Christophe Duhamel

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 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.

Optimal solutions for fault-tolerant topology control in wireless ad hoc networks

Topology control is one of the most important techniques used in wireless ad hoc and sensor networks to reduce energy consumption. Algorithms for topology control attempt to reduce the number of links and the power consumption in a network subject to connectivity constraints. We show that the related optimization problems may be classified into four main variants, regarding the topology of the input graph (symmetric or asymmetric) and of the solution (unidirectional or bidirectional). We present three mixed integer programming formulations for the k-connected minimum power consumption problem, which consists in finding a power assignment to the nodes of a wireless network so as that the resulting network topology be k-vertex connected (i.e., k-fault tolerant) and the total power consumption be minimum. These formulations are sufficiently general to encompass all four problem variants. We report computational experiments comparing the formulations. Optimal solutions for moderately sized networks are obtained using a commercial solver.

A GRASP heuristic for the capacitated minimum spanning tree problem using a memory-based local search strategy

We describe a new neighborhood structure for the capacitated minimum spanning tree problem. This neighborhood structure is used by a local search strategy, leading to good trade-offs between solution quality and computation time. We also propose a GRASP with path-relinking heuristic. It uses a randomized version of a savings heuristic in the construction phase and an extension of the above local search strategy, incorporating some short term memory elements of tabu search. Computational results on benchmark problems illustrate the effectiveness of this approach, which is competitive with the best heuristics in the literature in terms of solution quality. The GRASP heuristic using a memory-based local search strategy improved the best known solution for some of the largest benchmark problem.

Connecting a population dynamic model with a multi-period location-allocation problem for post-disaster relief operations

In this study, we propose a mathematical model and heuristics for solving a multi-period location-allocation problem in post-disaster operations, which takes into account the impact of distribution over the population. Logistics restrictions such as human and financial resources are considered. In addition, a brief review on resilience system models is provided, as well as their connection with quantitative models for post-disaster relief operations. In particular, we highlight how one can improve resilience by means of OR/MS strategies. Then, a simpler resilience schema is proposed, which better reflects an active system for providing humanitarian aid in post-disaster operations, similar to the model focused in this work. The proposed model is non-linear and solved by a decomposition approach: the master level problem is addressed by a non-linear solver, while the slave subproblem is treated as a black-box coupling heuristics and a Variable Neighborhood Descent local search. Computational experiments have been done using several scenarios, and real data from Belo Horizonte city in Brazil.

A hybrid evolutionary local search with depth first search split procedure for the heterogeneous vehicle routing problems

Routing Problems have been deeply studied over the last decades. Split procedures have proved their efficiency for those problems, especially within global optimization frameworks. The purpose is to build a feasible routing solution by splitting a giant tour into trips. This is done by computing a shortest path on an auxiliary graph built from the giant tour. One of the latest advances consists in handling extra resource constraints through the generation of labels on the nodes of the auxiliary graph. Lately, the development of a new generic split family based on a Depth First Search (DFS) approach during label generation has highlighted the efficiency of this new method for the routing problems, through extensive numerical evaluations on the location-routing problem. In this paper, we present a hybrid Evolutionary Local Search (hybrid ELS) for non-homogeneous fleet Vehicle Routing Problems (VRP) based on the application of split strategies. Experiments show our method is able to handle all known benchmarks, from Vehicle Fleet Mix Problems to Heterogeneous Fleet VRP (HVRP). We also propose a set of new realistic HVRP instances from 50 to more than 250 nodes coming from French counties. It relies on real distances in kilometers between towns. Since many classical HVRP instance sets are solved to optimality, this new set of instances could allow a fair comparative study of methods. The DFS split strategy shows its efficiency and attests the fact that it can be a promising line of research for routing problems including numerous additional constraints.

