12,358 research outputs found

    Multi-parametric mixed integer linear programming under global uncertainty

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    Major application areas of the process systems engineering, such as hybrid control, scheduling and synthesis can be formulated as mixed integer linear programming (MILP) problems and are naturally susceptible to uncertainty. Multi-parametric programming theory forms an active field of research and has proven to provide invaluable tools for decision making under uncertainty. While uncertainty in the right-hand side (RHS) and in the objective function's coefficients (OFC) have been thoroughly studied in the literature, the case of left-hand side (LHS) uncertainty has attracted significantly less attention mainly because of the computational implications that arise in such a problem. In the present work, we propose a novel algorithm for the analytical solution of multi-parametric MILP (mp-MILP) problems under global uncertainty, i.e. RHS, OFC and LHS. The exact explicit solutions and the corresponding regions of the parametric space are computed while a number of case studies illustrates the merits of the proposed algorithm

    Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework

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    This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.Peer ReviewedPostprint (published version

    On Robust Tie-line Scheduling in Multi-Area Power Systems

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    The tie-line scheduling problem in a multi-area power system seeks to optimize tie-line power flows across areas that are independently operated by different system operators (SOs). In this paper, we leverage the theory of multi-parametric linear programming to propose algorithms for optimal tie-line scheduling within a deterministic and a robust optimization framework. Through a coordinator, the proposed algorithms are proved to converge to the optimal schedule within a finite number of iterations. A key feature of the proposed algorithms, besides their finite step convergence, is the privacy of the information exchanges; the SO in an area does not need to reveal its dispatch cost structure, network constraints, or the nature of the uncertainty set to the coordinator. The performance of the algorithms is evaluated using several power system examples

    Diseño para operabilidad: Una revisión de enfoques y estrategias de solución

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    In the last decades the chemical engineering scientific research community has largely addressed the design-foroperability problem. Such an interest responds to the fact that the operability quality of a process is determined by design, becoming evident the convenience of considering operability issues in early design stages rather than later when the impact of modifications is less effective and more expensive. The necessity of integrating design and operability is dictated by the increasing complexity of the processes as result of progressively stringent economic, quality, safety and environmental constraints. Although the design-for-operability problem concerns to practically every technical discipline, it has achieved a particular identity within the chemical engineering field due to the economic magnitude of the involved processes. The work on design and analysis for operability in chemical engineering is really vast and a complete review in terms of papers is beyond the scope of this contribution. Instead, two major approaches will be addressed and those papers that in our belief had the most significance to the development of the field will be described in some detail.En las Ășltimas dĂ©cadas, la comunidad cientĂ­fica de ingenierĂ­a quĂ­mica ha abordado intensamente el problema de diseño-para-operabilidad. Tal interĂ©s responde al hecho de que la calidad operativa de un proceso esta determinada por diseño, resultando evidente la conveniencia de considerar aspectos operativos en las etapas tempranas del diseño y no luego, cuando el impacto de las modificaciones es menos efectivo y mĂĄs costoso. La necesidad de integrar diseño y operabilidad esta dictada por la creciente complejidad de los procesos como resultado de las cada vez mayores restricciones econĂłmicas, de calidad de seguridad y medioambientales. Aunque el problema de diseño para operabilidad concierne a prĂĄcticamente toda disciplina, ha adquirido una identidad particular dentro de la ingenierĂ­a quĂ­mica debido a la magnitud econĂłmica de los procesos involucrados. El trabajo sobre diseño y anĂĄlisis para operabilidad es realmente vasto y una revisiĂłn completa en tĂ©rminos de artĂ­culos supera los alcances de este trabajo. En su lugar, se discutirĂĄn los dos enfoques principales y aquellos artĂ­culos que en nuestra opiniĂłn han tenido mayor impacto para el desarrollo de la disciplina serĂĄn descriptos con cierto detalle.Fil: Blanco, Anibal Manuel. Consejo Nacional de Investigaciones CientĂ­ficas y TĂ©cnicas. Centro CientĂ­fico TecnolĂłgico Conicet - BahĂ­a Blanca. Planta Piloto de IngenierĂ­a QuĂ­mica. Universidad Nacional del Sur. Planta Piloto de IngenierĂ­a QuĂ­mica; ArgentinaFil: Bandoni, Jose Alberto. Consejo Nacional de Investigaciones CientĂ­ficas y TĂ©cnicas. Centro CientĂ­fico TecnolĂłgico Conicet - BahĂ­a Blanca. Planta Piloto de IngenierĂ­a QuĂ­mica. Universidad Nacional del Sur. Planta Piloto de IngenierĂ­a QuĂ­mica; Argentin

    Multi-parametric linear programming under global uncertainty

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    Multi-parametric programming has proven to be an invaluable tool for optimisation under uncertainty. Despite the theoretical developments in this area, the ability to handle uncertain parameters on the left-hand side remains limited and as a result, hybrid, or approximate solution strategies have been proposed in the literature. In this work, a new algorithm is introduced for the exact solution of multi-parametric linear programming problems with simultaneous variations in the objective function's coefficients, the right-hand side and the left-hand side of the constraints. The proposed methodology is based on the analytical solution of the system of equations derived from the first order Karush–Kuhn–Tucker conditions for general linear programming problems using symbolic manipulation. Emphasis is given on the ability of the proposed methodology to handle efficiently the LHS uncertainty by computing exactly the corresponding nonconvex critical regions while numerical studies underline further the advantages of the proposed methodology, when compared to existing algorithms

    Positive multi-criteria models in agriculture for energy and environmental policy analysis

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    Environmental consciousness and accompanying actions have been paralleled by the evolution of multi-criteria methods which have provided tools to assist policy makers in discovering compromises in order to muddle through. This paper recalls the development of multi-criteria methods in agriculture, focusing on their contribution to produce input or output functions useful for environmental and/or energy policy. Response curves generated by MC models can more accurately predict farmers’ response to market and policy parameters compared with classic profit maximizing behavior. Concrete examples from recent literature illustrate the above statements and ideas for further research are provided.multi-criteria models, interval programming, supply curves, bio-energy, policy analysis

    Multi-parametric Analysis for Mixed Integer Linear Programming: An Application to Transmission Planning and Congestion Control

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    Enhancing existing transmission lines is a useful tool to combat transmission congestion and guarantee transmission security with increasing demand and boosting the renewable energy source. This study concerns the selection of lines whose capacity should be expanded and by how much from the perspective of independent system operator (ISO) to minimize the system cost with the consideration of transmission line constraints and electricity generation and demand balance conditions, and incorporating ramp-up and startup ramp rates, shutdown ramp rates, ramp-down rate limits and minimum up and minimum down times. For that purpose, we develop the ISO unit commitment and economic dispatch model and show it as a right-hand side uncertainty multiple parametric analysis for the mixed integer linear programming (MILP) problem. We first relax the binary variable to continuous variables and employ the Lagrange method and Karush-Kuhn-Tucker conditions to obtain optimal solutions (optimal decision variables and objective function) and critical regions associated with active and inactive constraints. Further, we extend the traditional branch and bound method for the large-scale MILP problem by determining the upper bound of the problem at each node, then comparing the difference between the upper and lower bounds and reaching the approximate optimal solution within the decision makers' tolerated error range. In additional, the objective function's first derivative on the parameters of each line is used to inform the selection of lines to ease congestion and maximize social welfare. Finally, the amount of capacity upgrade will be chosen by balancing the cost-reduction rate of the objective function on parameters and the cost of the line upgrade. Our findings are supported by numerical simulation and provide transmission line planners with decision-making guidance
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