A branch-and-cut algorithm for a production scheduling problem with sequence-dependent and time-dependent setup times

This paper introduces and compares three different formulations of a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The setup is divided into two parts: one that can be performed at any time and another one that is restricted to be performed outside of a given time interval. As a result, the setup time between two jobs is a function of the completion time of the first job. The problem can be formulated as a time-dependent traveling salesman problem, where the travel time between two nodes is a function of the departure time from the first node. We show that the resulting formulation can be strengthened to provide better linear programming relaxation lower bounds. We also introduce several families of valid inequalities which are used within a branch-and-cut algorithm. Computational experiments show that this algorithm can solve some instances with up to 50 jobs within reasonable computing times.     

Heuristic approaches for the family traveling salesman problem

In this article, we address the family traveling salesman problem (FTSP), an NP‐hard problem that may be seen as a generalization of the traveling salesman problem. In the FTSP, the set of cities is partitioned into several families and one wants to find the minimum cost route that visits a given number of cities in each family. We propose two metaheuristics, a population‐based method and a local search method, and a hybrid algorithm, which combines a branch‐and‐cut algorithm with a local search procedure. All the proposed methods improve the best known upper bounds from the literature. The local search method and the hybrid algorithm improve the best known upper bounds for all the benchmark instances with unknown optimal value, while the population‐based method improves the best known upper bounds for all instances, except two. Furthermore, we developed an instance generator to create additional test instances with different visit patterns. These newly generated instances were considered in the computational experiment and, thus, we provide optimal values or upper bounds for each instance. Additionally, we created a website dedicated to the FTSP, where this information is made available to the scientific community ( http://familytsp.rd.ciencias.ulisboa.pt/ ).     

牛奶配送问题的两阶段平衡TSP优化算法研究

牛奶配送问题中包含访问次数不同的节点,该问题可以当做两阶段旅行商问题进行求解。为有效地求解节点个数处于平衡条件下的牛奶配送问题的两阶段旅行商问题,提出了一种启发式优化求解方法,有助提高目标问题的求解效率和性能。针对节点数量平衡性和节点访问次数不同的特点,提出一种基于节点划分的动态规划优化。通过对实例进行计算和比较,结果验证了所提方法的有效性和优越性。     

The symmetric travelling salesman problem II. New low bounds

The branch-and-bound method is adduced for the symmetric salesman problem where two lower bounds are proposed as bounds. The first bound is a solution to the problem of optimal 2-matching; the second one, to the problem of minimum spanning 1-tree. The last bound is enhanced by applying the problem of optimal 2-matching. Both these bounds considerably improve the symmetric traveling salesman problem as compared to the asymmetric problem.     

指针网络改进遗传算法求解旅行商问题

虽然遗传算法相较于其他算法能够更好地求解旅行商问题,但这种算法在使用的过程中容易陷入局部最优的问题,进而导致问题求解遭遇困境。文章在简要介绍旅行商问题的基础上,介绍了遗传算法求解旅行商问题的思路和方法,并明确算法应用中存在的不足。在此基础上提出基于指针网络改进遗传算法求解旅行商问题的新思路,为弥补遗传算法的缺陷提供相应的原理支持。     

Approximation algorithms for time-dependent orienteering

The time-dependent orienteering problem is dual to the time-dependent traveling salesman problem. It consists of visiting a maximum number of sites within a given deadline. The traveling time between two sites is in general dependent on the starting time.For any ε>0, we provide a (2+ε)-approximation algorithm for the time-dependent orienteering problem which runs in polynomial time if the ratio between the maximum and minimum traveling time between any two sites is constant. No prior upper approximation bounds were known for this time-dependent problem.     

