用遗传算法求解TSP问题

介绍TSP 问题和遗传算法的基本原理.针对解决TSP 问题,阐述遗传算法在编码表示和遗传操作算子等方面的应用情况,以及该算法在实现过程中的一些处理方法,最后给出该算法的运行结果和总结.     

基于QPSO方法优化求解TSP

针对粒子群优化算法PSO求解旅行商问题TSP收敛速度不够快的缺陷,提出利用量子粒子群优化算法QPSO求解TSP,在交换子和交换序概念的基础上,以Matlab语言为开发工具实现了TSP最佳路径的求解.实验表明改造QPSO算法用于优化求解14点的TSP,能够迅速得到最优解,收敛速度加快,搜索效率得到较大水平提高;QPSO方法在求解组合优化问题中将非常有效.     

用数据搅动算法求解TSP问题

TSP(旅行商问题)是一个典型的、易于描述的却难于处理的NP问题.本文采用数据搅动方法,给出了一个求解TSP问题算法.算法将距离矩阵的数据不断交换到路径特征点位置,路径长度会越来越短,渐渐靠近TSP的最优解.算法实现容易、运行速度较快.用该算法,找到了新的C-TSP路径,该路径比目前已得到的C-TSP最短路径缩短25公里.     

基于遗传算法求解TSP问题的一种算法

TSP问题是一个经典的NP难度的组合优化问题，遗传算法是求解TSP问题的有效方法之一。利用交换启发交叉算子实现局部搜索加快算法的收敛速度和利用变换变异算子维持群体的多样性防止算法早熟收敛，给出了一种求解TSP问题的遗传算法。仿真实验结果表明了该算法的有效性和可行性。     

基于人工代谢算法的TSP问题求解分析

通过分析生物体新陈代谢的生理机能,建立人工代谢算法模型.通过分析底物和生成物之间的浓度差建立多步催化反应动力学模型.通过对城市网络和代谢网络进行类比,建立基于浓度差的TSP问题寻优模型.实例推导表明,人工代谢算法能有效地实现TSP问题的寻优规划.     

旅行商问题(TSP)算法比较

将求解TSP问题的算法分为两大类:仿生算法和非仿生算法.通过实验比较两类算法在解决TSP问题时的优劣.实验结果表明,仿生算法是解决TSP问题的有效方法,在问题规模较大时,能够在允许的时间和误差内求得问题的解;而非仿生算法或者求解问题的规模很小,或者无法满足误差要求,因此都无法有效求解TSP问题.基于仿生算法在解决大规模组合优化问题时的有效性,论文提出了将仿生算法应用于云计算这一当今IT界热门话题的猜想.     

以TSP为代表的组合优化问题研究现状与展望

旅行商问题(TSP)是运筹学的著名命题,也是目前研究最为广泛的组合优化问题之一.对TSP的研究成果将对求解NP类问题产生重要影响.首先给出组合优化问题和TSP问题的基本概念.然后综述了以TSP为代表的组合优化问题的研究历史和现状,并着重对传统方法和启发式现代智能优化算法做了比较.最后对智能优化算法中的研究热点以及在TSP问题上的应用做了展望,预测了未来技术难点,并对今后可进一步研究的问题做了探讨.     

TSP问题的脂肪计算复杂性与启发式算法设计

旅行商问题(traveling salesman problem,简称TSP)是经典的NP-难解组合优化问题之一,求解它的高效启发式算法一直是计算机科学研究的热点.脂肪作为描述TSP结构特征的新工具,对启发式算法设计具有重要意义.目前,TSP问题的脂肪研究还处于初始阶段,缺乏理论分析结果及相关的启发式算法.首先分析了TSP问题的脂肪计算复杂性,通过构造偏移实例的技巧,证明了获取TSP的脂肪是NP-难解的,即在P(NP的假设下,不存在算法可以在多项式时间内获得完整脂肪.在此基础上,通过分析TSP问题局部最优解与脂肪的关系,给出了求解TSP问题的元启发式算法--动态候选集搜索(dynamic candidate set search,简称DCSS)算法.利用该算法,改进了目前求解TSP问题最好算法之一的LKH.TSPLIB典型实例的实验结果表明,改进后的算法在解的质量上有较为明显的提高.新的基于脂肪的启发式算法对于求解其他NP-难解问题具有一定的参考价值.     

一种并行ACS-2-opt算法处理TSP问题的方法

针对基本ACS算法模型求解TSP问题的缺陷,对ACS算法添加2-opt邻域搜索策略,增强算法对TSP问题解的构造能力,提高算法对TSP问题的求解精度。同时,根据ACS算法易于并行化的特点,使用并行化ACS算法与算法参数优化混合方案,提高ACS算法求解TSP问题的速度。最终实现了对中等规模TSP问题具有较好求解性能的并行ACS-2-opt算法。实验结果表明,2-opt策略对于提升ACS算法的求解精度具有明显的效果;采用不同参数设定信息素启发因子时,求解时间具有较大差异;在采用节点距离倒数作为期望启发值时,ACS算法模型呈现退化性;在并行条件下,ACS-2-opt算法处理TSP问题时具有良好的并行性能。     

求解TSP问题的一种启发式算法

TSP问题模型应用广泛,其求解策略的研究具有重要的理论和实践意义.根据TSP问题的特点,借鉴无向完全图上最小生成树的生成过程,设计了一种启发式算法对TSP问题进行求解.该算法的基本思想是以无向完全图上不同最小生成树为基础,采用启发式的方法构造不同闭合回路,最后取最短闭合回路作为最优解.文中采用C语言编程,同时分析了算法的性能和时间复杂度,并进行了大量仿真计算.结果表明设计的算法能够有效求得TSP问题的优化解.     

