José Andrés Moreno Pérez

Variable Neighbourhood Search

The basic idea of VNS is the change of neighbourhoods in the search for a better solution. VNS proceeds by a descent method to a local minimum exploring then, systematically or at random, increasingly distant neighbourhoods of this solution. Each time, one or several points within the current neighbourhood are used as initial solutions for a local descent. The method jumps from the current solution to a new one if and only if a better solution has been found. Therefore, VNS is not a trajectory following method (as Simulated Annealing or Tabu Search) and does not specify forbidden moves. In this work, we show how the variable neighbourhood search metaheuristic can be applied to train an artificial neural network. We define a set of nested neighbourhoods and follow the basic VNS scheme to carry out our experiments

Variable neighbourhood search: methods and applications

Variable neighbourhood search (VNS) is a metaheuristic, or a framework for building heuristics, based upon systematic changes of neighbourhoods both in descent phase, to find a local minimum, and in perturbation phase to emerge from the corresponding valley. It was first proposed in 1997 and has since then rapidly developed both in its methods and its applications. In the present paper, these two aspects are thoroughly reviewed and an extensive bibliography is provided. Moreover, one section is devoted to newcomers. It consists of steps for developing a heuristic for any particular problem. Those steps are common to the implementation of other metaheuristics.

Solving Feature Subset Selection Problem by a Parallel Scatter Search

The aim of this paper is to develop a Parallel Scatter Search metaheuristic for solving the Feature Subset Selection Problem in classification. Given a set of instances characterized by several features, the classification problem consists of assigning a class to each instance. Feature Subset Selection Problem selects a relevant subset of features from the initial set in order to classify future instances. We propose two methods for combining solutions in the Scatter Search metaheuristic. These methods provide two sequential algorithms that are compared with a recent Genetic Algorithm and with a parallelization of the Scatter Search. This parallelization is obtained by running simultaneously the two combination methods. Parallel Scatter Search presents better performance than the sequential algorithms.

Fuzzy location problems on networks

Location problems concern a wide set of fields where it is usually assumed that exact data are known. However, in real applications, the location of the facility considered can be full of linguistic vagueness, that can be appropriately modelled using networks with fuzzy values. Thus fuzzy location problems on networks arise; this paper deals with their general formulation and the description of the ways to solve them. Namely, we show the variety of problems that can be considered in this context and, for some of them, we propose the most operative approaches for their solution.

Variable neighborhood tabu search and its application to the median cycle problem

Abstract The variable neighborhood tabu search consists of a constructive phase and a series of local searches that use tabu tools. When the local search stops at a nontabu local minimum, a shake procedure starts a new local search. The local searches and the shake procedure are based on a series of standard moves. The local search consists of applying the best possible move until no such move exists. The shake procedure consists of applying a number of random moves. Since the shake could provide an infeasible solution, the local search considers as possible moves those providing a feasible solution or reducing the infeasibility. A location/allocation problem consists of selecting the location for some facilities and the allocation of the users to them. Two functions to be minimized are considered: the length of the solution, as a measure of the set of locations, and the total cost of the allocations. The standard moves for these problems are the add, drop and add/drop moves. The heuristic procedure is tested on the median cycle problem.

Nature of real-world multi-objective vehicle routing with evolutionary algorithms

The Vehicle Routing Problem with Time Windows (VRPTW) is an important logistics problem which in the real-world appears to be multi-objective. Most research in this area has been carried out using classic datasets designed for the single-objective case, like the well-known Solomons problem instances. Some unrealistic assumptions are usually made when using these datasets in the multi-objective case (e.g. assuming that one unit of travel time corresponds to one unit of travel distance). Additionally, there is no common VRPTW multi-objective oriented framework to compare the performance of algorithms because different implementations in the literature tackle different sets of objectives. In this work, we investigate the conflicting (or not) nature of various objectives in the VRPTW and show that some of the classic test instances are not suitable for conducting a proper multi-objective study. The insights of this study have led us to generate some problem instances using data from a real-world distribution company. Experiments in these new dataset using a standard evolutionary algorithm (NSGA-II) show stronger evidence of multi-objective features. Our contribution focuses on achieving a better understanding about the multi-objective nature of the VRPTW, in particular the conflicting relationships between 5 objectives: number of vehicles, total travel distance, makespan, total waiting time, and total delay time.

Multiple voting location problems

The facility voting location problems arise from the application of criteria derived from the voting processes concerning the location of facilities. The multiple location problems are those location problems in which the alternative solutions are sets of points. This paper extends previous results and notions on single voting location problems to the location of a set of facility points. The application of linear programming techniques to solve multiple facility voting location problems is analyzed. We propose an algorithm to solve Simpson multiple location problems from which the solution procedures for other problems are derived.

Relaxation of the Condorcet and Simpson conditions in voting location

Abstract A Condorcet point, in voting location, is a location point such that there is no other closer to more than half of the users. However, such Condorcet solution does not necessarily exist. This concept is based on two assumptions. First, two locations are indifferent only if they are at the same distance of the voter. Second, the number of voters needed to reject a location is more than half of them. We relax the Condorcet condition in two ways. First, by considering that two locations are indifferent for every user if the difference of the distances to them is within a positive threshold. Secondly, by considering that the proportion of users needed to reject a location is not one half. We consider the resulting new solution concepts that arise by applying both relaxations at the same time and develop algorithms for obtaining them in the finite case.

An exact procedure and LP formulations for the leader—follower location problem

The leader—follower location problem consists of determining an optimal strategy for two competing firms which make decisions sequentially. The leader optimisation problem is to minimise the maximum market share of the follower. The objective of the follower problem is to maximise its market share. We describe linear programming formulations for both problems and analyse the use of these formulations to solve the problems. We also propose an exact procedure based on an elimination process in a candidate list.

Exploring Feasible and Infeasible Regions in the Vehicle Routing Problem with Time Windows Using a Multi-objective Particle Swarm Optimization Approach

This paper investigates the ability of a discrete particle swarm optimization algorithm (DPSO) to evolve solutions from infeasibility to feasibility for the Vehicle Routing Problem with Time Windows (VRPTW). The proposed algorithm incorporates some principles from multi-objective optimization to allow particles to conduct a dynamic trade-off between objectives in order to reach feasibility. The main contribution of this paper is to demonstrate that without incorporating tailored heuristics or operators to tackle infeasibility, it is possible to evolve very poor infeasible route-plans to very good feasible ones using swarm intelligence.This paper investigates the ability of a discrete particle swarm optimization algorithm (DPSO) to evolve solutions from infeasibility to feasibility for the Vehicle Routing Problem with Time Windows (VRPTW). The proposed algorithm incorporates some principles from multi-objective optimization to allow particles to conduct a dynamic trade-off between objectives in order to reach feasibility. The main contribution of this paper is to demonstrate that without incorporating tailored heuristics or operators to tackle infeasibility, it is possible to evolve very poor infeasible route-plans to very good feasible ones using swarm intelligence.