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Hardness analysis

Hardness analysis. Tommy Messelis, Patrick De Causmaecker. Intro. Empirical Harndess Models model the empirical hardness performance of some algorithm(s) on a specific instance as a function of features computationally inexpensive ‘properties’ of the instance

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Hardness analysis

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  1. Hardness analysis Tommy Messelis, Patrick De Causmaecker

  2. Intro • Empirical Harndess Models • model the empirical hardness • performance of some algorithm(s) on a specific instance • as a function of features • computationally inexpensive ‘properties’ of the instance • allow for performance prediction • algorithm portfolio approach • parameter tuning

  3. Procedure • introduced by K. Leyton-Brown et al. • Identify a problem instance distribution • Selectone or morealgorithms • Choose a feature set • Generate an instance set from the distribution, calculate all features and determine all performance criteria • Eliminateredundant/uninformative features • Use machine learning techniques to select functions of the features that approximate the algorithm’s performance(s) K. Leyton-Brown, E. Nudelman, Y. Shoham. Learning the empirical hardness of optimisation problems: The case of combinatorial auctions. In LNCS, 2002

  4. So far • successful in: • Winner Determination Problem (combinatorial auctions) • Propositional Satisfiability Problem (SAT) • Scheduling & Timetabling • Nurse Rostering Problem (at least on a small scale) • directly on NRP representation • on a translation to SAT • slightly more accurate models !

  5. Conclusions • Translating to SAT is very usefull • abstract way of thinking • no expert knowledge needed • there is already an extensive set of features • what can we do for other problems?

  6. What is to come • MaxSAT • optimisation variant of SAT problems • literature only contains runtime predictions for SAT • predict other performance criteria • for other algorithms aiming to find an optimal solution

  7. What is to come • about translation of NRP instances into SAT • optimal solution for the resulting SAT problem is not the optimal solution for the NRP problem • one constraint generates an arbitrary number of clauses • there is no concept that keeps clauses together • no conservation of the objective function of the NRP instance • groupSAT as a new model • keep clauses together • adapt maxSAT algorithms • in the end: solve NRP by (adapted) state-of-the-art maxSAT algorithms

  8. Questions?

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