Polytechnic University of Catalonia

About: Polytechnic University of Catalonia is a education organization based out in Barcelona, Spain. It is known for research contribution in the topics: Finite element method & Population. The organization has 16006 authors who have published 45325 publications receiving 949306 citations. The organization is also known as: UPC - BarcelonaTECH & Technical University of Catalonia.

Existential arc consistency: getting closer to full arc consistency in weighted CSPs

Abstract: The weighted CSP framework is a soft constraint framework with a wide range of applications. Most current state-of-the-art complete solvers can be described as a basic depth-first branch and bound search that maintain some form of arc consistency during the search. In this paper we introduce a new stronger form of arc consistency, that we call existential directional arc consistency and we provide an algorithm to enforce it. The efficiency of the algorithm is empirically demonstrated in a variety of domains.

Extremal graph theory for metric dimension and diameter

Abstract: A set of vertices $S$ resolves a connected graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The metric dimension of $G$ is the minimum cardinality of a resolving set of $G$. Let ${\cal G}_{\beta,D}$ be the set of graphs with metric dimension $\beta$ and diameter $D$. It is well-known that the minimum order of a graph in ${\cal G}_{\beta,D}$ is exactly $\beta+D$. The first contribution of this paper is to characterise the graphs in ${\cal G}_{\beta,D}$ with order $\beta+D$ for all values of $\beta$ and $D$. Such a characterisation was previously only known for $D\leq2$ or $\beta\leq1$. The second contribution is to determine the maximum order of a graph in ${\cal G}_{\beta,D}$ for all values of $D$ and $\beta$. Only a weak upper bound was previously known.

Heuristic solutions to the problem of routing school buses with multiple objectives

Abstract: In this paper we address the problem of routing school buses in a rural area. We approach this problem with a node routing model with multiple objectives that arise from conflicting viewpoints. From the point of view of cost, it is desirable to minimise the number of buses used to transport students from their homes to school and back. From the point of view of service, it is desirable to minimise the time that a given student spends en route. The current literature deals primarily with single-objective problems and the models with multiple objectives typically employ a weighted function to combine the objectives into a single one. We develop a solution procedure that considers each objective separately and search for a set of efficient solutions instead of a single optimum. Our solution procedure is based on constructing, improving and then combining solutions within the framework of the evolutionary approach known as scatter search. Experimental testing with real data is used to assess the merit of our proposed procedure.