Exact stochastic constraint optimisation with applications in network analysis
We present an extensive study of methods for exactly solving stochastic constraint (optimisation) problems (SCPs) in network analysis. These problems are prevalent in science, governance and industry. The first method we study is generic and decomposes stochastic constraints into a multitude of smal...
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| Veröffentlicht in: | Artificial intelligence Jg. 304; S. 103650 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Amsterdam
Elsevier B.V
01.03.2022
Elsevier Science Ltd |
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| ISSN: | 0004-3702, 1872-7921 |
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| Abstract | We present an extensive study of methods for exactly solving stochastic constraint (optimisation) problems (SCPs) in network analysis. These problems are prevalent in science, governance and industry. The first method we study is generic and decomposes stochastic constraints into a multitude of smaller local constraints that are solved using a constraint programming (CP) or mixed-integer programming (MIP) solver. However, many SCPs are formulated on probability distributions with a monotonic property, meaning that adding a positive decision to a partial solution to the problem cannot cause a decrease in solution quality. The second method is specifically designed for solving global stochastic constraints on monotonic probability distributions (SCMDs) in CP. Both methods use knowledge compilation to obtain a decision diagram encoding of the relevant probability distributions, where we focus on ordered binary decision diagrams (OBDDs). We discuss theoretical advantages and disadvantages of these methods and evaluate them experimentally. We observed that global approaches to solving SCMDs outperform decomposition approaches from CP, and perform complementarily to MIP-based decomposition approaches, while scaling much more favourably with instance size. Both methods have many alternative design choices, as both knowledge compilation and constraint solvers are used in a single pipeline. To identify which configurations work best, we apply programming by optimisation. Specifically, we show how an automated algorithm configurator can be used to find optimised configurations of our pipeline. After configuration, our global SCMD solving pipeline outperforms its closest competitor (a MIP-based decomposition pipeline) on all test sets we considered by up to two orders of magnitude in terms of PAR10 scores. |
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| AbstractList | We present an extensive study of methods for exactly solving stochastic constraint (optimisation) problems (SCPs) in network analysis. These problems are prevalent in science, governance and industry. The first method we study is generic and decomposes stochastic constraints into a multitude of smaller local constraints that are solved using a constraint programming (CP) or mixed-integer programming (MIP) solver. However, many SCPs are formulated on probability distributions with a monotonic property, meaning that adding a positive decision to a partial solution to the problem cannot cause a decrease in solution quality. The second method is specifically designed for solving global stochastic constraints on monotonic probability distributions (SCMDs) in CP. Both methods use knowledge compilation to obtain a decision diagram encoding of the relevant probability distributions, where we focus on ordered binary decision diagrams (OBDDs). We discuss theoretical advantages and disadvantages of these methods and evaluate them experimentally. We observed that global approaches to solving SCMDs outperform decomposition approaches from CP, and perform complementarily to MIP-based decomposition approaches, while scaling much more favourably with instance size. Both methods have many alternative design choices, as both knowledge compilation and constraint solvers are used in a single pipeline. To identify which configurations work best, we apply programming by optimisation. Specifically, we show how an automated algorithm configurator can be used to find optimised configurations of our pipeline. After configuration, our global SCMD solving pipeline outperforms its closest competitor (a MIP-based decomposition pipeline) on all test sets we considered by up to two orders of magnitude in terms of PAR10 scores. |
| ArticleNumber | 103650 |
| Author | Nijssen, Siegfried Babaki, Behrouz Hoos, Holger H. Latour, Anna L.D. Fokkinga, Daniël Anastacio, Marie |
| Author_xml | – sequence: 1 givenname: Anna L.D. orcidid: 0000-0002-5802-8271 surname: Latour fullname: Latour, Anna L.D. email: a.l.d.latour@liacs.leidenuniv.nl organization: LIACS, Leiden University, P.O. Box 9512, 2300 RA Leiden, the Netherlands – sequence: 2 givenname: Behrouz orcidid: 0000-0002-0512-4323 surname: Babaki fullname: Babaki, Behrouz email: behrouz.babaki@polymtl.ca organization: Polytechnique Montréal, Montréal (Québec), H3T 1J4, Canada – sequence: 3 givenname: Daniël orcidid: 0000-0001-8507-6570 surname: Fokkinga fullname: Fokkinga, Daniël email: d.b.fokkinga@umail.leidenuniv.nl organization: LIACS, Leiden University, P.O. Box 9512, 2300 RA Leiden, the Netherlands – sequence: 4 givenname: Marie orcidid: 0000-0002-4039-2470 surname: Anastacio fullname: Anastacio, Marie email: m.i.a.anastacio@liacs.leidenuniv.nl organization: LIACS, Leiden University, P.O. Box 9512, 2300 RA Leiden, the Netherlands – sequence: 5 givenname: Holger H. surname: Hoos fullname: Hoos, Holger H. email: hh@liacs.nl organization: LIACS, Leiden University, P.O. Box 9512, 2300 RA Leiden, the Netherlands – sequence: 6 givenname: Siegfried orcidid: 0000-0003-2678-1266 surname: Nijssen fullname: Nijssen, Siegfried email: siegfried.nijssen@uclouvain.be organization: ICTEAM, UCLouvain, Place Sainte-Barbe 2 bte L5.02.01, B-1348 Louvain-la-Neuve, Belgium |
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| Keywords | Ordered binary decision diagrams Global constraints Constraint programming Automated algorithm configuration Probabilistic networks Monotonic probability distributions Probabilistic inference Stochastic constraints |
| Language | English |
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| SubjectTerms | Algorithms Automated algorithm configuration Configurations Constraint programming Decision theory Decomposition Global constraints Integer programming Linear programming Mixed integer Monotonic probability distributions Network analysis Optimization Ordered binary decision diagrams Probabilistic inference Probabilistic networks Probability theory Solvers Stochastic constraints |
| Title | Exact stochastic constraint optimisation with applications in network analysis |
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