基于递阶遗传算法的多旅行商问题优化*

旅行商问题是一个经典的NP问题,对多人旅行商问题的求解则更具有意义。为了解决所有旅行商路径总和最小为优化标准的多旅行商一类问题,提出了一种递阶遗传算法和矩阵解码方法。该算法根据问题的特点,采用一种递阶编码方案,此编码与多旅行商问题一一对应。用递阶遗传算法优化多旅行商问题无须设计专门的遗传算子,操作简单,并且解码方法适于求解距离对称和距离非对称的多旅行商问题。计算结果表明,递阶遗传算法是有效的,能适用于优化多旅行商问题。     

基于遗传算法的多旅行商问题研究

针对所有旅行商路径总和最小为优化标准的多旅行商一类问题,用遗传算法优化,并提出了矩阵解码方法。对距离非对称的多旅行商问题的实例进行了仿真,并对不同交叉算子性能进行了比较。结果表明,该算法是有效的,适用于距离对称和非对称的多旅行商问题求解。     

基于遗传算法的一类多旅行商问题研究

旅行商问题是一个经典的NP完全问题,对多人旅行商问题的求解则更具有意义。以往对求解多人旅行商问题的研究局限于以所有旅行商路径总和最小为优化标准,而对所有旅行商路径最大值最小的多旅行商一类问题研究的相对较少。针对所有旅行商路径最大值最小的多旅行商一类问题,用遗传算法优化,并且提出了矩阵解码方法。该方法适于距离对称和非对称的多旅行商问题求解。以距离非对称的多旅行商问题的实例进行了仿真,并对不同交叉算子性能进行了比较。     

用自适应离散微粒群算法求解旅行商问题

提出一种求解GTSP问题的自适应离散PSO算法,同时考虑到多种算法的混合,利用调节算子和交换序对PSO算法进行改进.通过对Buramal14,Oliver30和Eil51等测试数据进行实验,证明新算法不仅收敛速度快、鲁棒性更好,而且新的算法对于Burma14和Oliver30更易求得它们的最优解。     

基于GA的最小旅行时间的多旅行商问题研究*

以往对求解多人旅行商问题的研究局限于以所有旅行商路径总和最小为优化标准,而对最小完成时间的多旅行商一类问题研究得相对较少。针对所有旅行商最小完成时间的多旅行商一类问题,用遗传算法进行优化,且提出了矩阵解码方法。以距离非对称的多旅行商问题的实例进行了仿真,并对不同交叉算子性能进行了比较,适于距离对称和非对称的多旅行商问题求解。     

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.     

基于HGA的最小旅行时间多旅行商问题研究

为了解决最小化旅行时间的多旅行商一类问题,提出了一种递阶遗传算法和矩阵解码方法。该算法根据问题的特点,采用一种递阶编码方案,此编码与多旅行商问题一一对应。用递阶遗传算法优化多旅行商问题不需设计专门的遗传算子,操作简单,并且解码方法适于求解距离矩阵对称和距离矩阵非对称的多旅行商问题。计算结果表明,递阶遗传算法是有效的,能适用于优化最小化完成时间的多旅行商问题。     

指针网络改进遗传算法求解旅行商问题

虽然遗传算法相较于其他算法能够更好地求解旅行商问题,但这种算法在使用的过程中容易陷入局部最优的问题,进而导致问题求解遭遇困境。文章在简要介绍旅行商问题的基础上,介绍了遗传算法求解旅行商问题的思路和方法,并明确算法应用中存在的不足。在此基础上提出基于指针网络改进遗传算法求解旅行商问题的新思路,为弥补遗传算法的缺陷提供相应的原理支持。     

最小比率旅行商(MRTSP)问题竞争决策算法

针对最小比率旅行商问题,利用竞争决策算法的通用模型,给出了一种基于竞争决策思想、能求对称型最小比率旅行商问题的快速求解方法,经过数据测试和验证,获得了较好的结果。     

