Maria Battarra

Routing a heterogeneous fleet of vehicles

In the well-known Vehicle Routing Problem (VRP) a set of identical vehicles, based at a central depot, is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints.

An Exact Algorithm for the Static Rebalancing Problem arising in Bicycle Sharing Systems

Bicycle sharing systems can significantly reduce traffic, pollution, and the need for parking spaces in city centers. One of the keys to success for a bicycle sharing system is the efficiency of rebalancing operations, where the number of bicycles in each station has to be restored to its target value by a truck through pickup and delivery operations. The Static Bicycle Rebalancing Problem aims to determine a minimum cost sequence of stations to be visited by a single vehicle as well as the amount of bicycles to be collected or delivered at each station. Multiple visits to a station are allowed, as well as using stations as temporary storage. This paper presents an exact algorithm for the problem and results of computational tests on benchmark instances from the literature. The computational experiments show that instances with up to 60 stations can be solved to optimality within 2 hours of computing time.

An Iterated Local Search heuristic for the single machine total weighted tardiness scheduling problem with sequence-dependent setup times

The single machine total weighted tardiness problem with sequence-dependent setup times (often known as problem ) requires a given set of jobs to be sequenced on a single machine, where a setup time is required before the processing of each job that depends on both the preceding job and the job to be processed next. The goal is to minimise the sum of weighted tardiness, where the tardiness of a job is zero if it is completed by its due date and is equal to its completion time minus its due date otherwise. In this paper, we develop an Iterated Local Search (ILS) heuristic and compare its performance with the state-of-the-art metaheuristic algorithms from the literature. The proposed ILS algorithm obtains high-quality solutions using computation times that is comparable to its competitors.

Exact Algorithms for the Clustered Vehicle Routing Problem

This study presents new exact algorithms for the clustered vehicle routing problem CluVRP. The CluVRP is a generalization of the capacitated vehicle routing problem CVRP, in which the customers are grouped into clusters. As in the CVRP, all the customers must be visited exactly once, but a vehicle visiting one customer in a cluster must visit all the remaining customers therein before leaving it. Based on an exponential time preprocessing scheme, an integer programming formulation for the CluVRP is presented. The formulation is enhanced by a polynomial time graph reduction scheme. Two exact algorithms for the CluVRP, a branch and cut as well as a branch and cut and price, are presented. The computational performances of the algorithms are tested on benchmark instances adapted from the vehicle routing problem literature as well as real-world instances from a solid waste collection application.

Hybrid metaheuristics for the Clustered Vehicle Routing Problem

The Clustered Vehicle Routing Problem (CluVRP) is a variant of the Capacitated Vehicle Routing Problem in which customers are grouped into clusters. Each cluster has to be visited once, and a vehicle entering a cluster cannot leave it until all customers have been visited. This paper presents two alternative hybrid metaheuristic algorithms for the CluVRP. The first algorithm is based on an Iterated Local Search algorithm, in which only feasible solutions are explored and problem-specific local search moves are utilized. The second algorithm is a hybrid genetic search, for which the shortest Hamiltonian path between each pair of vertices within each cluster should be precomputed. Using this information, a sequence of clusters can be used as a solution representation and large neighborhoods can be efficiently explored, by means of bi-directional dynamic programming, sequence concatenation, and appropriate data structures. Extensive computational experiments are performed on benchmark instances from the literature, as well as new large scale instances. Recommendations on the choice of algorithm are provided, based on average cluster size.

The Traveling Salesman Problem with Pickups, Deliveries, and Handling Costs

This paper introduces a new variant of the one-to-many-to-one single vehicle pickup and delivery problems (SVPDP) that incorporates the handling cost incurred when rearranging the load at the customer locations. The simultaneous optimization of routing and handling costs is difficult, and the resulting loading patterns are hard to implement in practice. However, this option makes economical sense in contexts where the routing cost dominates the handling cost. We have proposed some simplified policies applicable to such contexts. The first is a two-phase heuristic in which the tour having minimum routing cost is initially determined by optimally solving an SVPDP, and the optimal handling policy is then determined for that tour. In addition, branch-and-cut algorithms based on integer linear programming formulations are proposed, in which routing and handling decisions are simultaneously optimized, but the handling decisions are restricted to three simplified policies. The formulations are strengthened by means of problem specific valid inequalities. The proposed methods have been extensively tested on instances involving up to 25 customers and hundreds of items. Our results show the impact of the handling aspect on the customer sequencing and indicate that the simplified handling policies favorably compare with the optimal one.

Tuning a parametric Clarke–Wright heuristic via a genetic algorithm

Almost all heuristic optimization procedures require the presence of a well-tuned set of parameters. The tuning of these parameters is usually a critical issue and may entail intensive computational requirements. We propose a fast and effective approach composed of two distinct stages. In the first stage, a genetic algorithm is applied to a small subset of representative problems to determine a few robust parameter sets. In the second stage, these sets of parameters are the starting points for a fast local search procedure, able to more deeply investigate the space of parameter sets for each problem to be solved. This method is tested on a parametric version of the Clarke and Wright algorithm and the results are compared with an enumerative parameter-setting approach previously proposed in the literature. The results of our computational testing show that our new parameter-setting procedure produces results of the same quality as the enumerative approach, but requires much shorter computational time.

An iterated local search algorithm for the Travelling Salesman Problem with Pickups and Deliveries

The Travelling Salesman Problem with Pickups and Deliveries (TSPPD) consists in designing a minimum cost tour that starts at the depot, provides either a pickup or delivery service to each of the customers and returns to the depot, in such a way that the vehicle capacity is not exceeded in any part of the tour. In this paper, the TSPPD is solved by considering a metaheuris-tic algorithm based on Iterated Local Search with Variable Neighbourhood Descent and Random neighbourhood ordering. Our aim is to propose a fast, flexible and easy to code algorithm, also capable of producing high quality solutions. The results of our computational experience show that the algorithm finds or improves the best known results reported in the literature within reasonable computational time.

Metaheuristics for the traveling salesman problem with pickups, deliveries and handling costs

This paper studies the Traveling Salesman Problem with Pickups, Deliveries, and Handling Costs. The subproblem of minimizing the handling cost for a fixed route is analyzed in detail. It is solved by means of an exact dynamic programming algorithm with quadratic complexity and by an approximate linear time algorithm. Three metaheuristics integrating these solution methods are developed. These are based on tabu search, iterated local search and iterated tabu search. The three heuristics are tested and compared on instances adapted from the related literature. The results show that the combination of tabu search and exact dynamic programming performs the best, but using the approximate linear time algorithm considerably decreases the CPU time at the cost of slightly worse solutions.

Exact algorithms for the traveling salesman problem with draft limits

This paper deals with the Traveling Salesman Problem (TSP) with Draft Limits (TSPDL), which is a variant of the well-known TSP in the context of maritime transportation. In this recently proposed problem, draft limits are imposed due to restrictions on the port infrastructures. Exact algorithms based on three mathematical formulations are proposed and their performance compared through extensive computational experiments. Optimal solutions are reported for open instances of benchmark problems available in the literature.