Heuristics procedures to solve the multi-commodity Pickup-and-Delivery Traveling Salesman Problem (original) (raw)
Related papers
Heuristics for the One-Commodity Pickup-and-Delivery Traveling Salesman Problem
Transportation Science, 2004
T his paper deals with a generalisation of the well-known traveling salesman problem (TSP) in which cities correspond to customers providing or requiring known amounts of a product, and the vehicle has a given upper limit capacity. Each customer must be visited exactly once by the vehicle serving the demands while minimising the total travel distance. It is assumed that any unit of product collected from a pickup customer can be delivered to any delivery customer. This problem is called one-commodity pickup-and-delivery TSP (1-PDTSP). We propose two heuristic approaches for the problem: (1) is based on a greedy algorithm and improved with a k-optimality criterion and is based on a branch-and-cut procedure for finding an optimal local solution. The proposal can easily be used to solve the classical "TSP with pickup-and-delivery," a version studied in literature and involving two commodities. The approaches have been applied to solve hard instances with up to 500 customers.
A hybrid heuristic approach for the multi-commodity pickup-and-delivery traveling salesman problem
European Journal of Operational Research, 2016
We address in this article the multi-commodity pickup-and-delivery traveling salesman problem, which is a routing problem for a capacitated vehicle that has to serve a set of customers that provide or require certain amounts of m different products. Each customer must be visited exactly once by the vehicle, and it is assumed that a unit of a product collected from a customer can be supplied to any other customer that requires that product. Each product is allowed to have several sources and several destinations. The objective is to minimize the total travel distance. We propose a hybrid three-stage heuristic approach that combines a procedure to generate initial solutions with several local search operators and shaking procedures, one of them based on solving an integer programming model. Extensive computational experiments on randomly generated instances with up to 400 locations and 5 products show the effectiveness of the approach.
The multi-commodity one-to-one pickup-and-delivery traveling salesman problem
European Journal of Operational Research, 2009
This paper treats of a generalization of the Traveling Salesman Problem (TSP) called Multi-commodity one-to-one Pickup-and-Delivery Traveling Salesman Problem (m-PDTSP) in which cities corresponds to customers providing or requiring known amounts of m different objects, and the vehicle has a given upper-limit capacity. Each object has exactly one origin and one destination, and the vehicle must visit each customer exactly once. This justifies the words "one-to-one" and "traveling salesman problem" in the name of the problem, respectively. We introduce a Mixer Integer Linear Programming model for the m-PDTSP, discuss decomposition techniques and describe some strategies to solve the problem based on a branchand-cut procedure. Preliminary computational experiments on randomly generated euclidian instances are shown.
A heuristic for the pickup and delivery traveling salesman problem
Computers & Operations Research, 2000
This paper deals with the pickup and delivery traveling salesman problem. First we show how to adapt some classical traveling salesman heuristics to solve this problem, then we propose a new and e$cient composite heuristic. The proposed heuristic is composed of two phases: a solution construction phase including a local optimization component and a deletion and re-insertion improvement phase. To evaluate its performance, the proposed heuristic was compared to the only available heuristic specially designed to solve this problem, to an adaptation of the most e$cient heuristic designed to solve the traveling salesman problem with backhaul, to an adaptation of the farthest as well as to an adaptation of the cheapest insertion methods. Each of these heuristics was followed by our deletion and re-insertion procedure which considerably improved their performance. Results based on a new set of test problems show that the proposed heuristic outperforms all these reinforced heuristics. Scope and purpose In several physical distribution problems, goods must be picked at an origin and delivered to a destination. Examples include the transportation of handicapped persons, the pickup and delivery of fast courier, of some medical supplies, etc. This problem di!ers from classical transportation problems because we have to deal with precedence constraints between the customers to be visited. This article describes a powerful heuristic for this di$cult problem.
