Jesús Sánchez-Oro

Variable neighborhood search for the Vertex Separation Problem

The Vertex Separation Problem belongs to a family of optimization problems in which the objective is to find the best separator of vertices or edges in a generic graph. This optimization problem is strongly related to other well-known graph problems; such as the Path-Width, the Node Search Number or the Interval Thickness, among others. All of these optimization problems are NP-hard and have practical applications in VLSI (Very Large Scale Integration), computer language compiler design or graph drawing. Up to know, they have been generally tackled with exact approaches, presenting polynomial-time algorithms to obtain the optimal solution for specific types of graphs. However, in spite of their practical applications, these problems have been ignored from a heuristic perspective, as far as we know. In this paper we propose a pure 0-1 optimization model and a metaheuristic algorithm based on the variable neighborhood search methodology for the Vertex Separation Problem on general graphs. Computational results show that small instances can be optimally solved with this optimization model and the proposed metaheuristic is able to find high-quality solutions with a moderate computing time for large-scale instances.

GRASP with Path Relinking for the Orienteering Problem

In this paper, we address an optimization problem resulting from the combination of the well-known travelling salesman and knapsack problems. In particular, we target the orienteering problem, originated in the context of sport, which consists of maximizing the total score associated with the vertices visited in a path within the available time. The problem, also known as the selective travelling salesman problem, is NP-hard and can be formulated as an integer linear program. Since the 1980s, several solution methods for this problem have been developed and applied to a variety of fields, particularly in routing and tourism. We propose a heuristic method—based on the Greedy Randomized Adaptive Search Procedure (GRASP) and the Path Relinking methodologies—for finding approximate solutions to this optimization problem. We explore different constructive methods and combine two neighbourhoods in the local search of GRASP. Our experimentation with 196 previously reported instances shows that the proposed procedure obtains high-quality solutions employing short computing times.

Greedy randomized adaptive search procedure with exterior path relinking for differential dispersion minimization

We propose several new hybrid heuristics for the differential dispersion problem, the best of which consists of a GRASP with sampled greedy construction with variable neighborhood search for local improvement. The heuristic maintains an elite set of high-quality solutions throughout the search. After a fixed number of GRASP iterations, exterior path relinking is applied between all pairs of elite set solutions and the best solution found is returned. Exterior path relinking, or path separation, a variant of the more common interior path relinking, is first applied in this paper. In interior path relinking, paths in the neighborhood solution space connecting good solutions are explored between these solutions in the search for improvements. Exterior path relinking, as opposed to exploring paths between pairs of solutions, explores paths beyond those solutions. This is accomplished by considering an initiating solution and a guiding solution and introducing in the initiating solution attributes not present in the guiding solution. To complete the process, the roles of initiating and guiding solutions are exchanged. Extensive computational experiments on 190 instances from the literature demonstrate the competitiveness of this algorithm.

Combining intensification and diversification strategies in VNS. An application to the Vertex Separation problem

The Vertex Separation problem (VSP) is an NP-hard problem with practical applications in VLSI design, graph drawing and computer language compiler design. VSP belongs to a family of optimization problems in which the objective is to find the best separator of vertices or edges in a generic graph. In this paper, we propose different heuristic methods and embed them into a Variable Neighborhood Search scheme to solve this problem. More precisely, we propose (i) a constructive algorithm, (ii) four shake procedures, (iii) two neighborhood structures, (iv) efficient algorithmic strategies to explore them, (v) an extended version of the objective function to facilitate the search process and finally, (vi) we embed these strategies in a Reduced Variable Neighborhood Search (RVNS), a Variable Neighborhood Descent (VND) and a General Variable Neighborhood Search (GVNS). Additionally, we provide an extensive experimental comparison among them and with the best previous method of the literature. We consider three different benchmarks, totalizing 162 representative instances. The experimentation reveals that our best procedure (GVNS) improves the state of the art in both quality and computing time. This fact is confirmed by non-parametric statistical tests. In addition, when considering only the largest instances, the other two proposed variants (RVNS and VND) also obtain statistically significant differences with respect to the best previous method identified in the state of the art.

