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。     

一种基于改进遗传算法的TSP问题求解方法

通过改进经典遗传算法的交叉算子和变异算子,提出了一种改进遗传算法。介绍了该算法的基本步骤及特点,并对TSP问题进行了仿真实验。实验结果表明改进算法有效地提高了算法的收敛速度与寻优质量,在解决TSP问题时表现出良好特性,与经典遗传算法相比具有明显优势。     

一种新的动态TSP模型及其求解方法

TSP问题是经典的NP难问题,学者们已经提出很多有效的方法,但大多都是基于静态情形的,然而现实中的TSP问题基本为动态的,动态TSP将是一个更符合实际TSP问题的研究领域。提出了一种基于高斯扰动的动态TSP模型,设计了扰动响应算法,并对反序交叉算子做了改进。实验证明该算法的有效性和新模型的现实意义。     

基于遗传算法的TSP问题求解算法及其系统

TSP问题为组合优化中的经典的NP完全问题。针对这一问题,首先设计了基于遗传算法的求解算法,包括编码设计、适应度函数选择、终止条件设定、选择算子设定、交叉算子设定以及变异算子设定等,给出了基于遗传算法求解TSP问题的一般性流程,然后设计并实现了基于遗传算法的TSP问题求解系统,给出了求解系统的体系结构,并给出了求解系统基于Ja-va语言的实现机制,最后通过实验结果的分析,表明了算法具有较好的寻优性能,系统具有较好的实用性。     

遗传算法在TSP问题中的应用

文章首先介绍TSP问题与遗传算法的基本特点及其基本步骤。接着讨论用遗传算法解决TSP问题的编码、适应度函数设计方面的采用的方法,以及选择算子,交叉算子和变异算子的应用现状以及效果,最后对解决TSP问题的前景提出了展望。     

旅行商问题的一种插入交叉算子

求解TSP问题是遗传算法应用的一个重要领域,其本质是TSP问题中巡回路径编码串的组合最优化问题。对于符号编码方式的遗传算法,通常需要设计特定的交叉算子以提高算法的运行效率和性能。该文针对自然数编码的方式,提出了一种较适合于大规模TSP问题求解的遗传交叉算子:插入交叉(InsertCrossover,简称IX)算子。该算子以优良的交叉策略,保证了算法的快速收敛和全局寻优。仿真实验结果证明,IX算子对于大规模TSP问题具有比较好的性能。     

基于改进反序-杂交算子的免疫克隆选择算法

反序-杂交算子在求解TSP时容易陷入局部最优。为了优化电路板布局,提高计算快速性,对反序-杂交算子进行了改进,设计了1st-Inver-over算子和2nd-Inver-over算子。采用1st-Inver-over算子和2nd-Inver-over算子作为主要免疫基因操作算子实现了求解TSP的免疫克隆算法,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的选取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。仿真结果表明,Inver-over ICSA比经典的GT算法具有更好的收敛性和搜索效率。     

一种求解欧式平面TSP问题的混合算法

TSP问题是一个经典的组合优化问题。本文采用基于凸多边形的插入方法来构造路径,然后使用调整算法对路径进行调整以缩短回路长度,最后采用遗传算法中的交叉算子,再对路径进行优化。实验结果表明,该算法具有较高精度和较强实用性。     

一种改进的TSP启发交叉算子

旅行商问题（TSP,Traveling Salesman Problem）是一种经典的NP组合优化问题。遗传算法在求解这类组合问题方面明显优于传统算法,同时也提出了许多求解较好路径的交叉算子。在对比分析唐立新提出的两种启发式交叉算法的基础上,提出了一种新的交叉算子。该算子通过判断父代的城市是否相邻来保存有效基因片断,通过加入一个移动的窗口来加快算法收敛。实验结果表明了该算子的有效性。     

求解TSP问题的一种混合遗传算法

文章针对TSP问题的特点,设计了一个求解TSP问题的混合遗传算法。该算法中设计了贪婪子路交叉算子,引入2OPT算子增强遗传算法的局部搜索能力,在选择算子设计中引入稳定状态选择机制。通过KroB100、pr136、pr144、kroB150、CHC144…问题的求解结果表明该遗传算法设计在求解TSP问题中是高效的。     

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.     

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.     