The one-commodity pickup-and-delivery traveling salesman problem: Inequalities and algorithms
Networks, 2007
This article concerns the "One-commodity Pickup-and-Delivery Traveling Salesman Problem" (1-PDTSP), in which a single vehicle of fixed capacity must either pick up or deliver known amounts of a single commodity to a given list of customers. It is assumed that the product collected from the pickup customers can be supplied to the delivery customers, and that the initial load of the vehicle leaving the depot can be any quantity. The problem is to find a minimum-cost sequence of the customers in such a way that the vehicle's capacity is never exceeded. This article points out a close connection between the 1-PDTSP and the classical "Capacitated Vehicle Routing Problem" (CVRP), and it presents new inequalities for the 1-PDTSP adapted from recent inequalities for the CVRP. These inequalities have been implemented in a branch-and-cut framework to solve to optimality the 1-PDTSP that outperforms a previous algorithm . Larger instances (with up to 100 customers) are now solved to optimality. The classical "Traveling Salesman Problem with Pickups and Deliveries" (TSPPD) is a particular case of the 1-PDTSP, and this observation gives an additional motivation for this article. The here-proposed algorithm for the 1-PDTSP was able to solve to optimality TSPPD instances with up to 260 customers.
Networks and Spatial Economics, 2015
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 N P-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.
The traveling salesman problem with pickup, delivery, and ride-time constraints
Networks, 2015
In the traveling salesman problem with pickup, delivery, and ride-time constraints (TSPPD-RT), a vehicle located at a depot is required to service a number of requests where the requests are known before the route is formed. Each request consists of (i) a pickup location (origin), (ii) a delivery location (destination), and (iii) a maximum allowable travel time from the origin to the destination (maximum ride-time). The problem is to design a tour for the vehicle that (i) starts and ends at the depot, (ii) services all requests, (iii) ensures that each request's ride-time does not exceed its maximum ride-time, and (iv) minimizes the total travel time required by the vehicle to service all requests (objective function). A capacity constraint that may be present is that the weight or volume of the undelivered requests on the vehicle must always be no greater than the vehicle's capacity. In this article, we concurrently analyze the TSPPD-RT with capacity constraints and without capacity constraints. We describe two mathematical formulations of the problem. These formulations are used to derive new lower bounds on the solution to the problem. Then, we provide two exact methods for finding the optimal route that minimizes the total travel cost. Our extensive computational analysis on both versions of the TSPPD-RT shows that the proposed algorithms are capable of solving to optimality instances involving up to 50 requests.
Greedy Heuristics Adapted for the Multi-commodity Pickup and Delivery Traveling Salesman Problem
arXiv (Cornell University), 2023
The convex hull cheapest insertion heuristic is a well-known method that efficiently generates good solutions to the Traveling Salesperson Problem. However, this heuristic has not been adapted to account for precedence constraints that restrict the order in which locations can be visited. Such constraints result in the precedence constrained traveling salesperson problem or the sequential ordering problem, which are commonly encountered in applications where items have to be picked up before they are delivered. In this paper, we present an adapted version of this heuristic that accounts for precedence constraints in the problem definition. This algorithm is compared with the widely used Nearest Neighbor heuristic on the TSPLIB benchmark data with added precedence constraints. It is seen that the proposed algorithm is particularly well suited to cases where delivery nodes are centrally positioned, with pickup nodes located in the periphery, outperforming the Nearest Neighbor algorithm in 97% of the examined instances.
2011
In the carrier-based coverage repair problem, a single mobile robot replaces damaged sensors by picking up spare ones in the region of interest or carrying them from a base station in wireless sensor and robot networks. The objective is to find the shortest path of the robot. The problem is an extension of the traveling salesman problem (TSP). Thus, it is also called the one-commodity traveling salesman problem with selective pickup and delivery (1-TSP-SELPD). In order to solve this problem in a larger sensor distribution scenario more efficiently, we propose a two-stage approach in this paper. In the first stage, the mature and effective Lin-Kernighan-Helsgaun (LKH) algorithm is used to form a Hamiltonian cycle for all delivery nodes, which is regarded as a heuristic for the second stage. In the second stage, elliptical regions are set for selecting pickup nodes‚ and an edge-ordered list (candidate edge list, CEL) is constructed to provide major axes for the ellipses. The process of selecting pickup nodes and constructing the CEL is repeated until all the delivery nodes are visited. The final CEL stores a feasible solution. To update it, three operations-expansion, extension, and constriction-are applied to the CEL. The experimental results show that the proposed method reduces the computing time and achieves better results in higher-dimensional problems, which may facilitate the provision of solutions for more complicated sensor networks and can contribute to the development of effective and efficient algorithms for the one-commodity pickup-and-delivery traveling salesman problem (1-PDTSP).