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

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)

Lagrangean Relaxation of the Hull-Reformulation of Linear Generalized Disjunctive Programs and its use in Disjunctive Branch and Bound

Abstract In this work, we present a Lagrangean relaxation of the hull-reformulation of discrete-continuous optimization problems formulated as linear generalized disjunctive programs (GDP). The proposed Lagrangean relaxation has three important properties. The first property is that it can be applied to any linear GDP. The second property is that the solution to its continuous relaxation always yields 0-1 values for the binary variables of the hull-reformulation. Finally, it is simpler to solve than the continuous relaxation of the hull-reformulation. The proposed Lagrangean relaxation can be used in different GDP solution methods. In this work, we explore its use as primal heuristic to find feasible solutions in a disjunctive branch and bound algorithm. The modified disjunctive branch and bound is tested with several instances. The results show that the proposed disjunctive branch and bound performs better than other versions of the algorithm that do not include this primal heuristic

Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.Spanish Ministry of Science and Innovation (CTQ2012-37039-C02-02)

An alternative disjunctive optimization model for heat integration with variable temperatures

This paper presents an alternative model to deal with the problem of optimal energy consumption minimization of non-isothermal systems with variable inlet and outlet temperatures. The model is based on an implicit temperature ordering and the “transshipment model” proposed by Papoulias and Grossmann (1983). It is supplemented with a set of logical relationships related to the relative position of the inlet temperatures of process streams and the dynamic temperature intervals. In the extreme situation of fixed inlet and outlet temperatures, the model reduces to the “transshipment model”. Several examples with fixed and variable temperatures are presented to illustrate the model's performance.The authors gratefully acknowledge financial support from the Spanish “Ministerio de Ciencia e Innovación” under project CTQ2012-37039-C02-02

Environmental and Economic Water Management in Shale Gas Extraction

This paper introduces a comprehensive study of the Life Cycle Impact Assessment (LCIA) of water management in shale gas exploitation. First, we present a comprehensive study of wastewater treatment in the shale gas extraction, including the most common technologies for the pretreatment and three different desalination technologies of recent interest: Single and Multiple-Effect Evaporation with Mechanical Vapor Recompression and Membrane Distillation. The analysis has been carried out through a generic Life Cycle Assessment (LCA) and the ReCiPe metric (at midpoint and endpoint levels), considering a wide range of environmental impacts. The results show that among these technologies Multiple-Effect Evaporation with Mechanical Vapor Recompression (MEE-MVR) is the most suitable technology for the wastewater treatment in shale gas extraction, taking into account its reduced environmental impact, the high water recovery compared to other alternatives as well as the lower cost of this technology. We also use a comprehensive water management model that includes previous results that takes the form of a new Mixed-Integer Linear Programming (MILP) bi-criterion optimization model to address the profit maximization and the minimization Life Cycle Impact Assessment (LCIA), based on its results we discuss the main tradeoffs between optimal operation from the economic and environmental points of view.This project has received funding from the Spanish «Ministerio de Economía, Industria y Competitividad» under the projects CTQ2016-77968-C3-1-P and CTQ2016-77968-C3-2-P (FEDER, UE)

Disjunctive model for the simultaneous optimization and heat integration with unclassified streams and area estimation

In this paper, we propose a disjunctive formulation for the simultaneous chemical process optimization and heat integration with unclassified process streams –streams that cannot be classified a priori as hot or cold streams and whose final classification depend on the process operating conditions–, variable inlet and outlet temperatures, variable flow rates, isothermal process streams, and the possibility of using different utilities. The paper also presents an extension to allow area estimation assuming vertical heat transfer. The model takes advantage of the disjunctive formulation of the ‘max’ operator to explicitly determine all the ‘kink’ points on the hot and cold balanced composite curves and uses an implicit ordering for determining adjacent points in the balanced composite curves for area estimation. The numerical performance of the proposed approach is illustrated with four case studies. Results show that the novel disjunctive model of the pinch location method has excellent numerical performance, even in large-scale models.The authors gratefully acknowledge the financial support by the Ministry of Economy, Industry, and Competitiveness of Spain (CTQ2016-77968-C3-02-P, AEI/FEDER, UE), and Call 2013 National Sub-Program for Training, Grants for pre-doctoral contracts for doctoral training (BES-2013-064791)

A novel disjunctive model for the simultaneous optimization and heat integration

This paper introduces a new disjunctive formulation for the simultaneous optimization and heat integration of systems with variable inlet and outlet temperatures in process streams as well as the possibility of selecting and using different utilities. The starting point is the original compact formulation of the Pinch Location Method, however, instead of approximating the “maximum” operator with smooth, but non-convex functions, these operators are modeled by means of a disjunction. The new formulation has shown to have equal or lower relaxation gap than the best alternative reformulation, thus reducing computational time and numerical problems related to non-convex approximations.The authors gratefully acknowledge the financial support by the Ministry of Economy and Competitiveness from Spain, under the projects CTQ2012-37039-C02-02, CTQ2016-77968-C3-2-P, and Call 2013 National Sub-Program for Training, Grants for pre-doctoral contracts for doctoral training (BES-2013-064791)

Modelling and analysis of offshore energy hubs

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