult to be solved optimally, and hence heuristics are used to obtain “good” solutions in reasonable time. One heuristic that has been successfully applied to a variety of problems is Simulated Annealing. The performance of Simulated Annealing depends on the appropriate choice of a key parameter, the annealing schedule. Researchers usually experiment with some manually created annealing schedules and then use the one that performs best in their algorithms.This work replaces this manual search by Genetic Programming, a method based on natural evolution. We demonstrate the potential of this new approach by optimizing the annealing schedule for a well-known combinatorial optimization problem, the Quadratic Assignment Problem. We introduce two new algorithms for solving the Quadratic Assignment Problem that perform extremely well and outperform existing Simulated Annealing algorithms.     

Routing relatively few customers per route

This paper presents a modification of the well-known Solomon (1987) sequential insertion heuristic I1 for the Vehicle Routing Problem with Time Windows (VRPTW). VRPTW involves servicing customers within a pre-specified service time window by homogeneously capacitated vehicles from a single depot. By using two new measures for the additional time needed to insert a customer in the route, significantly better solutions are obtained for relatively short routes compared to the original Solomon (1987) sequential insertion heuristic I1. Because high-quality initial heuristics often allow local searches and metaheuristics to achieve better solutions more quickly, the new approach is likely to help generating better solutions to practical routing problems.     

A branch and bound algorithm for extreme point mathematical programming problems

This paper deals with a class of nonconvex mathematical programs called Extreme Point Mathematical Programs. This class is a generalization of zero-one integer programs and is a special case of the Generalized Lattice Point Problem, and finds applications in various areas such as production scheduling, load balancing, and concave programming. The current work existing on this class of problems is limited to certain dual types of extreme point ranking methods (which do not find a feasible solution until optimality) and some non-convergent cutting plane algorithms. No computational experience exists. This paper develops a finitely convergent branch and bound algorithm for solving the problem. The principles involved in the design of this algorithm are quite general and apply to a wider class of mathematical programs including the Generalized Lattice Point Problem. A random problem generator is described which is capable of generating problems of varying levels of difficulty. Computational experience on such problems is provided.