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Title: Symmetry and degeneracy in nonconvex optimisation problems : application to heat recovery networks
Author: Kouyialis, Georgia
ISNI:       0000 0004 7659 014X
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2019
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Many optimisation problems are formulated with nonconvexities in the objective function and the set of constraints. Nonconvex optimisation has applications in a wide range of disciplines and this thesis examines scheduling and process network design problems. Two main solution approaches are used to deal with such problems: exact and approximation algorithms. Exact algorithms guarantee to solve a problem to global optimality but may require exponential time. On the other hand, approximation algorithms can generate near-optimal solutions in reasonable time. Both sets of algorithms could benefit from insights on the special structure of optimisation problems, e.g. symmetry and degeneracy. This thesis proposes novel structures i.e. matrices and graphs, for detecting symmetry in Quadratically Constrained Quadratic Programs. In several critically important engineering applications, such as Heat Exchanger Network Synthesis (HENS), symmetry and degeneracy have not been characterised yet. This work investigates the minimum number of matches, e.g. heat exchanger units, which is the current bottleneck in designing HENS. We classify special cases with many equivalent optimal solutions and define symmetry and degeneracy. Due to the aforementioned complexities, we report via computational results that state-of-the-art approaches cannot solve the minimum number of matches problem to global optimality for moderately-sized instances. Hence this thesis develops three classes of heuristics with performance guarantees to the minimum number of matches problem. Each of these heuristics is either novel or provably the best in its class. Our work has interesting implications for solving the problem exactly, e.g. the analysis into reducing big-M parameters or the possibility of quickly generating good primal feasible solutions. Detecting special structures in optimisation problems and dealing with instances of HENS is neither trivial nor easy. This thesis provides an in-depth analysis of these problems and develops fundamental tools to efficiently solve challenging optimisation problems via both exact and approximation approaches.
Supervisor: Misener, Ruth ; Parpas, Panos Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral