广义旅行商问题与旅行商问题的转化

广义旅行商问题（Generalized Traveling Salesman Problem，简称GTSP）是比旅行商问题（Traveling Salesman Problem，简称TSP）更为复杂的一类组合优化问题，TSP可视为GTSP的特例。GTSP的应用领域更广，但相对于TSP的研究而言，GTSP的研究成果很少。本文介绍了GTSP问题的定义与背景，研究了GTSP与TSP的转化，提出了转化的优缺点和研究方向。     

广义旅行商问题与旅行商问题的转化

广义旅行商问题(Generalized Traveling Salesman Problem,简称GTSP)是比旅行商问题(Traveling Salesman Problem,简称TSP)更为复杂的一类组合优化问题,TSP可视为GTSP的特例。GTSP的应用领域更广,但相对于TSP的研究而言,GTSP的研究成果很少。本文介绍了GTSP问题的定义与背景,研究了GTSP与TSP的转化,提出了转化的优缺点和研究方向。     

求解中国旅行商问题的新结果

迄今为止,中国旅行商问题的最优解是15904公里。本文运用模糊数学模拟人的思维过程,提出了一种新的寻优方法,用该方法求解中国旅行商问题,得到更优的结果——15512公里。     

求解旅行商问题的几种智能算法

旅行商问题（TSP）是一个典型的组合优化问题,易于描述却难于求解。对于大规模TSP问题,目前仍未有非常有效的方法,如何快速有效的求解TSP问题有着重要的理论价值和实际意义。文章介绍了什么是TSP,论述了目前求解旅行商问题较为有效的六种智能算法（遗传算法、蚁群算法、Hopfield神经网络算法、模拟退火算法、人工免疫算法、混合优化算法）,并简单阐述了其优缺点,给出了未来针对TSP问题的研究重点。     

旅行商问题(TSP)的几种求解方法

旅行商问题（TSP）是组合优化领域里的一个典型的、易于描述却难以处理的NP完全难题,其可能的路径数目与城市数目是呈指数型增长的,求解非常困难。而快速、有效地解决TSP有着重要的理论价值和极高的实际应用价值。该文首先介绍了什么是TSP,接着论述了六种目前针对TSP比较有效的解决方法（模拟退火算法、禁忌搜索算法、Hopfield神经网络优化算法、蚁群算法、遗传算法和混合优化策略）的基本思想,并且简单阐述了它们的求解过程,最后分别指出了各自的优缺点并对解决TSP的前景提出了展望。     

矩阵式旅行商问题的最优解

针对一类特殊的平面TSP问题,其中所有城市的位置都规整地排成矩阵,每一行（每一列）相邻城市的距离相等;对行距等于列距以及行距的其中一种情况,都分别给出了最优算法和证明,而对行距不等于列距的另一种情况也给出了三个算法以及它们的比较。     

一种解旅行商问题的并行模拟退火算法

本基于模拟退火思想，提出一种解旅行商问题的并行算法，并在Ｔｒａｎｓｐｕｔｅｒ多处理机系统上实现，该算法具有较高的优化程度和较快的运算速度。     

一种适用于求解旅行商问题的新型算法性能分析

二点组合算法是求解旅行商问题（TSP）的一种环路改造算法,与蚁群算法相比,时间复杂度、计算精度等性能皆优于后者,实际应用结果表明本算法在解决中小规模旅行商问题时的实用性。     

基于遗传算法的多人旅行商问题求解

旅行商问题是一个经典的XP完全问题,多人旅行商问题的求解则更具挑战性。以往对求解多人旅行商问题的研究局限于以所有成员路径总和最小为优化标准,面对以所有成员路径最大值最小为优化标准的另一类多人旅行商问题却未加注意。文章给出了这两类多人旅行商问题的形式化描述,探讨了利用遗传算法求解这两类多人旅行商问题的基本思想和具体方案,进行了仿真实验验证。仿真实验数据表明,这是一种高效而且适应性强的多人旅行商问题求解方法。     

Method of scaling in approximate solution of the traveling salesman problem

An empirical algorithm to solve the traveling salesman problem was proposed. It is distinguished for the consecutive rational decomposition of the given task into subtasks of lower dimensions. Each subtask can be solved using any existing method, exact or empirical, including the recursively applied algorithm described in the present paper.     

