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Hardness Studies for NRP

Hardness Studies for NRP. T. Messelis , S. Haspeslagh , P. De Causmaecker B. Bilgin , G. Vanden Berghe. Overview. Introduction Method Our work Conclusions Future work. Introduction. predict performance of one or more algorithms on a specific problem instance to be able to

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Hardness Studies for NRP

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  1. Hardness Studies for NRP T. Messelis, S. Haspeslagh, P. De Causmaecker B. Bilgin, G. VandenBerghe

  2. Overview T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. VandenBerghe Introduction Method Our work Conclusions Future work

  3. Introduction T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe • predict performance • of one or more algorithms • on a specific problem instance • to be able to • know in advance how good an algorithm will do • choose the ‘best’ algorithm out of a portfolio • choose the ‘best’ parameter setting

  4. Method T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe • Build empirical hardness models • empirical: performance of some algorithm • hardness: measured by some performance criteria • time spent by an algorithm searching for a solution • quality of an (optimal) solution • gap between found and optimal solution • Model hardness as a function of features • computationally inexpensive ‘properties’ • e.g. clauses-to-variables ratio (SAT) • e.g. maximum consecutive working days (NRP)

  5. General procedure T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe • Introduced by K. Leyton-Brown et al. • Select problem instance distribution • Select one or more algorithms • Create a set of features • Generate an instance set, calculate features and determine the algorithm performances • Eliminate redundant or uninformative features • Use machine learning techniques to select functions of the features that approximate the algorithm’s performances K. Leyton-Brown, E. Nudelman, Y. Shoham. Learning the empirical hardness of optimisation problems: The case of combinatorial auctions. In LNCS, 2002

  6. Our motivation T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe • This strategy has been successful in different areas: • combinatorial auction: winner determination problem • uniform random 3-SAT • accurate algorithm performance prediction • algorithm portfolio approach (SATzilla) • won several gold medals in SAT competitions • Apply it to Nurse Rostering!

  7. Nurse Rostering Problem T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe • problem of assigning nurses to shifts, given a set of hard and soft constraints • Performance: • time spent by a complete search algorithm to find the optimal roster • quality of this optimal roster • quality of a roster obtained by a heuristic algorithm, ran for some fixed period of time • quality gap between both solutions

  8. NRP: first approach T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe Translate NRP instances to SAT instances and use existing SAT features to build models translation based on numberings solve instances to optimum using CPLEX run a metaheuristic for 10 seconds

  9. NRP: first approach T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe Regression results on predicting CPLEX objective

  10. NRP: second approach T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe Come up with a feature set specifically for NRP and build models from these features on the same set of NRP instances for the same performance indicators

  11. NRP: second approach T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe • very simple set of features: • some problem parameters • max & min number of assignments • max & min number of consecutive working days • max & min number of consecutive free days • and ratio’s of those parameters • max cons working days / min cons working days • max num assignments / min cons working days • availability / coverage requirements (tightness) • ...

  12. NRP: second approach T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe Regression results on predicting CPLEX objective

  13. Conclusions T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe • We can build accurate models to predict algorithm performance, based on very basic properties of NRP instances. • objective values • models for the objective values of both CPLEX and the metaheuristic are fairly accurate • gap • less accurate predictions, however with a standard error of 0.95 • CPLEX running time • not very accurate, due to very high variability in the running time

  14. Future work T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe • building models on a larger scale • now only a very limited dataset • more (sophisticated) features for NRP instances • now only a very basic set with some aggregate functions of it • combining both SAT features and NRP features

  15. Questions? T. Messelis, S. Haspeslagh, P. De Causmaecker, B. Bilgin, G. Vanden Berghe

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