Abraham Duarte

The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of possible locations, in such a way that the sum of the distances between each customer and its nearest facility is maximized. The problem is NP-hard and can be formulated as an integer linear program. It was introduced in the 1990s, and a branch and cut method coupled with a tabu search has been recently proposed. In this paper, we propose a heuristic method – based on the GRASP methodology – for finding approximate solutions to this optimization problem. In particular, we consider an advanced GRASP design in which a filtering mechanism avoids applying the local search method to low quality constructed solutions. Empirical results indicate that the proposed implementation compares favorably to previous methods. This fact is confirmed with non-parametric statistical tests.

The Obnoxious p-Median Problem consists of selecting p locations, considered facilities, in a way that the sum of the distances from each non-facility location, called customers, to its nearest facility is maximized. This is an NP-hard problem that can be formulated as an integer linear program. In this paper, we propose the application of a Variable Neighborhood Search (VNS) method to effectively tackle this problem. First, we develop new and fast local search procedures to be integrated into the Basic VNS methodology. Then, some parameters of the algorithm are tuned in order to improve its performance. The best VNS variant is parallelized and compared with the best previous methods, namely Branch and Cut, Tabu Search and GRASP over a wide set of instances. Experimental results show that the proposed VNS outperforms previous methods in the state of the art. This fact is finally confirmed by conducting non-parametric statistical tests.

The evolution and spread of social networks have attracted the interest of the scientific community in the last few years. Specifically, several new interesting problems, which are hard to solve, have arisen in the context of viral marketing, disease analysis, and influence analysis, among others. Companies and researchers try to find the elements that maximize profit, stop pandemics, etc. This family of problems is collected under the term Social Network Influence Maximization problem (SNIMP), whose goal is to find the most influential users (commonly known as seeds) in a social network, simulating an influence diffusion model. SNIMP is known to be an $$\mathcal {NP}$$ NP -hard problem and, therefore, an exact algorithm is not suitable for solving it optimally in reasonable computing time. The main drawback of this optimization problem lies on the computational effort required to evaluate a solution. Since each node is infected with a certain probability, the objective function val...

The minimum sitting arrangement (MinSA) problem is a linear layout problem consisting in minimizing the number of errors produced when a signed graph is embedded into a line. This problem has been previously tackled by theoretical and heuristic approaches in the literature. In this paper we present a basic variable neighborhood search (BVNS) algorithm for solving the problem. First, we introduce a novel constructive scheme based on the identification of cliques from the input graph, when only the positive edges are considered. The solutions obtained by the constructive procedure are then used as a starting point for the proposed BVNS algorithm. Efficient implementations of the several configurations of the local search procedure within the BVNS are described. The algorithmic proposal is then compared with previous approaches in the state of the art for the MinSA over different sets of referred instances. The obtained results supported by non-parametric statistical tests, indicate that BVNS can be considered as the new state-of-the-art algorithm for the MinSA.

This paper generalizes the iterated greedy algorithm to solve a multi-objective facility location problem known as the Bi-objective p-Center and p-Dispersion problem ( B p C D ). The new algorithm is coined as Multi-objective Parallel Iterated Greedy (MoPIG) and optimizes more than one objective at the same time. The B p C D seeks to locate p facilities to service or cover a set of n demand points, and the goal is to minimize the maximum distance between facilities and demand points and, at the same time, maximize the minimum distance between all pairs of selected facilities. Computational results demonstrate the effectiveness of the proposed algorithm over the evolutionary algorithms NSGA-II, MOEA/D, and the Strength Pareto Evolutionary Algorithm 2 (SPEA2), comparing them with the optimal solution found by the ϵ -constraint method.

Community detection in social networks is becoming one of the key tasks in social network analysis, since it helps with analyzing groups of users with similar interests. As a consequence, it is possible to detect radicalism or even reduce the size of the data to be analyzed, among other applications. This paper presents a metaheuristic approach based on Greedy Randomized Adaptive Search Procedure (GRASP) methodology for detecting communities in social networks. The community detection problem is modeled as an optimization problem, where the objective function to be optimized is the modularity of the network, a well-known metric in this scientific field. The results obtained outperform classical methods of community detection over a set of real-life instances with respect to the quality of the communities detected.

Abstract The Vertex Bisection Problem (VBP) belongs to the family of well-known graph partitioning problems, where the main goal is to find a partition of the vertices maximizing or minimizing a given objective function. These optimization problems have relevant application in the context of scientific computing, VLSI design circuit, or task scheduling in multi-processor systems. This family of problems has gained importance due to its application in clustering and detection of cliques in social, pathological, and biological networks. In this paper we use Basic Variable Neighborhood Search (BVNS) methodology to solve the VBP. In particular, we propose three constructive procedures and six improvement methods. We introduce a novel scheme for calculating the objective function which substantially reduces the computing time as compared with the direct implementation. After a set of preliminary experiments, the best BVNS design is compared with the state-of-the-art over the same set of instances obtaining better results for both, quality of the solutions and execution time. These results are further confirmed by non-parametric statistical tests.

