Heuristic algorithms for the 2-period balanced Travelling Salesman Problem in Euclidean graphs

In the 2-period Travelling Salesman Problem some nodes, called double nodes, are visited in both of two periods while the remaining ones, called single nodes, are visited in either one of the periods. In this paper we study the case in which a balance constraint is also introduced. We require that the difference between the number of visited nodes in the two periods must be below a fixed threshold. Moreover, we suppose that distances between nodes are Euclidean. The problem is NP-hard, and exact methods, now available, appear inadequate. Here, we propose three heuristics. Computational experiences and a comparison between the algorithms are also given.     

Heuristic for the Asymmetric Travelling Salesman Problem

The paper describes a heuristic algorithm for the asymmetric travelling salesman problem. The procedure is a generalization of Webb's Simple Loss 1 Method and is of the sequential type, i.e. in each step one link of the tour is fixed. The method proved to produce "high quality" near optimal solutions in a computing time, which only grows proportional to n^1.82.     

Well-tuned algorithms for the Team Orienteering Problem with Time Windows

The Team Orienteering Problem with Time Windows (TOPTW) is the extension of the Orienteering Problem (OP) where each node is limited by a predefined time window during which the service has to start. The objective of the TOPTW is to maximize the total collected score by visiting a set of nodes with a limited number of paths. We propose two algorithms, Iterated Local Search and a hybridization of Simulated Annealing and Iterated Local Search (SAILS), to solve the TOPTW. As indicated in multiple research works on algorithms for the OP and its variants, determining appropriate parameter values in a statistical way remains a challenge. We apply Design of Experiments, namely factorial experimental design, to screen and rank all the parameters thereby allowing us to focus on the parameter search space of the important parameters. The proposed algorithms are tested on benchmark TOPTW instances. We demonstrate that well-tuned ILS and SAILS lead to improvements in terms of the quality of the solutions. More precisely, we are able to improve 50 best known solution values on the available benchmark instances.     

An approximation algorithm for a symmetric Generalized Multiple Depot, Multiple Travelling Salesman Problem

In this paper, we present an algorithm with an approximation factor of 2 for a Generalized, Multiple Depot, Multiple Travelling Salesman Problem (GMTSP) when the costs are symmetric and satisfy the triangle inequality. The algorithm requires finding a degree constrained minimum spanning tree which we compute using a Lagrangian relaxation.     

Exact and heuristic algorithms for routing problems

This is a summary of the authors PhD thesis supervised by Daniele Vigo and defended on 30 March 2010, at the Università di Bologna. The thesis is written in English and is available from the author upon request. Several rich routing problems attaining to the transportation area have been studied. “Simple” algorithms have been proposed to solve them, both exact and heuristic, producing high quality solutions and transferrable methods.     

多行程带时间窗口的车辆调度问题研究

为了提高车辆的使用率,企业往往会安排车辆在单位周期内,执行多次配送任务.为了研究多行程带时间窗口的车辆配送(VRPTW)中的车辆调度问题.模型以车辆的固定费用、车辆行驶过程中的等待费用、司机的工作小时费最小为目标,同时也融合了司机在执行不同路线时,由于熟悉的过程所弓I起的费用.通过对路线的时间窗口性质的分析,建立了调度问题的模型.     

旅行推销员问题的算法综述

本文综述了旅行推销员问题 (TSP)近几十年来的算法研究进展 ,给出了一些主要算法的求解思想及其时间复杂度     

New lower bounds for the Symmetric Travelling Salesman Problem

In this paper new lower bounds for the Symmetric Travelling Salesman Problem are proposed and combined in additive bounding procedures. Efficient implementations of the algorithms are given; in particular, fast procedures for computing the linear programming reduced costs of the Shortest Spanning Tree (SST) Problem and for finding all ther-SST of a given graph, are presented. Computational results on randomly generated test problems are reported.     

Some Simple Applications of the Travelling Salesman Problem

The travelling salesman problem arises in many different contexts. In this paper we report on typical applications in computer wiring, vehicle routing, clustering and job-shop scheduling. The formulation as a travelling salesman problem is essentially the simplest way to solve these problems. Most applications originated from real world problems and thus seem to be of particular interest. Illustrated examples are provided with each application.     

Some Applications of the Generalized Travelling Salesman Problem

In the Generalized Travelling Salesman Problem (GTSP), the aim is to determine a least cost Hamiltonian circuit or cycle through several clusters of vertices. It is shown that a wide variety of combinatorial optimization problems can be modelled as GTSPs. These problems include location-routeing problems, material flow system design, post-box collection, stochastic vehicle routeing and arc routeing.     

Branch-and-cut algorithms for the undirected m-Peripatetic Salesman Problem

In the m-Peripatetic Salesman Problem (m-PSP) the aim is to determine m edge disjoint Hamiltonian cycles of minimum total cost on a graph. This article describes exact branch-and-cut solution procedures for the undirected m-PSP. Computational results are reported on random and Euclidean graphs.     

Solving the Asymmetric Travelling Salesman Problem with time windows by branch-and-cut

Many optimization problems have several equivalent mathematical models. It is often not apparent which of these models is most suitable for practical computation, in particular, when a certain application with a specific range of instance sizes is in focus. Our paper addresses the Asymmetric Travelling Salesman Problem with time windows (ATSP-TW) from such a point of view. The real–world application we aim at is the control of a stacker crane in a warehouse.?We have implemented codes based on three alternative integer programming formulations of the ATSP-TW and more than ten heuristics. Computational results for real-world instances with up to 233 nodes are reported, showing that a new model presented in a companion paper outperforms the other two models we considered – at least for our special application – and that the heuristics provide acceptable solutions. Received: August 1999 / Accepted: September 2000?Published online April 12, 2001     

Visual Interactive (Computer) Solutions for the Travelling Salesman Problem

A visual interactive method of improving solutions for the travelling salesman problem is described. The travelling or multiple travelling salesman problem, when constraints are included, forms the core of the local delivery routing problem. The approach described in this note may be modified to give a visual interactive method of investigating practical physical distribution problem situations.     

An iterated local search algorithm for the Travelling Salesman Problem with Pickups and Deliveries

The Travelling Salesman Problem with Pickups and Deliveries (TSPPD) consists in designing a minimum cost tour that starts at the depot, provides either a pickup or delivery service to each of the customers and returns to the depot, in such a way that the vehicle capacity is not exceeded in any part of the tour. In this paper, the TSPPD is solved by considering a metaheuris-tic algorithm based on Iterated Local Search with Variable Neighbourhood Descent and Random neighbourhood ordering. Our aim is to propose a fast, flexible and easy to code algorithm, also capable of producing high quality solutions. The results of our computational experience show that the algorithm finds or improves the best known results reported in the literature within reasonable computational time.     

多时间窗车辆路径问题的智能水滴算法

研究了多时间窗车辆路径问题,考虑了车容量、多个硬时间窗限制等约束条件,以动用车辆的固定成本和车辆运行成本之和最小为目标,建立了整数线性规划模型。根据智能水滴算法的基本原理,设计了求解多时间窗车辆路径问题的快速算法,利用具体实例进行了模拟计算,并与遗传算法的计算结果进行了对比分析,结果显示,利用智能水滴算法求解多时间窗车辆路径问题,能够以很高的概率得到全局最优解,是求解多时间窗车辆路径问题的有效算法。     

A study of exponential neighborhoods for the Travelling Salesman Problem and for the Quadratic Assignment Problem

This paper deals with exponential neighborhoods for combinatorial optimization problems. Exponential neighborhoods are large sets of feasible solutions whose size grows exponentially with the input length. We are especially interested in exponential neighborhoods over which the TSP (respectively, the QAP) can be solved in polynomial time, and we investigate combinatorial and algorithmical questions related to such neighborhoods.?First, we perform a careful study of exponential neighborhoods for the TSP. We investigate neighborhoods that can be defined in a simple way via assignments, matchings in bipartite graphs, partial orders, trees and other combinatorial structures. We identify several properties of these combinatorial structures that lead to polynomial time optimization algorithms, and we also provide variants that slightly violate these properties and lead to NP-complete optimization problems. Whereas it is relatively easy to find exponential neighborhoods over which the TSP can be solved in polynomial time, the corresponding situation for the QAP looks pretty hopeless: Every exponential neighborhood that is considered in this paper provably leads to an NP-complete optimization problem for the QAP. Received: September 5, 1997 / Accepted: November 15, 1999?Published online February 23, 2000     

An Insert/Delete Heuristic for the Travelling Salesman Subset-Tour Problem with One Additional Constraint

The Travelling Salesman Subset-tour Problem (TSSP) differs from the well-known Travelling Salesman Problem (TSP) in that the salesman is not required to visit every city. Many problems, such as the prize collecting TSP, the orienteering problem, and the time constrained TSP, can be viewed as TSSPs with one additional constraint (TSSP + 1). In this paper, we present a heuristic approach for the TSSP + I class of problems. The general philosophy of our approach is to maintain tour feasibility with respect to the TSSP subproblem. This allows us to begin our approach with any TSSP tour. In each step, the insertion or deletion of a city is performed either to reduce infeasibility in the additional constraint or to improve upon the minimization objective. We present computational results that show our approach is superior to approaches using just insertion, and thus demonstrate the importance of considering the possible deletion of cities.     

基于交通流的多模糊时间窗车辆路径优化

研究了基于交通流的多模糊时间窗车辆路径问题,考虑了实际中不断变化的交通流以及客户具有多个模糊时间窗的情况,以最小化配送总成本和最大化客户满意度为目标,构建基于交通流的多模糊时间窗车辆路径模型。根据伊藤算法的基本原理,设计了求解该模型的改进伊藤算法,结合仿真算例进行了模拟计算,并与蚁群算法的计算结果进行了对比分析,结果表明,利用改进伊藤算法求解基于交通流的多模糊时间窗车辆路径问题,迭代次数小,效率更高,能够在较短的时间内收敛到全局最优解,可以有效的求解多模糊时间窗车辆路径问题。     

Exact and heuristic algorithms for the uncapacitated multiple allocation p-hub median problem

In this paper new MILP formulations for the multiple allocation p-hub median problem are presented. These require fewer variables and constraints than those traditionally used in the literature. An efficient heuristic algorithm, based on shortest paths, is described. LP based solution methods as well as an explicit enumeration algorithm are developed to obtain exact solutions. Computational results are presented for well known problems from the literature which show that exact solutions can be found in a reasonable amount of computational time. Our algorithms are also benchmarked on a different data set. This data set, which includes problems that are larger than those used in the literature, is based on a postal delivery network and has been treated by the authors in an earlier paper.