Andréa Cynthia Santos

Exact and heuristic algorithms for solving the generalized vehicle routing problem with flexible fleet size

The generalized vehicle routing problem with flexible fleet size (GVRP-flex) extends the classical capacitated vehicle routing problem (CVRP) by partitioning the set of required nodes into clusters and has interesting applications such as humanitarian logistics. The problem aims at minimizing the total cost for a set of routes, such that each cluster is visited exactly once and its total demand is delivered to one of its nodes. An exact method based on column generation (CG) and two metaheuristics derived from iterated local search are proposed for the case with flexible fleet size. On five sets of benchmarks, including a new one, the CG approach often provides good upper and lower bounds, whereas the metaheuristics find, in a few seconds, solutions with small optimality gaps.

Local search based metaheuristics for the robust vehicle routing problem with discrete scenarios

Graphical abstractDisplay Omitted HighlightsA robust version of the vehicle routing with uncertain travel times is studied.Uncertainties are given as a set of discrete scenarios.A mixed integer model (MIP), a local search and four meta-heuristics are developed.The meta-heuristics retrieve the optimal solutions of the MIP on small problems.Results are reported up to 100 customers for the meta-heuristics. The Capacitated Vehicle Routing Problem (CVRP) is extended here to handle uncertain arc costs without resorting to probability distributions, giving the Robust VRP (RVRP). The unique set of arc costs in the CVRP is replaced by a set of discrete scenarios. A scenario is for instance the travel time observed on each arc at a given traffic hour. The goal is to build a set of routes using the lexicographic min-max criterion: the worst cost over all scenarios is minimized but ties are broken using the other scenarios, from the worst to the best. This version of robust CVRP has never been studied before. A Mixed Integer Linear Program (MILP), two greedy heuristics, a local search and four metaheuristics are proposed: a Greedy Randomized Adaptive Search Procedure, an Iterated Local Search (ILS), a Multi-Start ILS (MS-ILS), and an MS-ILS based on Giant Tours (MS-ILS-GT) converted into feasible routes via a lexicographic splitting procedure. The greedy heuristics provide the other algorithms with good initial solutions. Tests on small instances (10-20 customers, 2-3 vehicles, 10-30 scenarios) show that the four metaheuristics retrieve all optima found by the MILP. On larger cases with 50-100 customers, 5-20 vehicles and 10-20 scenarios, MS-ILS-GT dominates the other approaches. As our algorithms share the same components (initial heuristic, local search), the positive contribution of using the giant tour approach is confirmed on the RVRP.

Strategies for designing energy-efficient clusters-based WSN topologies

Wireless Sensor Networks are used in several practical applications such as environmental monitoring and risk detection. In this work, we deal with the problem of organizing the network topology into clusters in order to minimize the total energy consumption. The problem is modeled as an Independent Dominating Problem with Connecting requirements. We first present a state-of-the-art on the problems to optimize energy consumption in WSN. Then, we propose a mixed integer linear programming formulation, constructive heuristics, a local search procedure, and a GRASP-based metaheuristic. Results are provided for large scale WSN instances.

Models and hybrid methods for the onshore wells maintenance problem

Workover rigs are used in onshore basins but they are often in limited number and they may not attend all the maintenance requests. We consider here the problem of scheduling the rigs over a time horizon in order to minimize the total oil loss due to the idle production states. Three mixed integer linear models are proposed. The first one improves an existing scheduling-based formulation. The second one uses an open vehicle routing approach and the third one is an extended model for which a column generation strategy is developed. Several improvements are presented as well as two heuristics coupled with column generation. To our knowledge, the first optimal values for medium-size instances of the problem are presented in this paper. The results show the potential of the column generation and its interest in a practical context.

A Robust optimization approach for the Vehicle Routing problem with uncertain travel cost

The Robust Vehicle Routing problem (RVRP) with discrete scenarios is studied here to handle uncertain traveling time, where a scenario represents a possible discretization of the travel time observed on each arc at a given traffic hour. The goal is to build a set of routes considering the minimization of the worst total cost over all scenarios. A Genetic Algorithm (GA) is proposed for the RVRP considering a bounded set of discrete scenarios and the asymmetric arc costs on the transportation network. Tests on small and medium size instances are presented to evaluate the performance of the proposed GA for the RVRP. On small-size instances, a maximum of 20 customers, 3 vehicles and 30 discrete scenarios are handled. For medium-size instances, 100 customers, 20 vehicles and 20 scenarios are tested. Computational results indicate the GA produces good solutions and retrives the majority of proven optima in a moderate computational time.

Heuristic Approaches for the Robust Vehicle Routing Problem

In this article, the Robust Vehicle Routing Problem (RVRP) with uncertain traveling costs is studied. It covers a number of important applications in urban transportation and large scale bio-terrorism emergency. The uncertain data are defined as a bounded set of discrete scenarios associated with each arc of the transportation network. The objective is to determine a set of vehicle routes minimizing the worst total cost over all scenarios. A mixed integer linear program is proposed to model the problem. Then, we adapt some classical VRP heuristics to the RVRP, such as Clarke and Wright, randomized Clarke and Wright, Sequential Best Insertion, Parallel Best Insertion and the Pilot versions of the Best Insertion heuristics. In addition, a local search is developed to improve the obtained solutions and be integrated in a Greedy Randomized Adaptive Search Procedure (GRASP). Computational results are presented for both the mathematical formulation and the proposed heuristics.

Heuristics for designing multi-sink clustered WSN topologies

In this study, the problem of building cluster-based topologies for Wireless Sensor Networks with several sinks is considered. The optimization relies on different levels of decision: choosing which sensors are masters and balancing the load among sinks. The topology associated with each sink is modeled as an Independent Dominating Set with Connecting requirements (IDSC). Thus, the solution is a partition of a given graph into as many IDSC as there are sinks. In addition, several optimization criteria are proposed to implicitly or explicitly balance the topology. The network lifetime is improved since it benefits from a clustered structure and the number of hops control. The former reduces the average amount of messages to be sent and the latter improves the average energy consumption for messages to be sent. Different combinations of criteria are proposed in lexicographical order. They are compared in terms of maximum number of clusters per topology, of deviation between the smallest and the biggest number of clusters considering all topologies, and of total number of clusters in the final topology. Two local searches, a two-step local search and a Variable Neighborhood Descent, are developed. Each one is embedded into a multi-start framework. Results are provided for instances with up to 10000 sensors and up to five sinks.

Modeling and solving the bi-objective minimum diameter-cost spanning tree problem

The bi-objective minimum diameter-cost spanning tree problem (bi-MDCST) seeks spanning trees with minimum total cost and minimum diameter. The bi-objective version generalizes the well-known bounded diameter minimum spanning tree problem. The bi-MDCST is a NP-hard problem and models several practical applications in transportation and network design. We propose a bi-objective multiflow formulation for the problem and effective multi-objective metaheuristics: a multi-objective evolutionary algorithm and a fast nondominated sorting genetic algorithm. Some guidelines on how to optimize the problem whenever a priority order can be established between the two objectives are provided. In addition, we present bi-MDCST polynomial cases and theoretical bounds on the search space. Results are reported for four representative test sets.

A linear programming based heuristic framework for min-max regret combinatorial optimization problems with interval costs

A heuristic framework for a class of robust optimization problems is proposed.The heuristic framework explores dual information.The heuristic is successfully applied to solve two robust optimization problems.The heuristic is able to outperform a widely used 2-approximation procedure.A robust optimization version of the restricted shortest path problem is introduced. This work deals with a class of problems under interval data uncertainty, namely interval robust-hard problems, composed of interval data min-max regret generalizations of classical NP-hard combinatorial problems modeled as 0-1 integer linear programming problems. These problems are more challenging than other interval data min-max regret problems, as solely computing the cost of any feasible solution requires solving an instance of an NP-hard problem. The state-of-the-art exact algorithms in the literature are based on the generation of a possibly exponential number of cuts. As each cut separation involves the resolution of an NP-hard classical optimization problem, the size of the instances that can be solved efficiently is relatively small. To smooth this issue, we present a modeling technique for interval robust-hard problems in the context of a heuristic framework. The heuristic obtains feasible solutions by exploring dual information of a linearly relaxed model associated with the classical optimization problem counterpart. Computational experiments for interval data min-max regret versions of the restricted shortest path problem and the set covering problem show that our heuristic is able to find optimal or near-optimal solutions and also improves the primal bounds obtained by a state-of-the-art exact algorithm and a 2-approximation procedure for interval data min-max regret problems.

On the Finite Optimal Convergence of Logic-Based Benders’ Decomposition in Solving 0–1 Min-Max Regret Optimization Problems with Interval Costs

This paper addresses a class of problems under interval data uncertainty composed of min-max regret versions of classical 0–1 optimization problems with interval costs. We refer to them as interval 0–1 min-max regret problems. The state-of-the-art exact algorithms for this class of problems work by solving a corresponding mixed integer linear programming formulation in a Benders’ decomposition fashion. Each of the possibly exponentially many Benders’ cuts is separated on the fly through the resolution of an instance of the classical 0–1 optimization problem counterpart. Since these separation subproblems may be NP-hard, not all of them can be modeled by means of linear programming, unless P = NP. In these cases, the convergence of the aforementioned algorithms are not guaranteed in a straightforward manner. In fact, to the best of our knowledge, their finite convergence has not been explicitly proved for any interval 0–1 min-max regret problem. In this work, we formally describe these algorithms through the definition of a logic-based Benders’ decomposition framework and prove their convergence to an optimal solution in a finite number of iterations. As this framework is applicable to any interval 0–1 min-max regret problem, its finite optimal convergence also holds in the cases where the separation subproblems are NP-hard.