6 research outputs found

    Designing Energy-Efficient Heat Recovery Networks using Mixed-Integer Nonlinear Optimisation

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    Many industrial processes involve heating and cooling liquids: a quarter of the EU 2012 energy consumption came from industry and industry uses 73% of this energy on heating and cooling. We discuss mixed-integer nonlinear optimisation and its applications to energy efficiency. Our particular emphasis is on algorithms and solution techniques enabling optimisation for large-scale industrial networks. As a first application, optimising heat exchangers networks may increase efficiency in industrial plants. We develop deterministic global optimisation algorithms for a mixed-integer nonlinear optimisation model that simultaneously incorporates utility cost, equipment area, and hot/cold stream matches. We automatically recognise and exploit special mathematical structures common in heat recovery. We also computationally demonstrate the impact on the global optimisation solver ANTIGONE and benchmark large-scale test cases against heuristic approaches. As a second application, we discuss special structure in nonconvex quadratically-constrained optimisation problems, particularly through the lens of stream mixing and intermediate blending on process systems engineering networks. We take a parametric approach to uncovering topological structure and sparsity of the standard pooling problem in its p-formulation. We show that the sparse patterns of active topological structure are associated with a piecewise objective function. Finally, the presentation explains the conditions under which sparsity vanishes and where the combinatorial complexity emerges to cross over the P/NP boundary. We formally present the results obtained and their derivations for various specialised instances

    Exploiting structure in nonconvex quadratic optimisation

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    Finding globally-optimal solutions in quadratic nonconvex optimisation problems deterministically at scale requires exploiting problem structure. Moreover, engineering/industrial applications often present combinatorial aspects, with a nonconvexity interplay from both nonlinearity and integrality constraints. The structure this interplay introduces is difficult to exploit due to different existing mathematical/algorithmic toolboxes for nonlinear-continuous versus discrete-polyhedral optimisation. This thesis addresses two arising challenges: specific commercially-relevant pooling problems that bundle bilinear nonconvexities with a topological and polyhedral structure; semidefinite relaxations (of nonlinear nonconvexity) that integrate with difficulty into polyhedral-based Branch & Cut global solvers. First, we parametrically study pooling structure and explicitly identify sparsity via dominant active topologies under relaxed flow availability for single quality instances. We associate sparse active topological patterns with explicit piecewise objective functions, validating a long-held and heuristically successful intuition. We formally derive strongly-polynomial solutions for several single quality pooling problem subclasses, including some previously-studied nonconvex instances. The conditions in which sparse strongly-polynomial piecewise structure vanishes due to combinatorial complexity has further implications for pooling relaxations in global solvers. Second, we develop an effective lightweight linear outer-approximation of semidefinite relaxations, which we show can easily integrate into global solvers. Compared to previous work, our proposed cuts are sparser in the number of row nonzeros and explicitly selected to improve the objective. We explore relevant engineering trade-offs for sparsity patterns on quadratic programming with box constraints, showing they may immediately extend to quadratically constrained instances. A neural network estimator is key to selecting which strong cuts to generate using objective structure: ranking each cut by expected objective improvement involves solving many semidefinite optimisation problems, an expensive proposition at each Branch & Cut node. The estimator, trained a priori of any instance to solve, predicts objective improvements, taking the computation offline as an application of machine learning in cut selection and global optimisation.Open Acces

    Approximation algorithms for process systems engineering

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    Designing and analyzing algorithms with provable performance guarantees enables efficient optimization problem solving in different application domains, e.g.\ communication networks, transportation, economics, and manufacturing. Despite the significant contributions of approximation algorithms in engineering, only limited and isolated works contribute from this perspective in process systems engineering. The current paper discusses three representative, NP-hard problems in process systems engineering: (i) pooling, (ii) process scheduling, and (iii) heat exchanger network synthesis. We survey relevant results and raise major open questions. Further, we present approximation algorithms applications which are relevant to process systems engineering: (i) better mathematical modeling, (ii) problem classification, (iii) designing solution methods, and (iv) dealing with uncertainty. This paper aims to motivate further research at the intersection of approximation algorithms and process systems engineering

    Approximation algorithms for process systems engineering

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