Alain Quilliot

A multi-start evolutionary local search for the two-dimensional loading capacitated vehicle routing problem

This paper addresses an extension of the capacitated vehicle routing problem where customer demand is composed of two-dimensional weighted items (2L-CVRP). The objective consists in designing a set of trips minimizing the total transportation cost with a homogenous fleet of vehicles based on a depot node. Items in each vehicle trip must satisfy the two-dimensional orthogonal packing constraints. A GRASPxELS algorithm is proposed to compute solutions of a simpler problem in which the loading constraints are transformed into resource constrained project scheduling problem (RCPSP) constraints. We denote this relaxed problem RCPSP-CVRP. The optimization framework deals with RCPSP-CVRP and lastly RCPSP-CVRP solutions are transformed into 2L-CVRP solutions by solving a dedicated packing problem. The effectiveness of our approach is demonstrated through computational experiments including both classical CVRP and 2L-CVRP instances. Numerical experiments show that the GRASPxELS approach outperforms all previously published methods.

Linear programming based algorithms for preemptive and non-preemptive RCPSP

Abstract In this paper, the RCPSP (resource constrained project scheduling problem) is solved using a linear programming model. Each activity may or may not be preemptive. Each variable is associated to a subset of independent activities (antichains). The properties of the model are first investigated. In particular, conditions are given that allow a solution of the linear program to be a feasible schedule. From these properties, an algorithm based on neighbourhood search is derived. One neighbour solution is obtained through one Simplex pivoting, if this pivoting preserves feasibility. Methods to get out of local minima are provided. The solving methods are tested on the PSPLIB instances in a preemptive setting and prove efficient. They are used when preemption is forbidden with less success, and this difference is discussed.

Models and Algorithms for Carsharing Systems and Related Problems

Abstract In a Carsharing System, a fleet of cars is distributed at specified stations in an urban area, users can take and return cars at any time and station. For operating such a system in a satisfactory way, the stations have to keep a good ratio between the total number of places and the number of cars in each station, in order to refuse as few customer requests as possible. In this work, we propose to model the resulting problem of balancing the load of the stations as a General Pickup and Delivery Problem. As problems of this type are known to be hard, we discuss possible heuristic approaches both for the static (offline) and the dynamic (online) version of the problem, and give approximation results for special cases.

Optimal preemptive scheduling on a fixed number of identical parallel machines

In this paper, we consider the preemptive scheduling problem on a fixed number of identical parallel machines. We present a polynomial-time algorithm for finding a minimal length schedule for an order class which contains properly interval orders.

A Relation between Multiprocessor Scheduling and Linear Programming

The general non preemptive multiprocessor scheduling problem (NPMS) is NP-Complete, while in many specific cases, the same problem is Time-polynomial. A first connection between PMS and linear programming was established by Yannanakis, Sauer and Stone, who associated to any PMS instance some specific linear program. The main result inside this paper consists in a characterization of the partially ordered structures which allow the optimal values of any associated PMS instance to be equal to the optimal values of the corresponding linear programs.

Security architecture for wireless sensor networks using frequency hopping and public key management

The security aspect of wireless sensor networks has taken the attention of numerous researchers in the past several years. It has recently been proven that public keys are now feasible in wireless sensor networks but still consume a lot of processing time and memory. In this paper we propose the use of public keys based on ECC to exchange symmetric keys that will be used to encrypt communications. In addition, we propose a time segmentation approach that enables frequency hopping time slotted communications. Nodes secretly exchange frequency hopping sequences that enable them to fight against jamming and eavesdropping.

Empirical analysis for the VRPTW with a multigraph representation for the road network

Abstract Vehicle routing problems have drawn researchers’ attention for more than fifty years. Most approaches found in the literature are based on the key assumption that for each pair of points of interest (e.g., customers, depot...), the best origin-destination path can be computed. Thus, the problem can be addressed via a simple graph representation, where nodes represent points of interest and arcs represent the best paths. Yet, in practice, it is common that several attributes are defined on road segments. Consequently, alternative paths presenting different trade-offs exist between points of interest. In this study, we investigate in depth a special representation of the road network proposed in the literature and called a multigraph. This representation enables one to maintain all these alternative paths in the solution space. We present an empirical analyses based on the Vehicle Routing Problem with Time Windows, as a test bed problem, solved with branch-and-price algorithms developed for the different types of graphs. Computational experiments on modified benchmarks from the literature and on instances derived from real data evaluate the impact of the modeling on solution quality.

An iterative two-step heuristic for the parallel drone scheduling traveling salesman problem

A recent evolution in urban logistics involves the usage of drones. In this article, we address a heuristic solution of the parallel drone scheduling traveling salesman problem, recently introduced by Murray and Chu. In this problem, deliveries are split between a vehicle and drones. The vehicle performs a classical delivery tour, while the drones are constrained to perform back and forth trips. The objective is to minimize completion time. We propose an iterative two-step heuristic, composed of: a coding step that transforms a solution into a customer sequence, and a decoding step that decomposes the customer sequence into a tour for the vehicle and trips for the drones. Decoding is expressed as a bicriteria shortest path problem and is carried out by dynamic programming. Experiments conducted on benchmark instances confirm the efficiency of the approach and give some insights on this drone delivery system.

Supply chain optimisation with both production and transportation integration: multiple vehicles for a single perishable product

This paper deals with an extension of the integrated production and transportation scheduling problem (PTSP) by considering multiple vehicles (PTSPm) for optimisation of supply chains. The problem reflects a real concern for industry since production and transportation subproblems are commonly addressed independently or sequentially, which leads to sub-optimal solutions. The problem includes specific capacity constraints, the short lifespan of products and the special case of the single vehicle that has already been studied in the literature. A greedy randomised adaptive search procedure (GRASP) with an evolutionary local search (ELS) is proposed to solve the instances with a single vehicle as a special case. The method has been proven to be more effective than those published and provides shorter computational times with new best solutions for the single vehicle case. A new set of instances with multiple vehicles is introduced to favour equitable future research. Our study extends previous research using an indirect resolution approach and provides an algorithm to solve a wide range of one-machine scheduling problems with the proper coordination of single or multiple vehicles.

General parametric scheme for the online uniform machine scheduling problem with two different speeds

In this paper, we consider the online uniform machine scheduling problem on m processors when speed s i = 1 for i = k+1, ..., m and s i = s, s > 1, for i = 1, ..., k. The objective is to minimize makespan. We propose a parametric scheme with the worst-case performance 2.618 when 1 1 when the ratio m/k tends to infinity.