A Logical Approach to Efficient Max-SAT solving

Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there has been considerable interest in finding efficient solving techniques. Most of this work focus on the computation of good quality lower bounds to be used within a branch and bound DPLL-like algorithm. Most often, these lower bounds are described in a procedural way. Because of that, it is difficult to realize the {\em logic} that is behind. In this paper we introduce an original framework for Max-SAT that stresses the parallelism with classical SAT. Then, we extend the two basic SAT solving techniques: {\em search} and {\em inference}. We show that many algorithmic {\em tricks} used in state-of-the-art Max-SAT solvers are easily expressable in {\em logic} terms with our framework in a unified manner. Besides, we introduce an original search algorithm that performs a restricted amount of {\em weighted resolution} at each visited node. We empirically compare our algorithm with a variety of solving alternatives on several benchmarks. Our experiments, which constitute to the best of our knowledge the most comprehensive Max-sat evaluation ever reported, show that our algorithm is generally orders of magnitude faster than any competitor

Limited discrepancy AND/OR search and its application to optimization tasks in graphical models

Many combinatorial problems are solved with a Depth-First search (DFS) guided by a heuristic and it is well-known that this method is very fragile with respect to heuristic mistakes. One standard way to make DFS more robust is to search by increasing number of discrepancies. This approach has been found useful in several domains where the search structure is a height-bounded OR tree. In this paper we investigate the generalization of discrepancy-based search to AND/OR search trees and propose an extension of the Limited Discrepancy Search (LDS) algorithm. We demonstrate the relevance of our proposal in the context of Graphical Models. In these problems, which can be solved with either a standard OR search tree or an AND/OR tree, we show the superiority of our approach. For a fixed number of discrepancies, the search space visited by the AND/OR algorithm strictly contains the search space visited by standard LDS, and many more nodes can be visited due to the multiplicative effect of the AND/OR decomposition. Besides, if the AND/OR tree achieves a significant size reduction with respect to the standard OR tree, the cost of each iteration of the AND/OR algorithm is asymptotically lower than in standard LDS. We report experiments on the minsum problem on different domains and show that the AND/OR version of LDS usually obtains better solutions given the same CPU time.Peer ReviewedPostprint (published version

Look-ahead with mini-bucket heuristics for MPE

The paper investigates the potential of look-ahead in the con-text of AND/OR search in graphical models using the Mini-Bucket heuristic for combinatorial optimization tasks (e.g., MAP/MPE or weighted CSPs). We present and analyze the complexity of computing the residual (a.k.a Bellman update) of the Mini-Bucket heuristic and show how this can be used to identify which parts of the search space are more likely to benefit from look-ahead and how to bound its overhead. We also rephrase the look-ahead computation as a graphical model, to facilitate structure exploiting inference schemes. We demonstrate empirically that augmenting Mini-Bucket heuristics by look-ahead is a cost-effective way of increasing the power of Branch-And-Bound search.Postprint (published version

Proof complexity for the maximum satisfiability problem and its use in SAT refutations

MaxSAT, the optimization version of the well-known SAT problem, has attracted a lot of research interest in the past decade. Motivated by the many important applications and inspired by the success of modern SAT solvers, researchers have developed many MaxSAT solvers. Since most research is algorithmic, its significance is mostly evaluated empirically. In this paper, we want to address MaxSAT from the more formal point of view of proof complexity. With that aim, we start providing basic definitions and proving some basic results. Then we analyse the effect of adding split and virtual, two original inference rules, to MaxSAT resolution. We show that each addition makes the resulting proof system stronger, even when virtual is restricted to empty clauses (0-virtual). We also analyse the power of our proof systems in the particular case of SAT refutations. We show that our strongest system, ResSV, is equivalent to circular and dual rail with split. We also analyse empirically some known gadget-based reformulations. Our results seem to indicate that the advantage of these three seemingly different systems over general resolution comes mainly from their ability of augmenting the original formula with hypothetical inconsistencies, as captured in a very simple way by the virtual rule.Under project RTI2018-094403-B-C33 funded by MCIN/AEI/ 10.13039/501100011033 and FEDER ”Una manera de hacer Europa"Peer ReviewedPostprint (author's final draft

Experiencia en Proyectos Fin de Carrera de cooperación con países en vías de desarrollo

