Branch-and-bound for the Precedence Constrained Generalized Traveling Salesman Problem

The Precedence Constrained Generalized Traveling Salesman Problem (PCGTSP) combines the Generalized Traveling Salesman Problem (GTSP) and the Sequential Ordering Problem (SOP). We present a novel branching technique for the GTSP which enables the extension of a powerful pruning technique. This is combined with some modifications of known bounding methods for related problems. The algorithm manages to solve problem instances with 12–26 groups within a minute, and instances with around 50 groups which are denser with precedence constraints within 24 h.     

GENI Ants for the Traveling Salesman Problem

In this paper, the probabilistic nearest neighbor heuristic, which is at the core of classical ant colony systems for the Traveling Salesman Problem, is replaced by an alternative insertion procedure known as the GENI heuristic. The benefits provided by GENI-based ants are empirically demonstrated on a set of benchmark problems, through a comparison with the classical ant colony system and an iterated GENI heuristic.     

The Attractive Traveling Salesman Problem

In the Attractive Traveling Salesman Problem the vertex set is partitioned into facility vertices and customer vertices. A maximum profit tour must be constructed on a subset of the facility vertices. Profit is computed through an attraction function: every visited facility vertex attracts a portion of the profit from the customer vertices based on the distance between the facility and customer vertices, and the attractiveness of the facility vertex. A gravity model is used for computing the profit attraction. The problem is formulated as an integer non-linear program. A linearization is proposed and strengthened through the introduction of valid inequalities, and a branch-and-cut algorithm is developed. A tabu search algorithm is also implemented. Computational results are reported.     

Expanding Neighborhood GRASP for the Traveling Salesman Problem

In this paper, we present the application of a modified version of the well known Greedy Randomized Adaptive Search Procedure (GRASP) to the TSP. The proposed GRASP algorithm has two phases: In the first phase the algorithm finds an initial solution of the problem and in the second phase a local search procedure is utilized for the improvement of the initial solution. The local search procedure employs two different local search strategies based on 2-opt and 3-opt methods. The algorithm was tested on numerous benchmark problems from TSPLIB. The results were very satisfactory and for the majority of the instances the results were equal to the best known solution. The algorithm is also compared to the algorithms presented and tested in the DIMACS Implementation Challenge that was organized by David Johnson.     

用嵌套插队算法解决TSP问题

本提出了一种求解TSP问题的近似算法—嵌套插队算法。这种算法结合了启发式算法和随机化算法以及局部寻优的思想。实验结果表明对于较小规模的。TSP问题，直接用插队算法(QJA)就能以很大的概率获得已知最优解。对于规模较大的问题实例。嵌套插队算法(NQJA)能获得质量高于名的启发式算法的解。另外，用嵌套插队算法找到的China144的最短路径优于目前已知的最短路径。嵌套插队算法是专门针对TSP问题而提出的，但其思想也可以给求解其他NP难解的组合优化问题以启发。     

Multi-objective Meta-heuristics for the Traveling Salesman Problem with Profits

We introduce and test a new approach for the bi-objective routing problem known as the traveling salesman problem with profits. This problem deals with the optimization of two conflicting objectives: the minimization of the tour length and the maximization of the collected profits. This problem has been studied in the form of a single objective problem, where either the two objectives have been combined or one of the objectives has been treated as a constraint. The purpose of our study is to find solutions to this problem using the notion of Pareto optimality, i.e. by searching for efficient solutions and constructing an efficient frontier. We have developed an ejection chain local search and combined it with a multi-objective evolutionary algorithm which is used to generate diversified starting solutions in the objective space. We apply our hybrid meta-heuristic to synthetic data sets and demonstrate its effectiveness by comparing our results with a procedure that employs one of the best single-objective approaches.      

灰色TSP问题的研究

在确定型TSP问题的基础上,融合灰色系统的思想提出了灰色TSP问题,构建了灰色TSP问题的动态规划模型,结合动态规划方法利用可能度及排序方法给出了求解灰色TSP问题的算法,并结合数值实例,对算法进行了说明.     

带有配额的在线Nomadic旅行商问题

由于自然灾害的频繁发生,灾后的应急物资车辆调度受到了社会的广泛重视,而应急车辆尽快地将应急物资送到受灾点显得尤为重要。针对应急车辆装载物资能力有限和应急车辆不必返回出发点的情形,提出了带有配额的在线Nomadic旅行商问题。分析了该问题在正半轴和一般网络上的下界,针对受灾点仅在正半轴上的情形设计了WTAIB算法,针对受灾点在一般网络上设计了WSB算法,并进一步分析了两个算法的竞争性能。     

非对称距离的旅行商问题的构造算法

章分析了非对称距离的旅行商问题,讨论了节约算法与最小生成树算法两种启发式方法,并用实例进行了说明,最后对算法的有效性进行了说明。     

一个关于非对称距离的旅行商问题的迭代算法

本对非对称距离的旅行商问题，给出了一个迭代算法，并分析了此迭代算法的复杂度为M^nO(N^4)，其中，N是问题中旅行商所要经过的城镇数，M是两城镇间的最大距离。最后用实例对此算法进行了验算和说明。     

A New Memetic Algorithm for the Asymmetric Traveling Salesman Problem

This paper introduces a new memetic algorithm specialized for the asymmetric instances of the traveling salesman problem (ATSP). The method incorporates a new local search engine and many other features that contribute to its effectiveness, such as: (i) the topological organization of the population as a complete ternary tree with thirteen nodes; (ii) the hierarchical organization of the population in overlapping clusters leading to the special selection scheme; (iii) efficient data structures. Computational experiments are conducted on all ATSP instances available in the TSPLIB, and on a set of larger asymmetric instances with known optimal solutions. The comparisons show that the results obtained by our method compare favorably with those obtained by several other algorithms recently proposed for the ATSP.     

A concise guide to the Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is one of the most famous problems in combinatorial optimization. Hundreds of papers have been written on the TSP and several exact and heuristic algorithms are available for it. Their concise guide outlines the most important and best algorithms for the symmetric and asymmetric versions of the TSP. In several cases, references to publicly available software are provided.     

求解旅行商问题的搜寻者遗传算法

针对简单遗传算法易陷入局部最优及收敛速度慢的不足,提出一种改进遗传算法-基于启发式策略的搜寻者遗传算法.首先将搜寻者优化算法中的模糊思想和近邻策略相结合改进变异算子,增强种群多样性,避免陷入局部最优;然后针对路径优化问题基于启发式策略设计反转算子,使得路径中不存在交叉边,加快收敛速度;最后将改进遗传算法用于求解旅行商问题.结果表明,改进遗传算法的求解精度和求解效率明显优于基本遗传算法.     

求解旅行商问题的一种改进粒子群算法

本文研究了求解旅行商问题的粒子群算法。针对标准粒子群算法在求解旅行商问题过程中容易出现早熟和停滞现象的缺点,提出了一种改进的粒子群算法。首先,在初始种群的选取过程中,利用改进的贪婪策略直接获得具有较高性能的初始种群以提高算法的搜索效率。其次,通过引入次优吸引子,使粒子在搜索过程中可以更加充分地利用群体的信息来提高自身的性能,有效抑制收敛过程中的停滞现象,提高算法的搜索能力。最后为了验证所提出的方法的有效性和可行性,对TSPLIB标准库中的多个实例进行了测试,并给出了数值结果。     

A Positive Semidefinite Approximation of the Symmetric Traveling Salesman Polytope

For a convex body B in a vector space V, we construct its approximation P_k, k =1 , 2, . . ., using an intersection of a cone of positive semidefinite quadratic forms with an affine subspace. We show that P_k is contained in B for each k. When B is the Symmetric Traveling Salesman Polytope on n cities T_n, we show that the scaling of P_k by n/k + O(1/n) contains T_n for . Membership for P_k is computable in time polynomial in n (of degree linear in k). We also discuss facets of T_n that lie on the boundary of P_k and we use eigenvalues to evaluate our bounds.     

基于混合的细菌觅食算法求解TSP问题

针对求解经典NP问题—旅行商难题(TSP),在标准细菌觅食算法上进行改进,提出了混合的细菌觅食算法(HBFA).一方面引入编码交叉思想对趋势步进行改进,使算法能更有效地处理离散优化问题;另一方面采用了自适应迁徙算子,使新生个体带有最优个体启发式信息的同时也增强了算法跳出局部最优能力.最后通过对TSPLIB中若干实例的实验仿真以及多种算法对比,验证了算法的可行性和有效性.     

A Tabu Search Approach for the Prize Collecting Traveling Salesman Problem

The Prize Collecting Traveling Salesman Problem is a generalization of the Traveling Salesman Problem. A salesman collects a prize for each visited city and pays a penalty for each non visited city. The objective is to minimize the sum of the travel costs and penalties, but collecting a minimum pre-established amount of prizes. This problem is here addressed by a simple, but efficient tabu search approach which had improved several upper bounds of the considered instances.     

启发式匈牙利法求解货郎担问题

针对利用动态规划求解货郎担问题的复杂难度,提出了启发式匈牙利法求解,给出了它的算法步骤及时间复杂度分析,并通过实例具体描述了启发式匈牙利法求解的过程,发现能够较快地找到最优方案,算法具有一定的实用性.     

A Simultaneous Enumeration Approach to the Traveling Salesman Problem

The solution procedure proposed in this paper uses certain principles of analog computers. The idea of using analog rather than digital computers to solve mathematical programming problems is not new—various methods have been proposed to solve linear programming, network flows, as well as shortest path problems (Dennis, 1959; Stern, 1965). These problems can be more efficiently solved with digital computers. To find a solution to the traveling salesman problem as well as other integer programming problems is difficult with existing hardware, especially if the number of variables is large. The question thus arises whether different hardware configurations make it possible to solve integer problems more efficiently. One such configuration is proposed below for the traveling salesman problem.