Solving the dynamic traveling salesman game problem

A game problem of the successive capture of a team of evaders by a single pursuer under conditions of “simple motions” of the players is analyzed. The performance criterion is the total time all the evaders are captured. It is assumed that the pursuer is guided by the parallel pursuit law. In such a case, the optimal response of the evaders is the straightforward motion with maximum speed. The original infinite-dimensional problem can therefore be reduced to two finite-dimensional problems.     

求解旅行商问题的整体优先算法

针对欧几里德旅行商问题,提出了一种“整体优先”算法。该算法的基本思路是边构造边调整路径,在调整中采用了独创的逆向调整方法,避免算法陷入局部优化陷阱。理论分析和大量实验结果表明,该算法不仅时间复杂度和空间复杂度低,寻优能力也相当强,其综合性能超过目前的一些主流算法。     

The generalized covering traveling salesman problem

In this paper we develop a problem with potential applications in humanitarian relief transportation and telecommunication networks. Given a set of vertices including the depot, facility and customer vertices, the goal is to construct a minimum length cycle over a subset of facilities while covering a given number of customers. Essentially, a customer is covered when it is located within a pre-specified distance of a visited facility on the tour. We propose two node-based and flow-based mathematical models and two metaheuristic algorithms including memetic algorithm and a variable neighborhood search for the problem. Computational tests on a set of randomly generated instances and on set of benchmark data indicate the effectiveness of the proposed algorithms.     

基于LINGO的旅行商问题的建模方法

旅行商问题是图论中一类经典的最优化问题,其研究对于其他图优化问题的解决具有重要的理论意义和实际价值。针对旅行商问题建模中的困难之处--如何避免“分割”现象,提供了三种不同的解决方法,并给出了基于当今最流行的优化计算软件LINGO的实证分析。     

A search algorithm for the traveling salesman problem

A search algorithm, based on the concepts of lexicographic search and sequential decision processes, is proposed for the solution of the traveling salesman problem. Starting with an initial trial solution, the search algorithm sequentially generates better tours until an optimal (least cost) tour is identified. The logical structure of the search algorithm is such that the computational effort required to solve a problem by the proposed approach is less than that by the branch and bound procedures.     

A hybrid heuristic for the traveling salesman problem

The combination of genetic and local search heuristics has been shown to be an effective approach to solving the traveling salesman problem (TSP). This paper describes a new hybrid algorithm that exploits a compact genetic algorithm in order to generate high-quality tours, which are then refined by means of the Lin-Kernighan (LK) local search. The local optima found by the LK local search are in turn exploited by the evolutionary part of the algorithm in order to improve the quality of its simulated population. The results of several experiments conducted on different TSP instances with up to 13,509 cities show the efficacy of the symbiosis between the two heuristics     

Estimation-based metaheuristics for the probabilistic traveling salesman problem

The probabilistic traveling salesman problem (PTSP) is a central problem in stochastic routing. Recently, we have shown that empirical estimation is a promising approach to devise highly effective local search algorithms for the PTSP. In this paper, we customize two metaheuristics, an iterated local search algorithm and a memetic algorithm, to solve the PTSP. This customization consists in adopting the estimation approach to evaluate the solution cost, exploiting a recently developed estimation-based local search algorithm, and tuning the metaheuristics parameters. We present an experimental study of the estimation-based metaheuristic algorithms on a number of instance classes. The results show that the proposed algorithms are highly effective and that they define a new state-of-the-art for the PTSP.     

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/ ).