Hipólito Hernández-Pérez

A branch-and-cut algorithm for a traveling salesman problem with pickup and delivery

We study a generalization of the well-known traveling salesman problem (TSP) where each customer provides or requires a given non-zero amount of product, and the vehicle in a depot has a given capacity. Each customer and the depot must be visited exactly once by the vehicle supplying the demand while minimizing the total travel distance. We assume that the product collected from pickup customers can be delivered to delivery customers. We introduce a 0-1 integer linear model for this problem and describe a branch-and-cut procedure for finding an optimal solution. The model and the algorithm are adapted to solve instances of TSP with pickup and delivery. Some computational results are presented to analyze the performance of our proposal.

A hybrid GRASP/VND heuristic for the one-commodity pickup-and-delivery traveling salesman problem

We address in this paper the one-commodity pickup-and-delivery traveling salesman problem, which is characterized by a set of customers, each of them supplying (pickup customer) or demanding (delivery customer) a given amount of a single product. The objective is to design a minimum cost Hamiltonian route for a capacitated vehicle in order to transport the product from the pickup to the delivery customers. The vehicle starts the route from a depot, and its initial load also has to be determined. We propose a hybrid algorithm that combines the GRASP and VND metaheuristics. Our heuristic is compared with other approximate algorithms described in Hernandez-Perez and Salazar-Gonzalez [Heuristics for the one-commodity pickup-and-delivery traveling salesman problem. Transportation Science 2004;38:245-55]. Computational experiments on benchmark instances reveal that our hybrid method yields better results than the previously proposed approaches.

The multi-commodity one-to-one pickup-and-delivery traveling salesman problem

This paper concerns 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 correspond to customers providing or requiring known amounts of m different commodities, and the vehicle has a given upper-limit capacity. Each commodity has exactly one origin and one destination, and the vehicle must visit each customer exactly once. The problem can also be defined as the capacitated version of the classical TSP with precedence constraints. This paper presents two mixed integer linear programming models, and describes a decomposition technique for each model to find the optimal solution. Computational experiments on instances from the literature and randomly generated compare the techniques and show the effectiveness of our implementation.

A hybrid heuristic approach for the multi-commodity pickup-and-delivery traveling salesman problem ☆

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.

Heuristic algorithm for the Split-Demand One-Commodity Pickup-and-Delivery Travelling Salesman Problem

Abstract This article addresses the problem of designing routes of minimum cost for a capacitated vehicle moving a commodity between a set of customers, allowing two characteristics uncommon in the pickup-and-delivery literature. One characteristic is that a customer may be visited several times. The other characteristic is that a customer may be used as intermediate location to temporarily collect and deliver product. The article describes a matheuristic algorithm that iteratively applies a constructive procedure and a refinement procedure. The constructive procedure represents each customer by a set of nodes each one associated with a potential visit|, decomposes each customer demand into partial demands associated with its nodes, and solves a one-commodity pickup-and-delivery Travelling Salesman Problem with a variable neighbourhood search. The refinement procedure is a branch-and-cut algorithm to optimize some pieces of a given solution. Exhaustive computational results on benchmark instances demonstrate the good performance of the algorithm when solving instances with up to 500 customers.

An Exact Algorithm for the Split-Demand One-Commodity Pickup-and-delivery Travelling Salesman Problem

This paper concerns the problem of designing a route of minimum cost for a capacitated vehicle moving a single commodity between a set of customers. The route must allow two characteristics uncommon in the literature. One characteristic is that a customer may be visited several times. The other characteristic is that a customer may be used as intermediate location to temporarily collect and deliver part of the load of the vehicle. Routes with these characteristics may lead to cost reductions when compared to routes without them. The paper describes a branch-and-cut algorithm based on a relaxation of a model of Mixed Integer Programming. Preliminary computational results on benchmark instances demonstrate the good performance of the algorithm compared with the original model.

International Network Optimization Conference, Tenerife 2013

Abstract International Network Optimization Conference (INOC) is the biennial meeting of the EURO working group on Network Optimization (ENOG). The last edition of this conference (INOC 2013) was held in Costa Adeje (Tenerife, Spain), May 20–22, 2013. This volume contains the short papers presented at INOC 2013.