General Variable Neighborhood Search for computing graph separators

Computing graph separators in networks has a wide range of real-world applications. For instance, in telecommunication networks, a separator determines the capacity and brittleness of the network. In the field of graph algorithms, the computation of balanced small-sized separators is very useful, especially for divide-and-conquer algorithms. In bioinformatics and computational biology, separators are required in grid graphs providing a simplified representation of proteins. This papers presents a new heuristic algorithm based on the Variable Neighborhood Search methodology for computing vertex separators. We compare our procedure with the state-of-the-art methods. Computational results show that our procedure obtains the optimum solution in all of the small and medium instances, and high-quality results in large instances.

Solving dynamic memory allocation problems in embedded systems with parallel variable neighborhood search strategies

Embedded systems have become an essential part of our lives, thanks to their evolution in the recent years, but the main drawback is their power consumption. This paper is focused on improving the memory allocation of embedded systems to reduce their power consumption. We propose a parallel variable neighborhood search algorithm for the dynamic memory allocation problem, and compare it with the state of the art. Computational results and statistical tests applied show that the proposed algorithm produces significantly better outcomes than the previous algorithm in shorter computing time.

Optimization procedures for the bipartite unconstrained 0-1 quadratic programming problem

The bipartite unconstrained 0-1 quadratic programming problem (BQP) is a difficult combinatorial problem defined on a complete graph that consists of selecting a subgraph that maximizes the sum of the weights associated with the chosen vertices and the edges that connect them. The problem has appeared under several different names in the literature, including maximum weight induced subgraph, maximum weight biclique, matrix factorization and maximum cut on bipartite graphs. There are only two unpublished works (technical reports) where heuristic approaches are tested on BQP instances. Our goal is to combine straightforward search elements to balance diversification and intensification in both exact (branch and bound) and heuristic (iterated local search) frameworks. We perform a number of experiments to test individual search components and also to create new benchmarks when comparing against the state of the art, which the proposed procedure outperforms.

Scatter search for the profile minimization problem

We study the problem of minimizing the profile of a graph and develop a solution method by following the tenets of scatter search. Our procedure exploits the network structure of the problem and includes strategies that produce a computationally efficient and agile search. Among several mechanisms, our search includes path relinking as the basis for combining solutions to generate new ones. The profile minimization problem PMP is NP-Hard and has relevant applications in numerical analysis techniques that rely on manipulating large sparse matrices. The problem was proposed in the early 1970s but the state-of-the-art does not include a method that could be considered powerful by todays computing standards. Extensive computational experiments show that we have accomplished our goal of pushing the envelope and establishing a new standard in the solution of the PMP.

Parallel variable neighborhood search for the min–max order batching problem

Warehousing is a key part of supply chain management. It primarily focuses on controlling the movement and storage of materials within a warehouse and processing the associated transactions, including shipping, receiving, and picking. From the tactical point of view, the main decision is the storage policy, that is, to decide where each product should be located. Every day a warehouse receives several orders from its customers. Each order consists of a list of one or more items that have to be retrieved from the warehouse and shipped to a specific customer. Thus, items must be collected by a warehouse operator. We focus on situations in which several orders are put together into batches, satisfying a fixed capacity constraint. Then, each batch is assigned to an operator, who retrieves all the items included in those orders grouped into the corresponding batch in a single tour. The objective is then to minimize the maximum retrieving time for any batch. In this paper, we propose a parallel variable neighborhood search algorithm to tackle the so-called min–max order batching problem. We additionally compare this parallel procedure with the best previous approach. Computational results show the superiority of our proposal, confirmed with statistical tests.

Beyond Unfeasibility: Strategic Oscillation for the Maximum Leaf Spanning Tree Problem

Given an undirected and connected graph, the maximum leaf spanning tree problem consists in finding a spanning tree with as many leaves as possible. This