遗传算法的应用举例

遗传算法作为一种通用、高效的优化算法,已应用到工程计算的各个领域。该文首先简要阐述了遗传算法的基本原理和其操作步骤。同时为了验证其全局的寻优能力,采用MATLAB语言编制程序实现遗传算法对数值优化和旅行商问题的求解,需要说明的是这两类问题的程序编制和求解分别依赖于不同的已有遗传算法工具箱。为了便于说明遗传算法的优越性,分别将对数值优化和旅行商问题的计算结果与用局域搜索法和模拟退火得出的优化结果进行比较。比较结果表明,对于数值优化问题,遗传算法比局域搜索法具有更佳的寻优能力;对于旅行商问题的求解也能得到满意的结果。     

An Algorithm for the One Commodity Pickup and Delivery Traveling Salesman Problem with Restricted Depot

In this paper we study the one commodity pickup-and-delivery traveling salesman problem with restricted depot (1-PDTSP-RD), which is a generalization of the classical traveling salesman problem (TSP). We first introduce a polynomial size integer programming formulation for the problem and then study the feasibility issue which is shown to be \(\mathcal {NP}\)-complete by itself. In particular, we prove sufficient conditions for the feasibility of the problem and provide a polynomial algorithm to find a feasible solution. We also develop a bound on the cost of the 1-PDTSP-RD solution in terms of the cost of the TSP solution. Based on this bound, we provide a heuristic algorithm to solve the 1PDTSP-RD. Extensive numerical experiments are performed to evaluate the efficiency of both the exact and approximation algorithms.     

论遗传算法在旅行商问题中的应用

旅行商问题是算法应用中的基本问题,遗传算法具有通用性、智能性、鲁棒性、全局性和并行性的特点,正好适合于该问题的求解。但基本遗传算法在解决旅行商问题时效率不高,并且容易陷于局部最优解。为了解决这一问题,提出了一种改进的遗传算法。文章首先对旅行商问题进行了描述,对遗传算法进行了介绍,对其中的个体选择、交叉算法等重要因素做了一定地改进。最后,用一个简单的实例对基本遗传算法和改进的遗传算法进行了比较,发现改进的遗传算法在解决旅行商问题上的效率问题上有了一定的提高。     

求解广义旅行商问题的混合染色体遗传算法

提出了针对广义旅行商问题（GTSP）的混合染色体遗传算法（HCGA）。目前,广义染色体遗传算法（GCGA）是求解GTSP问题的最好方法,但这种方法在编码设计上存在不足,使得算法全局搜索能力较差。在GCGA算法基础上,设计了二进制和整数混合编码的染色体,并更新了交叉和变异算子设计,得到改进算法HCGA。理论和实验结果都说明：HCGA比GCGA等多种算法具有更强的全局搜索能力。     

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.     

Improving Combinatorial Optimization Algorithms through Record Keeping in Constructive Multistart Search

Constructive multistart search algorithms are commonly used to address combinatorial optimization problems; however, constructive multistart search algorithm performance is fundamentally affected by two factors: (i) The choice of construction algorithm utilized and (ii) the rate of state space search redundancy. Construction algorithms are typically specific to a particular combinatorial optimization problem; therefore, we first investigate construction algorithms for iterative hill climbing applied to the traveling salesman problem and experimentally determine the best performing algorithms. We then investigate the more general problem of utilizing record‐keeping mechanisms to mitigate state space search redundancy. Our research shows that a good choice of construction algorithm paired with effective record keeping significantly improves the quality of traveling salesmen problem solutions in a constant number of state explorations. Particularly, we show that Bloom filters considerably improve time performance and solution quality for iterative hill climbing approaches to the traveling salesman problem.     

