Marc Sevaux

Metaheuristics for multiobjective optimisation

I Methodology.- A Tutorial on Evolutionary Multiobjective Optimization.- 2 Bounded Pareto Archiving: Theory and Practice.- 3 Evaluation of Multiple Objective Metaheuristics.- 4 An Introduction to Multiobjective Metaheuristics for Scheduling and Timetabling.- II Problem-oriented Contributions.- 5 A Particular Multiobjective Vehicle Routing Problem Solved by Simulated Annealing.- 6 A Dynasearch Neighborhood for the Bicriteria Traveling Salesman Problem.- 7 Pareto Local Optimum Sets in the Biobjective Traveling Salesman Problem: An Experimental Study.- 8 A Genetic Algorithm for Tackling Multiobjective Job-shop Scheduling Problems.- 9 RPSGAe - Reduced Pareto Set Genetic Algorithm: Application to Polymer Extrusion.

MA|PM : memetic algorithms with population management

A new metaheuristic for (combinatorial) optimization is presented: memetic algorithms with population management or MA|PM. An MA|PM is a memetic algorithm, that combines local search and crossover operators, but its main distinguishing feature is the use of distance measures for population management. Population management strategies can be developed to dynamically control the diversity of a small population of high-quality individuals, thereby avoiding slow or premature convergence, and achieve excellent performance on hard combinatorial optimization problems. The new algorithm is tested on two problems: the multidimensional knapsack problem and the weighted tardiness single-machine scheduling problem. On both problems, population management is shown to be able to improve the performance of a similar memetic algorithm without population management.

A genetic algorithm for a bi-objective capacitated arc routing problem

The capacitated arc routing problem (CARP) is a very hard vehicle routing problem for which the objective-in its classical form-is the minimization of the total cost of the routes. In addition, one can seek to minimize also the cost of the longest trip.In this paper, a multi-objective genetic algorithm is presented for this more realistic CARP. Inspired by the second version of the Non-dominated sorted genetic algorithm framework, the procedure is improved by using good constructive heuristics to seed the initial population and by including a local search procedure. The new framework and its different flavour is appraised on three sets of classical CARP instances comprising 81 files.Yet designed for a bi-objective problem, the best versions are competitive with state-of-the-art metaheuristics for the single objective CARP, both in terms of solution quality and computational efficiency: indeed, they retrieve a majority of proven optima and improve two best-known solutions.

Genetic algorithms to minimize the weighted number of late jobs on a single machine

The general one-machine scheduling problem is strongly NP-Hard when the objective is to minimize the weighted number of late jobs. Few methods exist to solve this problem. In an other paper, we developed a Lagrangean relaxation algorithm which gives good results on many instances. However, there is still room for improvement, and a metaheuristic might lead to better results. In this paper, we decided to use a genetic algorithm (GA). Although a GA is somewhat easy to implement, many variations exist, and we tested some of them to design the best GA for our problem. Three different engines to evaluate the fitness of a chromosome are considered, together with four types of crossover operators and three types of mutation operators. An improved GA is also proposed by applying local search on solutions determined from the chromosome by the engine. Numerical experiments on different tests of instances are reported. They show that starting from an initial population already containing a good solution is very effective. 2003 Elsevier B.V. All rights reserved.

A metaheuristic for the school bus routing problem with bus stop selection

Existing literature on routing of school buses has focused mainly on building intricate models that attempt to capture as many real-life constraints and objectives as possible. In contrast, the focus of this paper is on understanding the joint problem of bus route generation and bus stop selection – two important sub-problems – in its most basic form. To this end, this paper defines the school bus routing problem (SBRP) as a variant of the vehicle routing problem in which three simultaneous decisions have to be made: (1) determine the set of stops to visit, (2) determine for each student which stop (s)he should walk to, and (3) determine routes that lie along the chosen stops, so that the total traveled distance is minimized. An MIP model of this basic problem is developed.

A mathematical formulation for a school bus routing problem

The school bus routing problem discussed in this paper, is similar to the standard vehicle routing problem, but has several interesting additional features. In the standard VRP all stops to visit are given. In our school bus routing problem, we assume that a set of potential stops is given, as well as a set of students that can walk to one or more of these potential stops. The school buses used to pick up the students and transport them to their schools have a finite capacity. The goal of this routing problem is to select a subset of stops that would actually be visited by the buses, determine which stop each student should walk to and develop a set of tours that minimize the total distance travelled by all buses. We develop an integer programming formulation for this problem, as well as a problem instance generator. We then show how the problem can be solved using a commercial integer programming solver and discuss some of our results on small instances

An Exact Method to Minimize the Number of Tardy Jobs in Single Machine Scheduling

This paper considers the problem of scheduling n jobs on a single machine to minimize the number of tardy (or late) jobs. Each job has a release date, a processing time and a due date. The general case with non-equal release dates and different due dates is considered. Using new and efficient lower bounds and several dominance rules, a branch and bound scheme is proposed based on the definition of a master sequence, i.e. a sequence containing at least one optimal sequence. With this procedure, 95% of 140-job instances are optimally solved in a maximum of one-hour CPU time.

A genetic algorithm for robust schedules in a one-machine environment with ready times and due dates

Abstract.Computing a schedule for a single machine problem is often difficult, but when the data are uncertain, the problem is much more complicated. In this paper, we modify a genetic algorithm to compute robust schedules when release dates are subject to small variations. Two types of robustness are distinguished: quality robustness or robustness in the objective function space and solution robustness or robustness in the solution space. We show that the modified genetic algorithm can find solutions that are robust with respect to both types of robustness. Moreover, the risk associated with a specific solution can be easily evaluated. The modified genetic algorithm is applied to a just-in-time scheduling problem, a common problem in many industries.

A column generation approach to extend lifetime in wireless sensor networks with coverage and connectivity constraints

This paper addresses the maximum network lifetime problem in wireless sensor networks with connectivity and coverage constraints. In this problem, the purpose is to schedule the activity of a set of wireless sensors, keeping them connected while network lifetime is maximized. Two cases are considered. First, the full coverage of the targets is required, and second only a fraction of the targets has to be covered at any instant of time. An exact approach based on column generation and boosted by GRASP and VNS is proposed to address both of these problems. Finally, a multiphase framework combining these two approaches is built by sequentially using these two heuristics at each iteration of the column generation algorithm. The results show that our proposals are able to tackle the problem efficiently and that combining the two heuristic approaches improves the results significantly.

An exact approach for maximizing the lifetime of sensor networks with adjustable sensing ranges

This paper addresses the problem of target coverage for wireless sensor networks, where the sensing range of sensors can vary, thereby saving energy when only close targets need to be monitored. Two versions of this problem are addressed. In the first version, sensing ranges are supposed to be continuously adjustable (up to the maximum sensing range). In the second version, sensing ranges have to be chosen among a set of predefined values common to all sensors. An exact approach based on a column generation algorithm is proposed for solving these problems. The use of a genetic algorithm within the column generation scheme significantly decreases computation time, which results in an efficient exact approach.