A novel discretization scheme for the close enough traveling salesman problem

This paper addresses a variant of the Euclidean traveling salesman problem in which the traveler visits a node if it passes through the neighborhood set of that node. The problem is known as the close-enough traveling salesman problem. We introduce a new effective discretization scheme that allows us to compute both a lower and an upper bound for the optimal solution. Moreover, we apply a graph reduction algorithm that significantly reduces the problem size and speeds up computation of the bounds. We evaluate the effectiveness and the performance of our approach on several benchmark instances. The computational results show that our algorithm is faster than the other algorithms available in the literature and that the bounds it provides are almost always more accurate.     

改进的嵌套分区算法求解旅行商问题

嵌套分区算法是近年来提出的一种求解大规模优化问题的新型全局优化方法。介绍了嵌套分区算法（NPM）的基本思想,将其应用于求解旅行商问题。分析确定了嵌套分区算法各个算子的策略,提出了一种改进的嵌套分区算法。该算法采用加权抽样法求得初始最可能域,用全局数组记录下每个区域的历史最优解,用3-opt局部搜索算法改进每个区域解的质量。对TSPLIB中部分实例仿真结果表明,所提出的结合3-opt算法的改进嵌套分区算法在求解 TSP问题时可以获得高质量的解。     

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.     

A new and efficient ant-based heuristic method for solving the traveling salesman problem

Abstract: In this paper, we present an efficient metaheuristic approach for solving the problem of the traveling salesman. We introduce the multiple ant clans concept from parallel genetic algorithms to search solution space using different islands to avoid local minima in order to obtain a global minimum for solving the traveling salesman problem. Our simulation results indicate that the proposed novel traveling salesman problem method (called the ACOMAC algorithm) performs better than a promising approach named the ant colony system. This investigation is concerned with a real life logistics system design which optimizes the performance of a logistics system subject to a required service level in the vehicle routing problem. In this work, we also concentrate on developing a vehicle routing model by improving the ant colony system and using the multiple ant clans concept. The simulation results reveal that the proposed method is very effective and potentially useful in solving vehicle routing problems.     

A new genetic algorithm for the asymmetric traveling salesman problem

The asymmetric traveling salesman problem (ATSP) is one of the most important combinatorial optimization problems. It allows us to solve, either directly or through a transformation, many real-world problems. We present in this paper a new competitive genetic algorithm to solve this problem. This algorithm has been checked on a set of 153 benchmark instances with known optimal solution and it outperforms the results obtained with previous ATSP heuristic methods.     

An integer programming approach for the time-dependent traveling salesman problem with time windows

Congestion in large cities and populated areas is one of the major challenges in urban logistics, and should be addressed at different planning and operational levels. The Time Dependent Travelling Salesman Problem (TDTSP) is a generalization of the well known Traveling Salesman Problem (TSP) where the travel times are not assumed to be constant along the day. The motivation to consider the time dependency factor is that it enables to have better approximations to many problems arising from practice. In this paper, we consider the Time-Dependent Traveling Salesman Problem with Time Windows (TDTSP-TW), where the time dependence is captured by considering variable average travel speeds. We propose an Integer Linear Programming model for the problem and develop an exact algorithm, which is compared on benchmark instances with another approach from the related literature. The results show that the approach is able to solve instances with up to 40 customers.     

The period traveling salesman problem: a new heuristic algorithm

A new, simple and effective heuristic algorithm has been developed for the period traveling salesman problem. Computational results obtained from the test problems taken from the literature indicate that the algorithm compares well in terms of accuracy with other existing algorithms, finding a larger number of best solutions. Moreover, its average percentage error and its worst ratio of solution to the best-known solution are smaller than those of the other existing algorithms.Scope and purposeIn the period traveling salesman problem, a traveling salesman must visit each city a fixed number of times over a given m-day planning period. Each city specifies a set of sequences of visit days and the visit days are assigned to the city by selecting one of these sequences. Moreover, for each day of the planning period, a not empty tour must be generated by connecting the salesman home city and the cities that must be visited on that day. The salesman objective is to minimize the total distance traveled over the entire m-day period. For this problem, arising in various situations such as mail delivery or lawn-care services, the paper proposes a simple and effective heuristic algorithm where an improvement procedure is embedded within a tour construction type procedure.     

