Philippe Lacomme

Competitive Memetic Algorithms for Arc Routing Problems

The Capacitated Arc Routing Problem or CARP arises in applications like waste collection or winter gritting. Metaheuristics are tools of choice for solving large instances of this NP-hard problem. The paper presents basic components that can be combined into powerful memetic algorithms (MAs) for solving an extended version of the CARP (ECARP). The best resulting MA outperforms all known heuristics on three sets of benchmark files containing in total 81 instances with up to 140 nodes and 190 edges. In particular, one open instance is broken by reaching a tight lower bound designed by Belenguer and Benavent, 26 best-known solutions are improved, and all other best-known solutions are retrieved.

A GRASP×ELS approach for the capacitated location-routing problem

This paper addresses the capacitated location-routing problem (CLRP), raised by distribution networks involving depot location, fleet assignment and routing decisions. The CLRP is defined by a set of potential depot locations, with opening costs and limited capacities, a homogeneous fleet of vehicles, and a set of customers with known demands. The objective is to open a subset of depots, to assign customers to these depots and to design vehicle routes, in order to minimize both the cost of open depots and the total cost of the routes. The proposed solution method is a greedy randomized adaptive search procedure (GRASP), calling an evolutionary local search (ELS) and searching within two solution spaces: giant tours without trip delimiters and true CLRP solutions. Giant tours are evaluated via a splitting procedure that minimizes the total cost subject to vehicle capacity, fleet size and depot capacities. This framework is benchmarked on classical instances. Numerical experiments show that the approach outperforms all previously published methods and provides numerous new best solutions.

A Genetic Algorithm for the Capacitated Arc Routing Problem and Its Extensions

The NP-hard Capacitated Arc Routing Problem (CARP) allows to model urban waste collection or road gritting, for instance. Exact algorithms are still limited to small problems and metaheuristics are required for large scale instances. The paper presents the first genetic algorithm (GA) published for the CARP. This hybrid GA tackles realistic extensions like mixed graphs or prohibited turns. It displays excellent results and outperforms the best metaheuristics published when applied to two standard sets of benchmarks: the average deviations to lower bounds are 0.24 % and 0.69 % respectively, a majority of instances are solved to optimality, and eight best known solutions are improved.

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.

Evolutionary algorithms for periodic arc routing problems

The capacitated arc routing problem (CARP) involves the routing of vehicles to treat a set of arcs in a network. In many applications, the trips must be planned over a multiperiod horizon, giving a new problem called periodic CARP (PCARP). The paper describes several versions encountered in practice and suggests a simple classification, enabling the definition of a very general PCARP. For instance, the demand for each arc treatment may depend on the period or on the date of the previous visit. The proposed solution method is a memetic algorithm based on a sophisticated crossover, able to simultaneously change tactical (planning) decisions, such as the treatment days of each arc, and operational (scheduling) decisions, such as the trips performed for each day. Two versions are appraised on two sets of PCARP instances derived from standard CARP files. The results show significant savings compared to one insertion heuristic and a more elaborate two-phase method.

Lower and upper bounds for the mixed capacitated arc routing problem

This paper presents a linear formulation, valid inequalities, and a lower bounding procedure for the mixed capacitated arc routing problem (MCARP). Moreover, three constructive heuristics and a memetic algorithm are described. Lower and upper bounds have been compared on two sets of randomly generated instances. Computational results show that the average gaps between lower and upper bounds are 0.51% and 0.33%, respectively.

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.

An MILP for scheduling problems in an FMS with one vehicle

This paper concerns the mathematical formulation and optimal solutions for the Flexible Manufacturing Systems Scheduling Problem (FMSSP) with one vehicle. This linear formulation differs from the previously published ones as it takes into account the maximum number of jobs allowed in the system, limited input/output buffer capacities, empty vehicle trips and no-move-ahead trips simultaneously. Our objective is to propose optimal solutions for small and medium-sized instances and to examine a number of commonly used assumptions and heuristics. Computational experiments are carried out on instances adapted from Bilge and Ulusoy [Bilge, U., Ulusoy, G., 1995. A time window approach to simultaneous scheduling of machines and material handling system in an FMS. Operations Research 43, 1058-1070] and the following heuristics are evaluated: FIFO (First In First Out) rules for input/output buffer management; and FIFO, SPT (Shortest Processing Time), STT (Shortest Travel Time) and MOQS (Maximum Outgoing Queue Size) rules concerning the vehicle. The consequences of classical assumptions are also studied: ignoring empty trips, ignoring no-move-ahead constraints, and ignoring vehicle-disjunction constraints. The numerical experiments provide a set of optimal solutions and allow to evaluate the performances of heuristic search schemes.

Simultaneous job input sequencing and vehicle dispatching in a single-vehicle automated guided vehicle system: a heuristic branch-and-bound approach coupled with a discrete events simulation model

This paper addresses the scheduling problem in automated manufacturing environments, whose problem encompasses all the decisions related to the allocation of resources over the time horizon in order to best satisfy a set of objectives. It concentrates in particular on the job-input sequencing and vehicle-dispatching problems in a manufacturing environment using a single-vehicle automated guided vehicle system. The problem is solved using a branch-and-bound coupled with a discrete event simulation model. The branch-and-bound focuses on the job-input sequencing problem to determine the order in which the jobs enter the manufacturing system. The discrete event simulation model evaluates this job sequence under given vehicle and machine dispatching rules. The discrete event simulation model permits one to take into account all the working constraints: the maximal number of jobs simultaneously allowed in the system, the input/output buffers with finite capacities, the dynamic behaviour of the system under study and, thus, the impact of vehicle blocking and congestion as well as the impact of the machine blocking. A benchmark test is performed to investigate the system performances and the makespan depending on the job input sequencing, the vehicle and machine dispatching. The framework is benchmarked on 20 instances under different vehicle dispatching rules.

Improving robustness of solutions to arc routing problems

This paper considers the stochastic capacitated arc routing problem (SCARP), obtained by taking random demands in the CARP. For real-world problems, it is important to create solutions that are insensitive to changes in demand, because these quantities are not deterministic but randomly distributed. This paper provides the basic concept of a new technique to compute such solutions, based upon the best method published for CARP: a hybrid genetic algorithm (HGA). The simulation analysis was achieved with the well-known DeArmons, Egleses and Belenguers instances. This intensive evaluation process was carried out with 1000 replications providing high-quality statistical data. The results obtained prove that there is a great interest to optimize not only the solution cost but also the robustness of solutions. This work is a step forward to treat more realistic problems including industrial goals and constraints linked to demand variations.