Los Proyectos Fin de Carrera son una buena ocasión para implicar a los alumnos en proyectos de cooperación con países en vías de desarrollo. En este póster se presentan dos experiencias de proyectos ya finalizados y en explotación en los campamentos de refugiados de la República Árabe Saharaui Democrática. Se explica cómo se contactó con los usuarios finales, cómo se financió y los resultados obtenidos.Este trabajo ha sido apoyado por Ministerio de Ciencia y Tecnología de España (Proyecto TIN 2004-07739-C02-01

Choosing the root of the tree decomposition when solving WCSPs: preliminary results

In this paper we analyze the effect of selecting the root in a tree decomposition when using decomposition-based backtracking algorithms. We focus on optimization tasks for Graphical Models using the BTD algorithm. We show that the choice of the root typically has a dramatic effect in the solving performance. Then we investigate different simple measures to predict near optimal roots. Our study shows that correlations are often low, so the automatic selection of a near optimal root will require more sophisticated techniques.Projects RTI2018-094403-B-C33, funded by: FEDER/Ministerio de Ciencia e Innovación Agencia Estatal de Investigación,SpainPeer ReviewedPostprint (published version

Residual-guided look-ahead in AND/OR search for graphical models

We introduce the concept of local bucket error for the mini-bucket heuristics and show how it can be used to improve the power of AND/OR search for combinatorial optimization tasks in graphical models (e.g. MAP/MPE or weighted CSPs). The local bucket error illuminates how the heuristic errors are distributed in the search space, guided by the mini-bucket heuristic. We present and analyze methods for compiling the local bucket-errors (exactly and approximately) and show that they can be used to yield an effective tool for balancing look-ahead overhead during search. This can be especially instrumental when memory is restricted, accommodating the generation of only weak compiled heuristics. We illustrate the impact of the proposed schemes in an extensive empirical evaluation for both finding exact solutions and anytime suboptimal solutions.Peer ReviewedPostprint (published version

Análisis y explotación del framework Palabos para la resolución de problemas de aerodinámica utilizando el método Lattice-Boltzmann

Para el presente proyecto, se ha desarrollado un software de fluidodinámica computacional (CFD) que permite realizar simulaciones de aerodinámica externa utilizando el método Lattice-Boltzmann. Frente a otras soluciones, en las que se requiere un gran trabajo para obtener un mallado adecuado, pre-procesando la geometría de trabajo y posteriormente depurando la malla obtenida, con esta herramienta el proceso de discretización del dominio se realiza de manera automática, realizando unos ajustes mínimos en el fichero con la geometría de trabajo. Resulta especialmente interesante su facilidad de uso, como ya se ha indicado, y que se trate de una herramienta gratuita y Open Source, permitiendo así que cualquier persona puede acceder a su código y modificarlo para adaptarlo a sus necesidades. Para no tener que desarrollar todo el código desde cero, se ha utilizado el framework Palabos en el núcleo del programa, parte encargada de realizar la simulación, a la que se le ha dotado de una interfaz gráfica y un sistema de avisos en Python. Para comprobar el funcionamiento del túnel, se han realizado una serie de simulaciones, todas ellas con números de Reynolds bajos, ya que, como se explicará, haberlas realizado para números de Reynolds más elevados hubiera supuesto un coste computacional muy elevado, del cual no se disponía

Driving Innovation by Managing Entrepreneurial Orientation, Cooperation and Learning for the Sustainability of Companies in the Energy Sector

Nowadays, the attitude of companies seems to play a relevant role in detecting and exploiting opportunities to create value, especially in terms of knowledge and cooperation. Thereon, the concept of entrepreneurial orientation has become relevant over the last years. Firms are entrepreneurially oriented when their decision-making, techniques, and procedures allow them to identify opportunities, develop a proactive mindset, and use creative ways to achieve their objectives. The purpose of this paper is to empirically analyze the relationship between entrepreneurial orientation and companies’ innovation capacity, in addition to the mediating effect of entrepreneurial networks and firms’ learning capacity in this relationship. A sample of 197 Spanish companies in the energy sector is analyzed using the variance-based structural equation modeling technique (PLS-SEM), using the software “SmartPLS” in its version 3.9. The results show a direct positive and significant influence of entrepreneurial orientation on companies’ innovation capacity, as well as the existence of an indirect effect through the mediation of entrepreneurial networks and the learning capacity of firms. It is concluded that businesses must dedicate time and resources to develop a strong entrepreneurial orientation which, in addition to allowing them to exploit external entrepreneurial networks, boosts their learning and innovation capabilities, favoring the development of new sustainable possibilities for value creation