Ada M. Alvarez

A bi-objective vehicle routing problem with time windows: A real case in Tenerife

This work is motivated by a real problem posed to the authors by a company in Tenerife, Spain. Given a fleet of vehicles, daily routes have to be designed in order to minimize the total traveled distance while balancing the workload of drivers. This balance has been defined in relation to the length of the routes, regarding to the required time. A bi-objective mixed-integer linear model for the problem is proposed and a solution approach, based on the scatter search metaheuristic, is developed. An extensive computational experience is carried out, using benchmark instances with 25, 50 and 100 customers, to test several components of the proposed method. Comparisons with the exact Pareto fronts for instances up to 25 customers show that the proposed methods obtain good approximations. For comparison purposes, an NSGA-II algorithm has also been implemented. Results obtained on a real case instance are also discussed. In this case, the solution provided by the method proposed in this paper improves the solution implemented by the company.

Large-Scale Public R&D Portfolio Selection by Maximizing a Biobjective Impact Measure

This paper addresses R&D portfolio selection in social institutions, state-owned enterprises, and other nonprofit organizations which periodically launch a call for proposals and distribute funds among accepted projects. A nonlinear discontinuous bicriterion optimization model is developed in order to find a compromise between a portfolio quality measure and the number of projects selected for funding. This model is then transformed into a linear mixed-integer formulation to present the Pareto front. Numerical experiments with up to 25 000 projects competing for funding demonstrate a high computational efficiency of the proposed approach. The acceptance/rejection rules are obtained for a portfolio using the rough set methodology.

A tabu search approach to an urban transport problem in northern Spain

In this work we analyze an urban transport problem that the City Council of Burgos, a city in northern Spain, has posed to the authors. Given a fleet of buses and drivers, the problem consists in designing routes and assigning buses to the routes such that the service level is optimized. The optimality of the service level is measured in terms of the waiting time at the bus stops and the duration of the trip. Thus, the problem comprises two decision levels (route design and bus assignment) and differs from other urban transport models found in the literature. In order to solve the problem, we propose two algorithms: one with a local search strategy and another with a tabu search strategy. In both cases, the solutions of the two decision levels are modified in alternating steps. The proposed algorithms obtained significantly better results than the tools currently applied by the transport authorities. In addition, the solutions obtained are very robust with respect to variations on demand, as shown by the experiments.

Scatter Search for Network Design Problem

A fixed charge capacitated multicommodity network design problem on undirected networks is addressed. At the present time, there exists no algorithm that can solve large instances, common in several applications, in a reasonable period of time. This paper presents an efficient procedure using a scatter search framework. Computational experiments on a large set of randomly generated problems show that this procedure is capable of finding good solutions to large-scale problems within a reasonable amount of time.

Grasp Embedded Scatter Search for the Multicommodity Capacitated Network Design Problem

A GRASP embedded Scatter Search is developed for the multicommodity capacitated network design problem. Difficulty for this problem arises from the fact that selection of the optimal network design is an NP-complete combinatorial problem. There exist no polynomial exact algorithms which can solve this problem in a reasonable period of time for realistically sized instances. In such cases, heuristic procedures are commonly used. Two strategies were designed for GRASP: a traditional approach and a memory based technique. As for Scatter Search, 5 different strategies were used to update the reference set. Computational results on a large set of randomly generated instances show the convenience of the proposed procedures.

Optimizing Vehicle Routes in a Bakery Company Allowing Flexibility in Delivery Dates

The work addressed in this paper is motivated from a real problem proposed to the authors by a bakery company in Northern Spain. The objective is to minimize the total distance travelled for the daily routes over the week. In order to reduce this total distance, some flexibility in the dates of delivery is introduced. A mixed-integer linear model for the problem is formulated. In addition, a two-phase method based in GRASP and path-relinking metaheuristic strategies is proposed. Computational experiments show that the method performs very well, obtaining high-quality solutions in short computational times. Moreover, when it is applied to real-data-based instances, the obtained solutions considerably reduce transportation costs over the planning horizon.

A multi-start tabu search method for a single-machine scheduling problem with periodic maintenance and sequence-dependent set-up times

In this paper we study a problem of sequencing jobs in a machine with programmed preventive maintenance and sequence-dependent set-up times. The problem combines two NP-hard problems, so we propose a heuristic method for solving it, which hybridizes multi-start strategies with Tabu Search. We compare our method with the only published metaheuristic algorithm for this problem on a set of 420 instances. The comparison favors the method developed in this work, showing that is able to find high quality solutions in very short computational times.

Metaheuristics for the linear ordering problem with cumulative costs

The linear ordering problem with cumulative costs (LOPCC) is a variant of the well-known linear ordering problem, in which a cumulative propagation makes the objective function highly non-linear. The LOPCC has been recently introduced in the context of mobile-phone telecommunications. In this paper we propose two metaheuristic methods for this NP-hard problem. The first one is based on the GRASP methodology, while the second one implements an Iterated Greedy-Strategic Oscillation procedure. We also propose a post-processing based on Path Relinking to obtain improved outcomes. We compare our methods with the state-of-the-art procedures on a set of 218 previously reported instances. The comparison favors the Iterated Greedy – Strategic Oscillation with the Path Relinking post-processing, which is able to identify 87 new best objective function values.

A computational tool for optimizing the urban public transport: A real application

In this work, we have conducted a study to evaluate and improve the performance of an urban transportation system. Specifically, we have designed an algorithm for obtaining new routes and assigning buses to these routes. The objective is to optimize the service level, measured as the sum of the time the passengers have to wait at the bus stops plus the duration of their journey. As a result, a user-friendly computational tool has been designed, which is currently used by the Burgos City Council. The tool has an attractive graphic interface and is flexible, allowing modifications in the input data. The solutions yielded by the system show an improvement of almost 10% in the service level. The work includes an analysis to identify which set of stops could be “repositioned” to improve even more the service level.

Optimizing routes and stock

This work is motivated by a problem proposed to the authors by a bakery company in Northern Spain. The objective is to design the daily routes over the week in order to minimize the total traveled distance. For reducing this total distance, some flexibility in the dates of delivery is introduced, which will cause a stock. Therefore, we study the problem under the bi-objective perspective, “minimizing” simultaneously the total traveled distance and the stock. A bi-objective mixed-integer linear model for the problem is formulated and two methodologies of solution are presented. The first one is based on a series of linked variable neighborhood searches and the second one is based on NSGA-II provided of specific operators. Numerical results showing the obtained estimated Pareto front in both cases are presented.