基于MATLAB遗传算法优化工具箱的优化计算

采用Matlab语言编制的遗传算法工具箱（GAOT）可实现二进制编码和真值编码的模拟进化计算，此工具箱在遗传操作方面非常灵活。介绍了用遗传算法工具箱解决了连续优化问题和旅行商问题，并给出了两个实例。     

遗传算法在旅行商问题中的实践与探究

TSP问题是组合优化领域的经典问题之一,旨在求出遍历若干个城市的最短路径。本文通过遗传算法GA的选择和变异算子的确定和、交叉算子的改进,并在TSP问题中的实践来探索这个经典的NP(Nondeterministic Polynomial)难题。     

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.     

改进微粒群优化算法求解旅行商问题

对微粒群优化算法的速度位置算式进行了改进,提出一种改进的微粒群优化算法。该算法符合组合优化问题的特点,在求解旅行商问题上有较高的搜索效率。将改进的PSO算法分别应用于14点的TSP问题以及中国旅行商问题中,该算法在较短时间内获得了目前已知的最好解。     

Hopfield网络求解TSP的算法改进

本文在对Hopfield神经网络求解旅行商(TSP)问题的算法进行研究的基础上结合实例针对典型改进算法的优缺点作了进一步探讨。     

A competitive neural network algorithm for solving vehicle routing problem

This paper describes a self organization Neural Network algorithm for a class of Vehicle Routing Problems. Motivated by the outstanding performance of adaptive Neural Network approach in the Traveling Salesman Problem, we devised an algorithm to extend the domain of applicability of this approach to more complex problems. First, relevant adaptation is proposed to refine the model for the Multiple Traveling Salesman Problem. Then, an additional mechanism to satisfy further constraints are embodied into the algorithm. The effectiveness of the proposed algorithm is evaluated by considering a series of standard problems from the literature. The results show that the algorithm can yield solutions within a few percent of optimality.     

A Memetic Algorithm with a large neighborhood crossover operator for the Generalized Traveling Salesman Problem

The Generalized Traveling Salesman Problem (GTSP) is a generalization of the well-known Traveling Salesman Problem (TSP), in which the set of cities is divided into mutually exclusive clusters. The objective of the GTSP consists in visiting each cluster exactly once in a tour, while minimizing the sum of the routing costs. This paper addresses the solution of the GTSP using a Memetic Algorithm. The originality of our approach rests on the crossover procedure that uses a large neighborhood search. This algorithm is compared with other algorithms on a set of 54 standard test problems with up to 217 clusters and 1084 cities. Results demonstrate the efficiency of our algorithm in both solution quality and computation time.     

基于遗传算法的TSP问题优化求解

旅行商问题（TSP）是典型的NP完全问题,本文运用遗传算法求解TSP问题,提出了该算法在解决这一问题中的一些处理方法,使用该算法能够较快地求出一批最短路径,可根据需要设置叠代代数,求得理想最优解。     

GRASP with path relinking for the symmetric Euclidean clustered traveling salesman problem

In this paper, we propose new heuristics using several path-relinking strategies to solve the Clustered Traveling Salesman Problem (CTSP). The CTSP is a generalization of the Traveling Salesman Problem (TSP) in which the set of vertices is partitioned into clusters and the objective is to find a minimum cost Hamiltonian cycle such that the vertices of each cluster are visited continuously. A comparison among the performance of the several different adopted path-relinking strategies is presented using instances with up to 2000 vertices and clusters varying between 4 and 150 vertices. Also computational experiments were performed to compare the performance of the proposed heuristics with an exact algorithm and a Genetic Algorithm. The obtained computational results showed that the proposed heuristics were able to obtain competitive results related to the quality of the solutions and computational execution time.     

Exponential Lower Bounds on the Complexity of?a?Class of?Dynamic Programs for Combinatorial Optimization Problems

We prove exponential lower bounds on the running time of Dynamic Programs (DP) of a certain class for some Combinatorial Optimization Problems. The class of DPs for which we derive the lower bounds is general enough to include well-known DPs for Combinatorial Optimization Problems, such as the ones developed for the Shortest Path Problem, the Knapsack Problem, or the Traveling Salesman Problem. The problems analyzed include the Traveling Salesman Problem (TSP), the Bipartite Matching Problem (BMP), the Min and the Max Cut Problems (MCP), the Min Partition Problem (MPP), and the Min Cost Test Collection Problem (MCTCP). We draw a connection between Dynamic Programs and algorithms for polynomial evaluation. We then derive and use complexity results of polynomial evaluation to prove similar results for Dynamic Programs for the TSP or the BMP. We define a reduction between problems that allows us to generalize these bounds to problems for which either the TSP or the BMP transforms to. Moreover, we show that some standard transformations between problems are of this kind. In this fashion, we extend the lower bounds to other Combinatorial Optimization Problems.