基于递阶遗传算法的多旅行商问题优化*

旅行商问题是一个经典的NP问题,对多人旅行商问题的求解则更具有意义。为了解决所有旅行商路径总和最小为优化标准的多旅行商一类问题,提出了一种递阶遗传算法和矩阵解码方法。该算法根据问题的特点,采用一种递阶编码方案,此编码与多旅行商问题一一对应。用递阶遗传算法优化多旅行商问题无须设计专门的遗传算子,操作简单,并且解码方法适于求解距离对称和距离非对称的多旅行商问题。计算结果表明,递阶遗传算法是有效的,能适用于优化多旅行商问题。     

基于遗传算法的多旅行商问题研究

针对所有旅行商路径总和最小为优化标准的多旅行商一类问题,用遗传算法优化,并提出了矩阵解码方法。对距离非对称的多旅行商问题的实例进行了仿真,并对不同交叉算子性能进行了比较。结果表明,该算法是有效的,适用于距离对称和非对称的多旅行商问题求解。     

旅行商问题的DNA算法

旅行商问题是求仅一次遍访指定城市并返回出发城市的最短旅行路线的问题,它是图论中一个经典的NP完全问题,用电子计算机需要指数级的时间才能得到解决,该文基于分子生物技术并利用Adleman-Lipton模型给出旅行商问题的DNA算法,这个DNA算法理论上能在多项式的时间内解决这个NP完全问题。具体地对n个城市的旅行商问题,首先将它视为一个具有顶点和边的图,并将顶点、边分别用DNA链编码表示,边的方向通过顶点的编码获得;再将这些DNA链投放在试管中进行生物化学反应,利用DNA计算的高效并行性,通过基本的生物实验操作最后得到旅行商问题的解,其过程的复杂度为O(n)。该算法的创新之处在于表示城市和路径的DNA链长度的设计,能使我们在合理小的范围内寻找旅行商问题的解,较大地简化了问题的复杂度。     

蚁群算法在求解旅行商问题中的应用综述

旅行商问题作为组合优化研究中最具挑战的问题之一, 自被提出以来就引起了学术界的广泛关注并提出了大量的方法来解决它. 蚁群算法是求解复杂组合优化问题的一种启发式仿生进化算法, 是求解旅行商问题的有效手段. 本文分别介绍蚁群算法中几个有代表性的算法, 综述了蚁群算法的改进、融合和应用的文献研究进展, 以评价近年来不同版本的蚁群算法为解决旅行商问题的发展和研究成果, 并针对改进蚁群算法结构框架、算法参数的设置及优化、信息素优化和混合算法等方面, 对现被提出的改进算法进行了分类综述. 对蚁群算法在未来对旅行商问题及其他不同领域的研究内容和研究热点的进一步发展提供了展望和依据.     

Randomized heuristics for the family traveling salesperson problem

This paper introduces the family traveling salesperson problem (FTSP), a variant of the generalized traveling salesman problem. In the FTSP, a subset of nodes must be visited for each node cluster in the graph. The objective is to minimize the distance traveled. We describe an integer programming formulation for the FTSP and show that the commercial grade integer programming solver CPLEX 11 can only solve small instances of the problem in reasonable running time. We propose two randomized heuristics for finding optimal and near‐optimal solutions of this problem. These heuristics are a biased random‐key genetic algorithm and a GRASP with evolutionary path‐relinking. Computational results comparing both heuristics are presented in this study.     

动态搜索算法求解时间依赖型旅行商问题研究

时间依赖型旅行商问题(TDTSP)是旅行商问题(TSP)的延伸.在该问题中,任意两节点间的旅行时间(成本)不仅取决于节点间的距离,还依赖于一天中具体时段或节点在哈密顿圈中所处的具体位置.对基于节点所处哈密顿圈中具体位置的TDTSP问题建立相应的数学模型,并提出求解该问题的动态搜索算法.通过实验仿真,验证了动态搜索算法优于目前在邻域搜索领域求解该问题最有效的动态规划启发式算法.     

论遗传算法在旅行商问题中的应用

旅行商问题是算法应用中的基本问题,遗传算法具有通用性、智能性、鲁棒性、全局性和并行性的特点,正好适合于该问题的求解。但基本遗传算法在解决旅行商问题时效率不高,并且容易陷于局部最优解。为了解决这一问题,提出了一种改进的遗传算法。文章首先对旅行商问题进行了描述,对遗传算法进行了介绍,对其中的个体选择、交叉算法等重要因素做了一定地改进。最后,用一个简单的实例对基本遗传算法和改进的遗传算法进行了比较,发现改进的遗传算法在解决旅行商问题上的效率问题上有了一定的提高。     

