129 research outputs found

    Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems

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    We address nonconvex mixed-integer bilinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized. This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a mixed-integer linear relaxation of the bilinear problem. Besides showing that it can provide tighter bounds than a commercial global optimization solver within a given computational time, we propose to also take advantage of the relaxed formulation for contracting the variables domain and further reduce the optimality gap. Through the solution of a real-life case study from a hydroelectric power system, we show that this can be an efficient approach depending on the problem size. The relaxed formulation from multiparametric formulation is provided for a generic numeric representation system featuring a base between 2 (binary) and 10 (decimal)

    Optimal Scheduling of Combined Heat and Power Generation Considering Heating Grid Dynamics

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    As the share of renewable generation increases in electric grids, the traditionally heat driven operation of combined heat and power plants (CHPs) reaches its limits. Thermal storage is required for a flexible operation of CHPs. This work proposes three novel methods to use a heating grid as thermal storage by exploiting its thermal dynamics. These include the first approach proving global optimality, a novel linear formulation of grid dynamics and an easily real world applicable approach

    A novel dual-decomposition method for non-convex mixed integer quadratically constrained quadratic problems

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    In this paper, we propose the novel p-branch-and-bound method for solving two-stage stochastic programming problems whose deterministic equivalents are represented by non-convex mixed-integer quadratically constrained quadratic programming (MIQCQP) models. The precision of the solution generated by the p-branch-and-bound method can be arbitrarily adjusted by altering the value of the precision factor p. The proposed method combines two key techniques. The first one, named p-Lagrangian decomposition, generates a mixed-integer relaxation of a dual problem with a separable structure for a primal non-convex MIQCQP problem. The second one is a version of the classical dual decomposition approach that is applied to solve the Lagrangian dual problem and ensures that integrality and non-anticipativity conditions are met in the optimal solution. The p-branch-and-bound method's efficiency has been tested on randomly generated instances and demonstrated superior performance over commercial solver Gurobi. This paper also presents a comparative analysis of the p-branch-and-bound method efficiency considering two alternative solution methods for the dual problems as a subroutine. These are the proximal bundle method and Frank-Wolfe progressive hedging. The latter algorithm relies on the interpolation of linearisation steps similar to those taken in the Frank-Wolfe method as an inner loop in the classic progressive hedging.Comment: 19 pages, 5 table

    Optimal Antibody Purification Strategies Using Data-Driven Models

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    Optimisation approaches for the synthesis of water treatment plants

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    Efficient water treatment design has progressively been growing in importance as the usage of water resources increases with population rise and industrial development. Their availability has been reduced with the more evident effects of climate change. Addressing this challenge necessitates more and efficient purification plants which can be realised by optimal design at conceptual stage. In this work, a mixed integer nonlinear programming (MINLP) model for the synthesis and optimisation of water treatment processes is proposed. Due to its numerous non-linearities and consequently, its non-stability, various linearisation, approximation and reformulation techniques have been implemented. Consequently, two improved formulations are derived, i.e. a partially linearised MINLP (plMINLP) and a mixed integer linear fractional programming (MILFP) models. The applicability of the mathematical formulations are investigated in case studies of seawater desalination and surface water treatment for the production of potable water. Finally, the models performance is analysed and compared against each other

    Optimal Antibody Purification Strategies Using Data-Driven Models

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    This work addresses the multiscale optimization of the purification processes of antibody fragments. Chromatography decisions in the manufacturing processes are optimized, including the number of chromatography columns and their sizes, the number of cycles per batch, and the operational flow velocities. Data-driven models of chromatography throughput are developed considering loaded mass, flow velocity, and column bed height as the inputs, using manufacturing-scale simulated datasets based on microscale experimental data. The piecewise linear regression modeling method is adapted due to its simplicity and better prediction accuracy in comparison with other methods. Two alternative mixed-integer nonlinear programming (MINLP) models are proposed to minimize the total cost of goods per gram of the antibody purification process, incorporating the data-driven models. These MINLP models are then reformulated as mixed-integer linear programming (MILP) models using linearization techniques and multiparametric disaggregation. Two industrially relevant cases with different chromatography column size alternatives are investigated to demonstrate the applicability of the proposed models

    Global optimisation of large-scale quadratic programs: application to short-term planning of industrial refinery-petrochemical complexes