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.

The Order Batching Problem is an optimization problem belonging to the operational management aspect of a warehouse. It consists of grouping the orders received in a warehouse (each order is composed by a list of items to be collected) in a set of batches in such a way that the time needed to collect all the orders is minimized. Each batch has to be collected by a single picker without exceeding a capacity limit. In this paper we propose several strategies based on the Variable Neighborhood Search methodology to tackle the problem. Our approach outperforms, in terms of quality and computing time, previous attempts in the state of the art. These results are confirmed by non-parametric statistical tests. HighlightsWe address the Order Batching Problem (OBP).We implement a two-stage Variable Neighborhood Search to tackle the OBP.We develop several mechanisms that can be helpful in similar problem.We additionally propose an improved Combined routing strategy.We perform computational experiments that show the superiority of our proposal.

The maximum leaf spanning tree problem consists in finding a spanning tree of a graph that maximizes the number of leaves that the tree has. This problem has been found to be $$\mathcal {NP}$$NP-hard for general graphs. It has several relevant applications in the context of telecommunication networks. In this paper, we tackle this problem by proposing the use of a parallel algorithm based on the strategic oscillation methodology. In particular, we propose two different parallel approaches and we compare our best variant with previous algorithms of the state of the art. The proposed approach outperforms previous ones in the state of the art, which is also confirmed by the use of statistical tests.

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 $$\mathcal {NP}$$-hard problem has practical applications in telecommunication networks, circuit layouts, and other graph-theoretic problems. An interesting application appears in the context of broadcasting in telecommunication networks, where it is interesting to reduce the number of broadcasting computers in the network. These components are relatively expensive and therefore its is desirable to deploy as few of them as possible in the network. This optimization problem is equivalent to maximize the number of non-broadcasting computers. We present a strategic oscillation approach for solving the maximum leaf spanning tree problem. The results obtained by the proposed algorithm are compared with the best previous algorithm found in the literature, showing the superiority of our proposal.

In this work we describe the URJC&UNED participation in the ImageCLEF 2013 Photo Annotation Task. We use visual information to find similar images and textual information extracted from the training set to label the test images. We propose two additional visual features apart from the provided by the organization and a method to expand the textual information available. The new visual features proposed define the images in terms of color and texture, and the textual method uses WordNet to obtain synonyms and hyperonyms of the textual information provided. The score of each concept is obtained by using a co-ocurrence matrix that matches concepts and textual information of the training images. The experimental results show that the proposal is able to obtain competitive results in all the performance measures used.

ABSTRACT We are presenting in this volume selected, peer-reviewed, short papers that were presented at the 3rd International Conference on Variable Neighborhood Search (VNS'14) which took place in Djerba, Tunisia, during October 8-11, 2014.

ABSTRACT Resumen En este trabajo se propone un algoritmo basado en Scat-ter Search para resolver el problema de la minimización del Profile. Se utiliza la estrategia Path Relinking como método base para la genera-ción de nuevas soluciones mediante combinación. El problema del Profile (PMP) es NP-duro y tiene aplicaciones relevantes en técnicas de análi-sis numérico basadas en la manipulación de matrices de gran tamaño. Fue propuesto a comienzos de los 70 pero en el estado del arte no se encuentra ningún método eficiente para la resolución del problema. La amplia experimentación llevada a cabo en este trabajo demuestra que se ha cumplido el objetivo de establecer un nuevo estándar en la solución del PMP.

In this paper we present an evolutionary Path Relin king algorithm for solving unconstrained high dimensional optimization problems. We target 19 types of global optimization functions, for which we test how the optimization strategies that we are proposing perform with increasing dimension. We include in our computational comparison three algorithms from the state-of-the-art, and show that our algorithm is competitive with the m in high dimensional problems.

