Understanding the empirical hardness of random optimisation problems

McCreesh, C. , Pettersson, W. and Prosser, P. (2019) Understanding the empirical hardness of random optimisation problems. In: 25th International Conference on Principles and Practice of Constraint Programming, Stamford, CT, USA, 30 Sep - 04 Oct 2019, pp. 333-349. (doi:10.1007/978-3-030-30048-7_20)

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Abstract

We look at the empirical complexity of the maximum clique problem, the graph colouring problem, and the maximum satisfiability problem, in randomly generated instances. Although each is NP-hard, we encounter exponential behaviour only with certain choices of instance generation parameters. To explain this, we link the difficulty of optimisation to the difficulty of a small number of decision problems, which are already better-understood through phenomena like phase transitions with associated complexity peaks. However, our results show that individual decision problems can interact in very different ways, leading to different behaviour for each optimisation problem. Finally, we uncover a conflict between anytime and overall behaviour in algorithm design, and discuss the implications for the design of experiments and of search strategies such as variable- and value-ordering heuristics.

Item Type:Conference Proceedings
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Prosser, Dr Patrick and Pettersson, Dr William and Mccreesh, Dr Ciaran
Authors: McCreesh, C., Pettersson, W., and Prosser, P.
College/School:College of Science and Engineering > School of Computing Science
Journal Name:Lecture Notes in Computer Science
Publisher:Springer
ISSN:0302-9743
ISSN (Online):0302-9743
Published Online:23 September 2019
Copyright Holders:Copyright © 2019 Springer Nature Switzerland AG
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
3005250Modelling and Optimisation with GraphsPatrick ProsserEngineering and Physical Sciences Research Council (EPSRC)EP/P026842/1Computing Science
3008080IP-MATCH: Integer Programming for Large and Complex Matching ProblemsDavid ManloveEngineering and Physical Sciences Research Council (EPSRC)EP/P028306/1Computing Science