The online Prize-Collecting Traveling Salesman Problem

We study the online version of the Prize-Collecting Traveling Salesman Problem (PCTSP), a generalization of the Traveling Salesman Problem (TSP). In the TSP, the salesman has to visit a set of cities while minimizing the length of the overall tour. In the PCTSP, each city has a given weight and penalty, and the goal is to collect a given quota of the weights of the cities while minimizing the length of the tour plus the penalties of the cities not in the tour. In the online version, cities are disclosed over time. We give a 7/3-competitive algorithm for the problem, which compares with a lower bound of 2 on the competitive ratio of any deterministic algorithm. We also show how our approach can be combined with an approximation algorithm in order to obtain an O(1)-competitive algorithm that runs in polynomial time.     

An efficient hybrid algorithm for the Traveling Car Renter Problem

This paper tackles a Traveling Salesman Problem variant called Traveling Car Renter Problem, where one car renter desires to travel among cities using a rented vehicle. Basically, the car renter has two options when he/she arrives in a city: to return the vehicle and rent another one or to keep the same car until the next city. Every time a car is delivered in a city, a return fee must be paid. Travel cost between any pair of cities also depends on the chosen car. The objective is to establish a Hamiltonian cycle minimizing the travel costs and returning fees. An evolutionary algorithm (EA) and a hybrid method called Adaptive Local Search Procedure (ALSP) are proposed for this problem. Both were compared to the best known algorithm in literature and obtained better results for non-Euclidean instances. Such algorithms compose an efficient model for a better exploration of the problem solutions space. From the expert system point-of-view, we propose a novel inference engine with minimized results error.     

基于自组织优化算法的一类多旅行商问题

多旅行商问题作为旅行商问题的一个扩展,是一个经典的组合优化问题,具有更高的复杂性,也具有更广泛的实际意义。针对每个旅行商允许经过的城市数有上限的多旅行商问题,通过引入虚拟城市把多旅行商问题转化为单旅行商问题,并且应用自组织优化算法进行了求解。虚拟城市局部适值的定义很好地处理了此类问题的能力约束,针对多旅行商问题的实例进行的仿真表明自组织优化算法可以很好地求解此类问题。     

Profit maximization of TSP through a hybrid algorithm

Here a new model of Traveling Salesman Problem (TSP) with uncertain parameters is formulated and solved using a hybrid algorithm. For this TSP, there are some fixed number of cities and the costs and time durations for traveling from one city to another are known. Here a Traveling Salesman (TS) visits and spends some time in each city for selling the company’s product. The return and expenditure at each city are dependent on the time spent by the TS at that city and these are given in functional forms of t. The total time limit for the entire tour is fixed and known. Now, the problem for the TS is to identify a tour program and also to determine the stay time at each city so that total profit out of the system is maximum. Here the model is solved by a hybrid method combining the Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO). The problem is divided into two subproblems where ACO and PSO are used successively iteratively in a generation using one’s result for the other. Numerical experiments are performed to illustrate the models. Some behavioral studies of the models and convergences of the proposed hybrid algorithm with respect to iteration numbers and cost matrix sizes are presented.     

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。     

一种改进的求解TSP问题的演化算法

演化算法是解决组合优化问题的高效搜索算法．该文在现有求解TSP问题的演化算法的基础上,通过引入映射算子、优化算子以及增加一些控制策略,提出了一种高效的演化搜索算法．实验表明,该算法是有效的,通过对CHN144以及国际通用的TSPLIB中不同城市规模的数据进行测试表明,其中实例CHN144得到的最短路径为30353．860997,优于吴斌等运用分段算法得到的最短路径30354．3,亦优于朱文兴等人的结果,实例st70和kroB150得到的最短路径分别与运用分段算法得到的最短路径值相同,实例pr136得到的最短路径值为96770．924122,优于TSPLIB中提供的最短路径96772,对于其它实例也均能快速地得到和TSPLIB中提供的最优路径相同或更优的路径,该算法不仅很容易收敛到问题的最优解,而且求解速度极快．     

遗传算法在旅行商问题的研究与应用

旅行商问题（TSP）是一类典型的非确定性多项式（NP）完全组合优化问题.针对基本遗传算法在求解这类问题时容易出现局部收敛现象,提出了改进,采用轮盘赌和优秀个体复制相结合的方法进行选择,对11个城市的旅行商问题进行研究,通过比较发现取得良好的收敛,该方法在解决很多NP完全组合优化问题上同样适用.     

求解TSP问题的拟人算法

基于贪心算法提出了一种改进的求解旅行商问题(TSP)的拟人算法.该算法采用邻域定义,主要思想是:给定一个所有城市的全排列,依此全排列的指挥用贪心算法生成一个回路.通过城市交换和城市序列平移,在当前的邻域中搜索比它更好的解,如能找到如此的解,则使之成为新的当前解,然后重复上述过程.在搜索的过程中,采取跳坑策略以跳出局部最...