ABSTRACT Resumen Dado un grafo conexo y no dirigido G = (V, E) y un lími-te entero positivo b, el problema del Vertex Separator (VS) consiste en encontrar el conjunto de vértices C, que eliminado divide G en com-ponentes aisladas A, B, donde max(|A|, |B|) ≤ b. Este es un problema de optimización NP-completo y puede ser utilizado en un amplio rango de aplicaciones. Por ejemplo, en redes de telecomunicaciones un separa-dor determina la capacidad y fragilidad de la red. En el campo de los algoritmos para grafos, el cálculo de pequeños separadores balanceados es mu util, especialmente en los algoritmos del tipo divide y vencerás. Este trabajo presenta un nuevo algoritmo heurístico basado en el méto-do Variable Neighborhood Search (VNS) para el cálculo de separadores. El método es comparado con el estado del arte (dos procedimientos de ramificación y poda recientes). Los resultados muestran que el método obtiene la solució optima en todas las instancias pequeñas y medianas, y obtiene buenos resultados en instancias grandes. Aunque los métodos anteriores aseguran encontrar la solució optima, tienen un tiempo de ejecución mucho mayor que el método presentado (aunqué este no ase-gura que la solución obtenida sea lá optima). 1. Introducción Se define un grafo G = (V, E) mediante su conjunto de vértices V y de aristas E. Sea c j el coste asociado con cada vértice j ∈ V . Un separador en G se define como un subconjunto de vértices o aristas que al ser eliminados convierten el grafo en inconexo. Los separadores también son conocidos por otros nombres, incluyendo bisectores, bifurcadores, cortes balanceados y particiones. Este trabajo se centra en el problema del Vertex Separator (VS), que consiste en encontrar una partición de V en tres conjuntos no vacíos A, B y C, tal que no existe ninguna arista entre A y B, el tamaño de ambos conjuntos esta limitado por un entero positivo b (normalmente representado como una función de |V |), y que minimiza la suma de los pesos de los vértices en C. Dado un grafo G = (V, E), una solución x para el problema del VS puede representarse como tres conjuntos A, B, y C tales que A ∪ B ∪ C = V y A ∩ B =

The maximally diverse grouping problem (MDGP) is an NP-hard problem that consists of forming groups from a given set of elements in such a way that the diversity in the groups is maximized. The MDGP has applications in academics, such as creating diverse teams of students, or in design of VLSI circuits. In this paper we propose a new procedure based on the tabu search methodology to obtain high quality solutions for this optimization problem. Specifically, our method includes a short-term memory component and makes use of the strategic oscillation. Our experimentation shows that the proposed methods compares favorably with previous metaheuristics.

Advances in optical networks have allowed researchers and engineers to develop new services such as real-time on-line gaming, voice over IP (VoIP), video sharing and mobile Internet. In real optical networks, the strength of an optical signal is deteriorated as long as it moves away from the source. Therefore, it is necessary to regenerate the signals periodically using regenerators. The Regenerator Location Problem (RLP) consists of deploying as few of these regenerators as possible, while ensuring all nodes can communicate with each other. The RLP is an NP-hard problem. In this paper we propose a GRASP metaheuristic for the regenerator location problem. Computational experiments show that the proposed procedure outperforms previous heuristics described in the literature in terms of quality solution.

ABSTRACT Resumen En este trabajo se introducen las características ge-nerales de una nueva metaheurística denominada Algoritmos Sociales Jerárquicos o algoritmos HS (Hierarchical Social (HS) Algorithms), inspirados en el comportamiento jerárquico observado en di-versidad de organizaciones humanas y sistemas bio-lógicos. Los algoritmos HS se basan en la optimiza-ción simultánea (competitiva) de un conjunto de so-luciones factibles y disjuntas. En principio, el pro-blema se modela como una sociedad que se divi-de jerárquicamente en grupos, donde cada uno de ellos representa una solución (completa o incom-pleta). Cada grupo evoluciona en modo autónomo o compite con sus grupos vecinos, encontrando solu-ciones mejores por medio de las estrategias que mo-delan la evolución social. En esta evolución social, los grupos de "peor calidad" tienden a desaparecer, enriqueciendo a los grupos de "mejor calidad". Al final del proceso social, sólo sobrevive un grupo que contiene una solución aproximada quasi-óptima al problema planteado.

ABSTRACT Resumen En este trabajo se propone un análisis comparativo de la implementación paralela y secuencial de un algoritmo basado en el es-quema Variable Neighborhood Search. La paralelización se lleva a cabo utilizando NVIDIA CUDA sobre GPU. Para ilustrar el comportamiento de ambas propuestas se utiliza el problema de la maximización del corte (MaxCut Problem -MCP). Dado un grafo G no dirigido, se define un corte como la división del conjunto de vértices de G en dos subconjuntos S y S ′ de forma que S ′ = V \ S. El MCP consiste entonces en encontrar el corte de máximo valor en G de entre todos los posibles. Para resolver dicho problema se propone un esquema basado en la estrategia Basic VNS. La paralelización se aplica a la búsqueda local, analizando las di-ferencias entre la búsqueda local paralela y la secuencial. Los resultados obtenidos muestran como la paralelización de la búsqueda local en GPU consigue reducir en gran medida el tiempo de ejecución, proporcionando soluciones de mayor calidad. 1. Introducción Se define un grafo G = (V, E), con n = |V | y m = |E|, como un conjunto de vértices V y el conjunto de aristas que los unen E. Siendo w ij el peso asociado con la arista (i, j) ∈ E, se define un corte(S, S ′) como la división de V en dos conjuntos S y S ′ = V \S. El valor de dicho corte se calcula mediante la expresión corte(S, S ′) =