Multi-label Classification for the Generation of Sub-problems in Time-constrained Combinatorial Optimization

his paper addresses the resolution of combinatorial optimization problems presenting some kind of recurrent structure, coupled with machine learning techniques. Stemming from the assumption that such recurrent problems are the realization of an unknown generative probabilistic model, data is collected from previous resolutions of such problems and used to train a supervised learning model for multi-label classification. This model is exploited to predict a subset of decision variables to be set heuristically to a certain reference value, thus becoming fixed parameters in the original problem. The remaining variables then form a smaller sub-problem whose solution, while not guaranteed to be optimal for the original problem, can be obtained faster, offering an advantageous tool for tackling time-sensitive tasks.

[1]  Marco Fraccaro,et al.  Machine learning meets mathematical optimization to predict the optimal production of offshore wind parks , 2018, Comput. Oper. Res..

[2]  Le Song,et al.  2 Common Formulation for Greedy Algorithms on Graphs , 2018 .

[3]  Le Song,et al.  Learning to Branch in Mixed Integer Programming , 2016, AAAI.

[4]  Thorsten Koch,et al.  Branching rules revisited , 2005, Oper. Res. Lett..

[5]  Michel Gendreau,et al.  Handbook of Metaheuristics , 2010 .

[6]  He He,et al.  Learning to Search in Branch and Bound Algorithms , 2014, NIPS.

[7]  Grigorios Tsoumakas,et al.  Random k -Labelsets: An Ensemble Method for Multilabel Classification , 2007, ECML.

[8]  Emmanuel Rachelson,et al.  Combining Mixed Integer Programming and Supervised Learning for Fast Re-planning , 2010, 2010 22nd IEEE International Conference on Tools with Artificial Intelligence.

[9]  Andrea Lodi,et al.  Learning a Classification of Mixed-Integer Quadratic Programming Problems , 2017, CPAIOR.

[10]  Yoshua Bengio,et al.  Predicting Solution Summaries to Integer Linear Programs under Imperfect Information with Machine Learning , 2018, ArXiv.

[11]  Marco E. Lübbecke,et al.  Learning When to Use a Decomposition , 2017, CPAIOR.

[12]  Geoff Holmes,et al.  Classifier chains for multi-label classification , 2009, Machine Learning.

[13]  Louis Wehenkel,et al.  A Machine Learning-Based Approximation of Strong Branching , 2017, INFORMS J. Comput..

[14]  M. Carrion,et al.  A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem , 2006, IEEE Transactions on Power Systems.

[15]  Luca Mossina,et al.  Naive Bayes Classification for Subset Selection , 2017, ArXiv.

[16]  Alberto Ceselli,et al.  Random sampling and machine learning to understand good decompositions , 2018, Ann. Oper. Res..

[17]  Eyke Hüllermeier,et al.  Bayes Optimal Multilabel Classification via Probabilistic Classifier Chains , 2010, ICML.

[18]  Laurence A. Wolsey,et al.  Reformulation and Decomposition of Integer Programs , 2009, 50 Years of Integer Programming.

[19]  Saltelli Andrea,et al.  Global Sensitivity Analysis: The Primer , 2008 .

[20]  Andrea Lodi,et al.  On learning and branching: a survey , 2017 .

[21]  Richard C. Larson,et al.  Model Building in Mathematical Programming , 1979 .

[22]  Juliane Jung,et al.  The Traveling Salesman Problem: A Computational Study , 2007 .

[23]  Louis Wehenkel,et al.  Supervised learning of intra-daily recourse strategies for generation management under uncertainties , 2009, 2009 IEEE Bucharest PowerTech.

[24]  Anne Auger,et al.  Theory of Randomized Search Heuristics: Foundations and Recent Developments , 2011, Theory of Randomized Search Heuristics.

[25]  N.P. Padhy,et al.  Unit commitment-a bibliographical survey , 2004, IEEE Transactions on Power Systems.

[26]  George B. Dantzig,et al.  Solution of a Large-Scale Traveling-Salesman Problem , 1954, Oper. Res..

[27]  Darko Zupanic.  Values Suggestion in Mixed Integer Programming by Machine Learning Algorithm , 1999, Electron. Notes Discret. Math..

[28]  Min-Ling Zhang,et al.  A Review on Multi-Label Learning Algorithms , 2014, IEEE Transactions on Knowledge and Data Engineering.

[29]  Patrick Siarry,et al.  A sensitivity analysis method aimed at enhancing the metaheuristics for continuous optimization , 2017, Artificial Intelligence Review.

[30]  David K. Smith.  Theory of Linear and Integer Programming , 1987 .