Solving Over-Constrained Problems with SAT Technology

We present a new generic problem solving approach for overconstrained problems based on Max-SAT. We first define a clausal form formalism that deals with blocks of clauses instead of individual clauses, and that allows one to declare each block either as hard (i.e., must be satisfied by any solution) or soft (i.e., can be violated by some solution). We then present two Max-SAT solvers that find a truth assignment that satisfies all the hard blocks of clauses and the maximum number of soft blocks of clauses. Our solvers are branch and bound algorithms equipped with original lazy data structures; the first one incorporates static variable selection heuristics while the second one incorporates dynamic variable selection heuristics. Finally, we present an experimental investigation to assess the performance of our approach on a representative sample of instances (random 2-SAT, Max-CSP, and graph coloring).Research partially supported by projects TIN2004-07933-C3-03 and TIC2003-00950 funded by the Ministerio de Educación y Ciencia. The second author is supported by a grant Ramón y Cajal

The Complexity of 3-Valued Lukasiewicz Rules

It is known that determining the satisfiability of n-valued Łukasiewicz rules is NP-complete for n ≥ 4, as well as that it can be solved in time linear in the length of the formula in the Boolean case (when n = 2). However, the complexity for n = 3 is an open problem. In this paper we formally prove that the satisfiability problem for 3-valued Łukasiewicz rules is NP-complete. Moreover, we also prove that when the consequent of the rule has at most one element, the problem is polynomially solvable. © Springer International Publishing Switzerland 2015.Research partially supported by the Generalitat de Catalunya grant AGAUR 2014-SGR-118, and the Ministerio de Economía y Competividad projects AT CONSOLIDER CSD2007-0022, INGENIO 2010, CO-PRIVACY TIN2011-27076-C03-03, EDETRI TIN2012-39348-C02-01 and HeLo TIN2012-33042. The second author was supported by Mobility Grant PRX14/00195 of the Ministerio de Educación, Cultura y DeportePeer reviewe

Modeling energy consumption in automated vacuum waste collection systems

In a world where resources are scarce and urban areas consume the vast majority of these resources, it is vital to make cities greener and more sustainable. A smart city is a city in which information and communications technology are merged with traditional infrastructures, coordinated and integrated using new digital technologies. The increasing amount of waste generated, and the collection and treatment of waste poses a major challenge to modern urban planning in general, and to smart cities in particular. To cope with this problem, automated vacuum waste collection (AVWC) uses air suction on a closed network of underground pipes to transport waste from the drop off points scattered throughout the city to a central collection point, reducing greenhouse gas emissions and the inconveniences of conventional methods (odours, noise, etc.). Since a significant part of the cost of operating AVWC systems is energy consumption, we have developed a model with the aim of applying constraint programming technology to schedule the daily emptying sequences of the drop off points in such a way that energy consumption is minimized. In this paper we describe how the problem of deciding the drop off points that should be emptied at a given time can be modeled as a constraint integer programming (CIP) problem. Moreover, we report on experiments using real data from AVWC systems installed in different cities that provide empirical evidence that CIP offers a suitable technology for reducing energy consumption in AVWC.This work has been partially funded by projects: ARINF (TIN2009-14704-C03-01/03) and TASSAT (TIN2010-20967-C04-01/ 03) from Spain MICINN and project Newmatica (IPT-2011-1496- 310000) from program INNPACTO funded by MICINN (until 2011) and MINECO (from 2011)

Analyzing the instances of the MaxSAT evaluation

The MaxSAT Evaluation [1] is an affiliated event of the SAT Conference that is held every year since 2006, and is devoted to empirically evaluate exact MaxSAT algorithms solving any of the following problems: MaxSAT, Weighted MaxSAT (WMaxSAT), Partial MaxSAT (PMaxSAT), and Weighted Partial MaxSAT (WPMaxSAT). The objective of this paper is to analyze the instances of the 2010 MaxSAT Evaluation in order to gain new insights into their computational hardness, answer some questions that have been asked to us as organizers, and evaluate how appropriate are the current settings of parameters such as timeout and available RAM memory. To this end, we conducted a number of experiments, which were performed on a cluster with 160 2 GHz AMD Opteron 248 Processors with 1 GB of RAM memory. In the experiments, we considered the 2,675 instances of the 2010 MaxSAT Evaluation: 544 MaxSAT instances, 349 WMaxSAT instances, 1,122 PMaxSAT instances, and 660 WPMaxSAT instances. Instances were assigned to one of the following three categories: random, crafted and industrial. We used the 17 solvers that participated in MaxSAT-2010. They can be classified into three main types: branch and bound (B&B) solvers, satisfiability-based (sat-based) and unsatisfiability-based (unsat-based) solvers. In the first type, we find 10 solvers: akmaxsat, akmaxsat ls, IncMaxSatz, IncWMaxSatz, Maxsat Power, LS Power, WMaxsat Power, LSW Power, WMaxSatz-2009, and WMaxSatz+. In the second type, we find 2 solvers: SAT4J-Maxsat,and QMaxSAT. In the third type, we find 5 solvers: WPM1, PM2, WPM2, wbo 1.4a, and wbo 1.4b.Research supported by Generalitat de Catalunya (2009-SGR-1434), Ministerio de Ciencia e Innovación (CONSOLIDER CSD2007-0022, INGENIO 2010, Accion Integrada HA2008- ´ 0017, TIN2009-14704-C03-01, and TIN2010-20967-C04-01/03), and the Secretaría General de Universidades del Ministerio de Educacion: Programa Nacional de Movilidad de Recursos ´ Humanos