旅行商问题的DNA算法

旅行商问题是求仅一次遍访指定城市并返回出发城市的最短旅行路线的问题,它是图论中一个经典的NP完全问题,用电子计算机需要指数级的时间才能得到解决,该文基于分子生物技术并利用Adleman-Lipton模型给出旅行商问题的DNA算法,这个DNA算法理论上能在多项式的时间内解决这个NP完全问题。具体地对n个城市的旅行商问题,首先将它视为一个具有顶点和边的图,并将顶点、边分别用DNA链编码表示,边的方向通过顶点的编码获得;再将这些DNA链投放在试管中进行生物化学反应,利用DNA计算的高效并行性,通过基本的生物实验操作最后得到旅行商问题的解,其过程的复杂度为O(n)。该算法的创新之处在于表示城市和路径的DNA链长度的设计,能使我们在合理小的范围内寻找旅行商问题的解,较大地简化了问题的复杂度。     

A new formulation and approach for the black and white traveling salesman problem

This paper proposes a new formulation and a column generation approach for the black and white traveling salesman problem. This problem is an extension of the traveling salesman problem in which the vertex set is divided into black vertices and white vertices. The number of white vertices visited and the length of the path between two consecutive black vertices are constrained. The objective of this problem is to find the shortest Hamiltonian cycle that covers all vertices satisfying the cardinality and the length constraints. We present a new formulation for the undirected version of this problem, which is amenable to the Dantzig–Wolfe decomposition. The decomposed problem which is defined on a multigraph becomes the traveling salesman problem with an extra constraint set in which the variable set is the feasible paths between pairs of black vertices. In this paper, a column generation algorithm is designed to solve the linear programming relaxation of this problem. The resulting pricing subproblem is an elementary shortest path problem with resource constraints, and we employ acceleration strategies to solve this subproblem effectively. The linear programming relaxation bound is strengthened by a cutting plane procedure, and then column generation is embedded within a branch-and-bound algorithm to compute optimal integer solutions. The proposed algorithm is used to solve randomly generated instances with up to 80 vertices.     

An Explicit Lower Bound for TSP with Distances One and Two

We show that, for any ?>0 , it is NP-hard to approximate the asymmetric traveling salesman problem with distances one and two within 2805/2804-? . For the special case where the distance function is constrained to be symmetric, we show a lower bound of 5381/5380-? , for any ?>0 . While it was previously known that there exists some constant, strictly greater than one, such that it is NP-hard to approximate the traveling salesman problem with distances one and two within that constant, this result is a first step towards the establishment of a good bound. In our proof we develop a new gadget construction to reduce from systems of linear equations mod 2 with two unknowns in each equation and at most three occurrences of each variable. Compared with earlier reductions to the traveling salesman problem with distances one and two, ours reduces the number of cities to less than a tenth of what was previously necessary.     

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.     

Hybrid elitist-ant system for a symmetric traveling salesman problem: case of Jordan

This work investigates the performance of a hybrid population-based meta-heuristic with an external memory structure of a hybrid elitist-ant system (elitist-AS). This memory is known as an elite pool, which contains high quality and diverse solutions to maintain a balance between diversity and quality of the search. This may guarantee the effectiveness and efficiency of the search, which could enhance the performance of the algorithm across different instances. A very well known and intensively studied NP-hard optimization problem has been selected to test the performance of the hybrid elitist-AS via its consistency, effectiveness and efficiency. This famous problem is the symmetric traveling salesman problem. The elitist-AS is a class of ant colony optimization techniques which are known to be outstanding for the traveling salesman problem where they have the ability to find the shortest tours guided by the heuristic and the pheromone trail information. An iterated local search is combined with elitist-AS to intensify the search around elite solution and maintains the solution’s exploitation mechanism. Experimental results showed that the performance, compared to the best known results, is optimal for many instances. This finding indicates the effectiveness, efficiency and consistency in diversifying the search while intensifying high-quality solutions. This outstanding performance is due to the utilization of an elite pool along with diversification and intensification mechanisms. In addition, this work proposes two instances that consist of 26 Jordanian cities and 1094 Jordanian locations which have been generated based on coordinates and distances similar to the format of the selected symmetric traveling salesman problem. This step is meant to contribute to finding a solution for a real-world problem and further test the performance of the hybrid elitist-AS.