A GRASP×ELS for the vehicle routing problem with basic three-dimensional loading constraints

This paper addresses an extension of the capacitated vehicle routing problem where the client demand consists of three-dimensional weighted items (3L-CVRP). The objective is to design a set of trips for a homogeneous fleet of vehicles based at a depot node which minimizes the total transportation cost. Items in each vehicle trip must satisfy the three-dimensional orthogonal packing constraints. This problem is strongly connected to real-life transportation systems where the packing of items to be delivered by each vehicle can have a significant impact on the routes. We propose a new way to solve the packing sub-problem. It consists of a two-step procedure in which the z-constraints are first relaxed to get a (x,y) positioning of the items. Then, a compatible z-coordinate is computed to get a packing solution. Items can be rotated but additional constraints such as item fragility, support and LIFO are not considered. This method is included in a GRASPxELS hybrid algorithm dedicated to the computation of VRP routes. The route optimization alternates between two search spaces: the space of VRP routes and the space of giant trips. The projection from one to the other is done by dedicated procedures (namely the Split and the concatenation algorithms). Moreover, a Local Search is defined on each search space. Furthermore, hash tables are used to store the result of the packing checks and thus save a substantial amount of CPU time. The effectiveness of our approach is illustrated by computational experiments on 3L-CVRP instances from the literature. A new set of realistic instances based on the 96 French districts are also proposed. They range from 19 nodes for the small instances to 255 nodes for the large instances and they can be stated as realistic since they are based on true travel distances in kilometers between French cities. The impact of the hash tables is illustrated as well.

Variable neighborhood descent with iterated local search for routing and wavelength assignment

In this work we treat the Routing and Wavelength Assignment (RWA) with focus on minimizing the number of wavelengths to route demand requests. Lightpaths are used to carry the traffic optically between origin-destination pairs. The RWA is subjected to wavelength continuity constraints, and a particular wavelength cannot be assigned to two different lightpaths sharing a common physical link. We develop a Variable Neighborhood Descent (VND) with Iterated Local Search (ILS) for the problem. In a VND phase we try to rearrange requests between subgraphs associated to subsets of a partition of the set of lightpath requests. In a feasible solution, lightpaths belonging to a subset can be routed with the same wavelength. Thus, the purpose is to eliminate one subset of the partition. When VND fails, we perform a ILS phase to disturb the requests distribution among the subsets of the partition. An iteration of the algorithm alternates between a VND phase and a ILS phase. We report computational experiments that show VND-ILS was able to improve results upon powerful methods proposed in the literature.

Heuristics for Designing Energy-efficient Wireless Sensor Network Topologies

Wireless Sensor Networks (WSN) have been studied in several contexts. There are many challenges involving WSN design such as the energy resources optimization, the robustness and the network coverage. We address here the problem of energy-efficient topology design. A welldesigned dynamic topology and efficient routing algorithms may allow a large reduction on the energy consumption, which is one of the main concerns of WSN nodes. In this work, we propose to model the problem of clustering a WSN topology as a variation of the independent dominating set optimization problem. Then, we describe two heuristics to generate a WSN topology and two ways to evaluate the energy consumption. Computational results are presented for instances with up to 500 nodes.

A Branch and Price algorithm for the k-splittable maximum flow problem

The Maximum Flow Problem with flow width constraints is an NP-hard problem. Two models are proposed: the first model is a compact node-arc model using two flow conservation blocks per path. For each path, one block defines the path while the other one sends the right amount of flow on it. The second model is an extended arc-path model, obtained from the first model after a Dantzig-Wolfe reformulation. It is an extended model as it relies on the set of all the paths between the source and the sink nodes. Some symmetry breaking constraints are used to improve the model. A Branch and Price algorithm is proposed to solve the problem. The column generation procedure reduces to the computation of a shortest path whose cost depends on weights on the arcs and on the path capacity. A polynomial-time algorithm is proposed to solve this subproblem. Computational results are shown on a set of medium-sized instances to show the effectiveness of our approach.