Efficient Incremental Modelling and Solving

In various scenarios, a single phase of modelling and solving is either not sufficient or not feasible to solve the problem at hand. A standard approach to solving AI planning problems, for example, is to incrementally extend the planning horizon and solve the problem of trying to find a plan of a particular length. Indeed, any optimization problem can be solved as a sequence of decision problems in which the objective value is incrementally updated. Another example is constraint dominance programming (CDP), in which search is organized into a sequence of levels. The contribution of this work is to enable a native interaction between SAT solvers and the automated modelling system Savile Row to support efficient incremental modelling and solving. This allows adding new decision variables, posting new constraints and removing existing constraints (via assumptions) between incremental steps. Two additional benefits of the native coupling of modelling and solving are the ability to retain learned information between SAT solver calls and to enable SAT assumptions, further improving flexibility and efficiency. Experiments on one optimisation problem and five pattern mining tasks demonstrate that the native interaction between the modelling system and SAT solver consistently improves performance significantly.

[1]  Tias Guns,et al.  Towards Improving Solution Dominance with Incomparability Conditions: A case-study using Generator Itemset Mining , 2019, ArXiv.

[2]  Ian Miguel,et al.  Automatically Improving SAT Encoding of Constraint Problems Through Common Subexpression Elimination in Savile Row , 2015, CP.

[3]  Florian Lemmerich,et al.  Fast Discovery of Relevant Subgroup Patterns , 2010, FLAIRS Conference.

[4]  Nicolas Pasquier,et al.  Discovering Frequent Closed Itemsets for Association Rules , 1999, ICDT.

[5]  Anton Dries,et al.  Dominance Programming for Itemset Mining , 2013, 2013 IEEE 13th International Conference on Data Mining.

[6]  Luc De Raedt,et al.  Constraint programming for itemset mining , 2008, KDD.

[7]  Ian Miguel,et al.  Closed Frequent Itemset Mining with Arbitrary Side Constraints , 2018, 2018 IEEE International Conference on Data Mining Workshops (ICDMW).

[8]  Amedeo Napoli,et al.  Towards Rare Itemset Mining , 2007, 19th IEEE International Conference on Tools with Artificial Intelligence(ICTAI 2007).

[9]  Vasco M. Manquinho,et al.  Open-WBO: A Modular MaxSAT Solver, , 2014, SAT.

[10]  Rakesh Agarwal,et al.  Fast Algorithms for Mining Association Rules , 1994, VLDB 1994.

[11]  Christopher Mears,et al.  Learning from Learning Solvers , 2016, CP.

[12]  Peter Nightingale,et al.  Essence' Description , 2016, ArXiv.

[13]  Ian P. Gent,et al.  Automatically improving constraint models in Savile Row , 2017, Artif. Intell..

[14]  Masao Mori,et al.  A genetic algorithm for multi-mode resource constrained project scheduling problem , 1997, Eur. J. Oper. Res..

[15]  Gilles Audemard,et al.  On the Glucose SAT Solver , 2018, Int. J. Artif. Intell. Tools.

[16]  Olivier Roussel,et al.  The International SAT Solver Competitions , 2012, AI Mag..

[17]  Jean-François Boulicaut,et al.  Approximation of Frequency Queris by Means of Free-Sets , 2000, PKDD.

[18]  Ian P. Gent,et al.  Minion: A Fast Scalable Constraint Solver , 2006, ECAI.

[19]  Mohammed J. Zaki.  Scalable Algorithms for Association Mining , 2000, IEEE Trans. Knowl. Data Eng..

[20]  Francesco Bonchi,et al.  On closed constrained frequent pattern mining , 2004, Fourth IEEE International Conference on Data Mining (ICDM'04).

[21]  Rainer Kolisch,et al.  PSPLIB - A project scheduling problem library: OR Software - ORSEP Operations Research Software Exchange Program , 1997 .

[22]  Inês Lynce,et al.  Conflict-Driven Clause Learning SAT Solvers , 2009, Handbook of Satisfiability.

[23]  Jiawei Han,et al.  Discriminative Frequent Pattern Analysis for Effective Classification , 2007, 2007 IEEE 23rd International Conference on Data Engineering.

[24]  Bilal Syed Hussain,et al.  Automated Symmetry Breaking and Model Selection in Conjure , 2013, CP.

[25]  Tias Guns,et al.  Exploiting Incomparability in Solution Dominance: Improving General Purpose Constraint-Based Mining , 2020, ECAI.