基于遗传算法的一类多旅行商问题研究

旅行商问题是一个经典的NP完全问题,对多人旅行商问题的求解则更具有意义。以往对求解多人旅行商问题的研究局限于以所有旅行商路径总和最小为优化标准,而对所有旅行商路径最大值最小的多旅行商一类问题研究的相对较少。针对所有旅行商路径最大值最小的多旅行商一类问题,用遗传算法优化,并且提出了矩阵解码方法。该方法适于距离对称和非对称的多旅行商问题求解。以距离非对称的多旅行商问题的实例进行了仿真,并对不同交叉算子性能进行了比较。     

利用遗传算法求解圆排列问题

圆排列问题是一个典型的组合优化问题,也是一个NP完全问题.遗传算法是根据自然界生物学进化而发展起来的一种进化方法,其具有简单、易行、抽象性与鲁棒性特征,已成功地解决了许多工程优化问题.给出基于改进遗传算法给出求解圆排列问题的新方法.首先,分析了圆排列问题与旅行商问题之间的关系.然后,将圆排列问题转化为旅行商问题.接着,利用所给改进遗传算法进行了求解.最后,在仿真实验中,与已有算法进行了比较,结果表明,所给算法是一种能够简单有效地求解圆排列问题的新方法.     

A memetic algorithm for the generalized traveling salesman problem

The generalized traveling salesman problem (GTSP) is an extension of the well-known traveling salesman problem. In GTSP, we are given a partition of cities into groups and we are required to find a minimum length tour that includes exactly one city from each group. The recent studies on this subject consider different variations of a memetic algorithm approach to the GTSP. The aim of this paper is to present a new memetic algorithm for GTSP with a powerful local search procedure. The experiments show that the proposed algorithm clearly outperforms all of the known heuristics with respect to both solution quality and running time. While the other memetic algorithms were designed only for the symmetric GTSP, our algorithm can solve both symmetric and asymmetric instances.     

遗传算法的应用举例

遗传算法作为一种通用、高效的优化算法,已应用到工程计算的各个领域。该文首先简要阐述了遗传算法的基本原理和其操作步骤。同时为了验证其全局的寻优能力,采用MATLAB语言编制程序实现遗传算法对数值优化和旅行商问题的求解,需要说明的是这两类问题的程序编制和求解分别依赖于不同的已有遗传算法工具箱。为了便于说明遗传算法的优越性,分别将对数值优化和旅行商问题的计算结果与用局域搜索法和模拟退火得出的优化结果进行比较。比较结果表明,对于数值优化问题,遗传算法比局域搜索法具有更佳的寻优能力;对于旅行商问题的求解也能得到满意的结果。     

Solving the traveling salesman problem with annealing-basedheuristics: a computational study

Recently, several general optimization algorithms based on the demon algorithm from statistical physics have been developed and tested on a few traveling salesman problems with encouraging results. In this paper, we conduct an extensive computational study of 11 annealing-based heuristics for the traveling salesman problem. We code versions of simulated annealing, threshold accepting, record-to-record travel and eight heuristics based on the demon algorithm. We apply each heuristic to 29 traveling salesman problems taken from a well-known online library, compare the results with respect to accuracy and running time and provide insights and suggestions for future work     

Improving Combinatorial Optimization Algorithms through Record Keeping in Constructive Multistart Search

Constructive multistart search algorithms are commonly used to address combinatorial optimization problems; however, constructive multistart search algorithm performance is fundamentally affected by two factors: (i) The choice of construction algorithm utilized and (ii) the rate of state space search redundancy. Construction algorithms are typically specific to a particular combinatorial optimization problem; therefore, we first investigate construction algorithms for iterative hill climbing applied to the traveling salesman problem and experimentally determine the best performing algorithms. We then investigate the more general problem of utilizing record‐keeping mechanisms to mitigate state space search redundancy. Our research shows that a good choice of construction algorithm paired with effective record keeping significantly improves the quality of traveling salesmen problem solutions in a constant number of state explorations. Particularly, we show that Bloom filters considerably improve time performance and solution quality for iterative hill climbing approaches to the traveling salesman problem.     

多目标旅行商问题竞争决策算法

竞争决策算法是在分析大自然生物世界特别是人类的各种竞争机制和决策原理的基础上,利用竞争造就优化、决策左右结果的特性来到达优化目的的新型寻优算法。给出了用竞争决策算法求解多目标旅行商问题的算法,经过大量数据测试和验证,获得了较好的结果。