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    This thesis is driven by an industrial problem arising in the short-term planning of an integrated refinery-petrochemical complex (IRPC) in Colombia. The IRPC of interest is composed of 60 industrial plants and a tank farm for crude mixing and fuel blending consisting of 30 additional units. It considers both domestic and imported crude oil supply, as well as refined product imports such as low sulphur diesel and alkylate. This gives rise to a large-scale mixed-integer quadratically constrained quadratic program (MIQCQP) comprising about 7,000 equality constraints with over 35,000 bilinear terms and 280 binary variables describing operating modes for the process units. Four realistic planning scenarios are recreated to study the performance of the algorithms developed through the thesis and compare them to commercial solvers. Local solvers such as SBB and DICOPT cannot reliably solve such large-scale MIQCQPs. Usually, it is challenging to even reach a feasible solution with these solvers, and a heuristic procedure is required to initialize the search. On the other hand, global solvers such as ANTIGONE and BARON determine a feasible solution for all the scenarios analysed, but they are unable to close the relaxation gap to less than 40% on average after 10h of CPU runtime. Overall, this industrial-size problem is thus intractable to global optimality in a monolithic way. The first main contribution of the thesis is a deterministic global optimisation algorithm based on cluster decomposition (CL) that divides the network into groups of process units according to their functionality. The algorithm runs through the sequences of clusters and proceeds by alternating between: (i) the (global) solution of a mixed-integer linear program (MILP), obtained by relaxing the bilinear terms based on their piecewise McCormick envelopes and a dynamic partition of their variable ranges, in order to determine an upper bound on the maximal profit; and (ii) the local solution of a quadratically-constrained quadratic program (QCQP), after fixing the binary variables and initializing the continuous variables to the relaxed MILP solution point, in order to determine a feasible solution (lower bound on the maximal profit). Applied to the base case scenario, the CL approach reaches a best solution of 2.964 MMUSD/day and a relaxation gap of 7.5%, a remarkable result for such challenging MIQCQP problem. The CL approach also vastly outperforms both ANTIGONE (2.634 MMUSD/day, 32% optimality gap) and BARON (2.687 MMUSD/day, 40% optimality gap). The second main contribution is a spatial Lagrangean decomposition, which entails decomposing the IRPC short-term planning problem into a collection of smaller subproblems that can be solved independently to determine an upper bound on the maximal profit. One advantage of this strategy is that each sub-problem can be solved to global optimality, potentially providing good initial points for the monolithic problem itself. It furthermore creates a virtual market for trading crude blends and intermediate refined–petrochemical streams and seeks an optimal trade-off in such a market, with the Lagrange multipliers acting as transfer prices. A decomposition over two to four is considered, which matches the crude management, refinery, petrochemical operations, and fuel blending sections of the IRPC. An optimality gap below 4% is achieved in all four scenarios considered, which is a significant improvement over the cluster decomposition algorithm.Open Acces

    Optimisation Methodologies for the Design and Planning of Water Systems

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    This thesis addresses current topics of design and planning of water systems from water treatment units to a country-wide resources management schemes. The methodologies proposed are presented as models and solution approaches using mathematical programming, and mixed integer linear (MILP) and non-linear (MINLP) programming techniques. In Part I of the thesis, a synthesis problem for water treatment processes using superstructure optimisation is studied. An MINLP model is developed for the minimisation of water production cost considering physicochemical properties of water and operating conditions of candidate technologies. Next, new alternative path options are introduced to the superstructure. The resulting MINLP model is then partially linearised (plMINLP) and also presented as a mixed integer linear fractional programming (MILFP) model in order to improve the convergence of the optimisation model. Various linearisation and approximation techniques are developed. As a solution procedure to the fractional model, a variation of the Dinkelbach's algorithm is proposed. The models are tested on theoretical examples with industrial data. In Part II, an optimisation approach formulated as a spatially-explicit multi-period MILP model is proposed for the design of planning of water resources at regional and national scales. The optimisation framework encompasses decisions such as installation of new purification plants, capacity expansion, trading schemes among regions and pricing, and water availability under climate change. The objective is to meet water demand while minimising the total cost associated with developing and operating the water supply chain. Additionally, a fair trade-o between the total cost and reliability of the supply chain is incorporated in the model. The solution method is applied based on game theory using the concept of Nash equilibrium. The methodology is implemented on a case study based on Australian water management systems
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