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 optimum assignments and a new heuristic approach for the traveling salesman problem

In this paper the equivalent problem approach to the n × n optimum assignment problem is exploited for providing a heuristic solution to the traveling salesman problem. It is shown that the simplified problem of finding an optimum tour using the n ? k arcs of the cycles of an n × n optimum assignment and k other arcs is NP-hard. Next by using the “nearest neighbor rule” for zero cost cycles, an O(n²) algorithm is presented for obtaining a suboptimal solution to the simplified problem. Using the notion of a path switching operation that always results in a new tour having a lower cost than the original tour, an algorithm for a systematic refinement of the suboptimal tour is given. The algorithm presented in this paper efficiently solves the problem for k = 2,3 for any n. Examples illustrating the algorithm are given, and the time complexities as well as error bounds have been studied. Further work needed in the area is indicated.     

On the solution of the traveling salesman problem once again

The procedure is suggested for the construction of Hamiltonian cycles optimized along the length in weighted graphs by the method of the stagewise isolation and lengthening of the linear portions of paths of the minimized length. The procedure makes it possible to process both nonoriented and oriented graphs, i.e., to solve symmetric and nonsymmetric problems of the traveling salesman. At each stage of the procedure (starting from the first stage), the subgraphs of the initial (original) graph of the problem are processed, the complexity of which decreases in the transitions from stage to stage. The isolation and the lengthening of linear portions of the paths are the simplest operations for the detection of vertices of degree 2 with the possible removal of some edges (arcs) of a subgraph. These characteristics of the procedure (the stagewise decrease of the complexity of the processable subgraphs and the exceptional simplicity of operations for the isolation and lengthening of the linear portions of paths) permits us to hope for a high effectiveness of the use of the procedure for the solution of the traveling salesman problems of large dimensions.     

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.     

MMAS-EC算法求解旅行商问题

针对蚁群算法在求解旅行商问题容易出现搜索精度不高的问题,提出一种结合排出算法的最大-最小蚁群系统算法（MMAS-EC）。算法采用全局寻优和局部搜索结合的策略,利用寻优效果较好的最大-最小蚁群系统指导全局搜索方向,同时引入排出算法来探索局部解空间,并采用2-opt操作减小了排出算法对初始位置的依赖,提高了解的稳定性。仿真实验表明：结合了排出算法的最大-最小蚁群系统算法与标准蚁群算法相比,在时间开销增加较小的情况下,取得了质量更高的解。     

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/ ).     

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     

A two-dimensional mapping for the traveling salesman problem

The traveling salesman problem (TSP) is a classic problem in combinatorial optimization. An N-city asymmetric TSP has (N − 1)! tours. We develop a conceptual mapping of an N-city problem to a two-dimensional space and computer code for the defining function and its inverse. The transformation is implemented using color graphics and allows one to better understand the topography of the solution space and study the effects of different search techniques visually, leading to improvements in solution algorithms.     

求解旅行商问题的二阶段演化算法

对Inver-over算子进行了改进,提出了1st-Inver-over算子和2nd-Inver-over算子,实现了求解TSP问题的基于改进Inver-over算子的二阶段演化算法（Two-stage Inver-over EA）。在算法前期,只采用1st-Inver-over算子来保证算法的收敛速度;在算法后期,根据种群的多样性自适应地选取1st-Inver-over算子和2nd-Inver-over算子来协调算法的收敛速度和种群的多样性。在TSPLIB（Traveling Salesman Problem Library）中的典型实例上的实验结果表明,Two-stage Inver-over EA比经典的GT算法具有更好的收敛性和搜索效率。     

一种求解TSP问题的ACO&SS算法设计

提出一种求解旅行商(TSP)问题的新型分散搜索算法.将蚁群算法(ACO)的构解方法引入分散搜索(SS)算法,在搜索过程中既考虑解的质量,又考虑解的分散性.采用一种将蚁群算法的信息素更新技术与分散搜索的组合机制相结合的新型子集组合成新解的构解机制,同时采用动态更新参考集与临界准则策略来加快收敛速度.实验结果表明,该算法优于其他现有的方法,获得了较好的结果.