Automatic Identification and Exploitation of Dominance Relations in Constraint Optimization Problems
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| Publicado en: | PQDT - Global (2022) |
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ProQuest Dissertations & Theses
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| Acceso en línea: | Citation/Abstract Full Text - PDF |
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| Resumen: | Constraint Optimization Problems (COPs) are ubiquitous and challenging in computer science. Constraint Programming (CP), which encompasses the Branch and Bound (BnB) algorithm augmenting with various constraint techniques, is a typical paradigm for solving COPs. Dominance relations describe relations among solutions of COPs, where some solutions are known to be subordinate compared to others concerning satisfiability of constraints and/or optimality of the objective. Dominance breaking is a technique to exclude dominated solutions from the search space and can speed up the solving time of the BnB algorithm for many real-life problems. Identification of dominance relations in COPs, however, usually requires a deep understanding of the problems and sometimes even ingenuity. In this thesis, we present several contributions to automatic dominance breaking in COPS.First, we propose a theoretical framework to enable automatic dominance breaking for a class of COPs consisting of efficiently checkable objectives and constraints. Constraints for dominance breaking are usually of various forms for different problems. We overcome this difficulty by restricting the form of constraints to be nogood constraints, which are elementary constraints and can be handled easily in CP. Our framework formulates the generation of dominance breaking nogoods as constraint satisfaction. We give theorems on the sufficient conditions governing when the generated nogood constraints are valid dominance breaking constraints in COPs. Experimentation on a diversified set of benchmarks confirms the effectiveness of automatically generated nogoods, which compares favorably against manually identified dominance breaking constraints both in efficiency and ease of use.Second, we further extend the applicability and improve the efficiency of the proposed framework with two theoretical and practical innovations. Our first innovation opens up possibilities to apply automatic dominance breaking on COPs with non-efficiently checkable constraints. We give conditions on when and how non-efficiently checkable constraints can be ignored in nogood generation, and yet our method still produces sufficient useful dominance breaking nogoods for solving COPs. The second innovation identifies redundant and useless dominance breaking nogoods in solving COPs. The constraint satisfaction problems for nogood generation are strengthened using the notion of Common Assignment Elimination to avoid generating nogoods that are redundant with respect to others, and thus the nogood generation time is reduced substantially. Our experimental results confirm the enhanced applicability of our theory-backed innovations, which allow us to tackle previously impractical benchmarks.Third, we enable automatic dominance breaking for COPs containing nested function calls. Such COPs are usually transformed into normalized COPs with introduced variables and functional constraints. We generalize the theory of dominance to normalized COPs and propose a rewriting system for automatic derivation of sufficient conditions in nogood generation based on functional constraints and their properties such as monotonicity, commutativity, and associativity. Experimentation on various benchmarks confirms the efficiency of the generated nogoods to solve problems with ineffective or no known dominance breaking constraints. Even when nogoods are costly to generate, we give case studies to show how we discover new dominance (symmetry) breaking constraints by recognizing the nogood patterns of small instances.The proposed framework also sharpens our understandings of dominance breaking methods. We give case studies on various COPs comparing the strength of the dominance breaking constraints given in the literature with the generated dominance nogoods, and demonstrate the generality of our proposed framework. |
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| ISBN: | 9798304980746 |
| Fuente: | ProQuest Dissertations & Theses Global |