- Author:
- Athanassios G. Siapas,
- Supervisor:
- Gerald Jay Sussman
Local search methods constitute one of the most successful approaches to solving large-scale combinatorial optimization problems. The objective of this thesis is to investigate the effects of parallelizing such methods. It will be demonstrated that as parallelism is increased, optimization performance initially improves, but then abruptly degrades to no better than random search beyond a certain point. This transition is surprisingly sharp and will be shown to share many of the characteristics of thermodynamic phase transitions. Its existence will be demonstrated for a family of generalized spin-glass models and the traveling salesman problem. Techniques from statistical mechanics are used to make the correspondence between the physics of phase transitions and the performance of parallelized optimizing systems more precise, demonstrating strong connections between these seemingly unrelated fields. Finite-size scaling is used to characterize size-dependent effects near the transition, and analytical insight is obtained through a mean-field approximation. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
Cited By
- Low Y, Bickson D, Gonzalez J, Guestrin C, Kyrola A and Hellerstein J (2012). Distributed GraphLab, Proceedings of the VLDB Endowment, 5:8, (716-727), Online publication date: 1-Apr-2012.
- Roli A Criticality and Parallelism in Structured SAT Instances Proceedings of the 8th International Conference on Principles and Practice of Constraint Programming, (714-719)
- Gomes C, Selman B, Crato N and Kautz H (2019). Heavy-Tailed Phenomena in Satisfiability and Constraint Satisfaction Problems, Journal of Automated Reasoning, 24:1-2, (67-100), Online publication date: 1-Feb-2000.
- Mavridou T and Pardalos P (2019). Simulated Annealing and Genetic Algorithms for the Facility LayoutProblem, Computational Optimization and Applications, 7:1, (111-126), Online publication date: 1-Jan-1997.
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