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 leavi...

This paper presents new structural properties for the carrier–vehicle traveling salesman problem. The authors provide a mixed-integer second-order conic optimization formulation, with associated optimality cuts based on properties, and an iterated local search (ILS) algorithm. Computational experiments instances from literature demonstrate superiority of formulation to existing models algorithm...

This paper introduces the pickup and delivery traveling salesman problem with handling costs (PDTSPH). In the PDTSPH, a single vehicle has to transport loads from origins to destinations. Loading and unloading of the vehicle is operated in a last-in-firstout (LIFO) fashion. However, if a load must be unloaded that was not loaded last, additional handling operations are allowed to unload and rel...

This paper describes an exact ε-constraint method for bi-objective combinatorial optimization problems with integer objective values. This method tackles multi-objective optimization problems by solving a series of single objective subproblems, where all but one objective are transformed into constraints. We show in this paper that the Pareto front of bi-objective problems can be efficiently ge...

Vehicle routing is an area of both practical and theoretical importance. Unfortunately, routing problems are notably difficult to solve since almost all vehicle routing problems are NP-hard. However, we have discovered that when reduced to its simplest form, solving a single vehicle routing problem, without capacity and time window constraints is quite similar to the Traveling Salesman Problem ...

In this article we introduce the Quadratic Capacitated Vehicle Routing Problem (QCVRP), a combinatorial optimization problem that arises in practical applications in logistics and transportation. The QCVRP extends two other known problems, the Capacitated Vehicle Routing Problem (CVRP) and the Quadratic Symmetric Traveling Salesman Problem (QSTSP), the former by considering a modified cost matr...

We consider a generalization of the capacitated vehicle routing problem known as the cumulative vehicle routing problem in the literature. Cumulative VRPs are known be a simple model for fuel consumption in VRPs. We examine four variants of the problem, and give constant factor approximation algorithms. Our results are based on a well-known heuristic of partitioning the traveling salesman tours...

In this paper, we propose a novel research scheme to solve the single vehicle pickup and delivery problem (PDPTW) with time window constraints. The family competition genetic algorithm (FCGA) is a modern approach that has been successfully applied to solve the traveling salesman problem. We illustrate the family competition GA and give the experimental results that show the FCGA is a brilliant ...