Browsing by Author "Grossmann, Ignacio E."
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- Deterministic optimization of the thermal Unit Commitment problem: A Branch and Cut searchPublication . Marcovecchio, Marian G.; Novais, Augusto Q.; Grossmann, Ignacio E.This paper proposes a novel deterministic optimization approach for the Unit Commitment (UC) problem, involving thermal generating units. A mathematical programming model is first presented, whichincludes all the basic constraints and a set of binary variables for the on/off status of each generator ateach time period, leading to a convex mixed-integer quadratic programming (MIQP) formulation. Then,an effective solution methodology based on valid integer cutting planes is proposed, and implementedthrough a Branch and Cut search for finding the global optimal solution. The application of the pro-posed approach is illustrated with several examples of different dimensions. Comparisons with other mathematical formulations are also presented.
- Effective decomposition algorithm for multistage batch plant schedulingPublication . Castro, Pedro; Harjunkoski, Iiro; Grossmann, Ignacio E.This paper presents a new algorithm for the scheduling of batch plants with a large number of orders and sequence-dependent changeovers. Such problems are either intractable or yield poor solutions with full-space approaches. We use decomposition on the entire set of orders and derive the complete schedule in several iterations. The key idea is to allow for partial rescheduling without altering the main decisions in terms of unit assignments and sequencing, so that the complexity is kept at a manageable level. It has been implemented with a unit-specific continuous-time model and tested for different decomposition settings. The results show that a real-life 50-order, 17-unit, 6-stage problem can effectively be solved in roughly 6 minutes of computational time.
- Global optimization of bilinear programs with a multiparametric disaggregation techniquePublication . Kolodziej, Scott; Castro, Pedro; Grossmann, Ignacio E.In this paper, we present the derivation of the multiparametric disaggregation technique (MDT) by Teles et al. (J. Glob. Optim., 2011) for solving nonconvex bilinear programs. Both upper and lower bounding formulations corresponding to mixed-integer linear programs are derived using disjunctive programming and exact linearizations, and incorporated into two global optimization algorithms that are used to solve bilinear programming problems. The relaxation derived using the MDT is shown to scalemuchmore favorably than the relaxation that relies on piecewise McCormick envelopes, yielding smallermixed-integer problems and faster solution times for similar optimality gaps. The proposed relaxation also compares well with general global optimization solvers on large problems.
- On the computational studies of deterministic global optimization of head dependent short-term hydro schedulingPublication . Lima, Ricardo M.; Marcovecchio, Marian G.; Novais, Augusto Q.; Grossmann, Ignacio E.This paper addresses the global optimization of the short term scheduling for hydroelectric power generation. A tailored deterministic global optimization approach, denominated sHBB, is developed and its performance is analyzed. This approach is applied to the optimization of a mixed integer nonlinear programming (MINLP) model for cascades of hydro plants, each one with multiple turbines, and characterized by a detailed representation of the net head of water, and a nonlinear hydropower generation function. A simplified model is also considered where only the linear coefficients of the forebay and tailrace polynomial functions are retained. For comparison purposes, four case studies are addressed with the proposed global optimization strategy and with a commercial solver for global optimization. The results show that the proposed approach is more efficient than the commercial solver in terms of finding a better solution with a smaller optimality gap, using less CPU time. The proposed method can also find alternative and potentially more profitable power production schedules. Significant insights were also obtained regarding the effectiveness of the proposed relaxation strategies.
- Optimal maintenance scheduling of a gas engine power plant using generalized disjunctive programmingPublication . Castro, Pedro; Grossmann, Ignacio E.; Veldhuizen, Patrick; Esplin, DouglasA new continuous-time model for long-term scheduling of a gas engine power plant with parallel units is presented. Gas engines are shut down according to a regular maintenance plan that limits the number of hours spent online. To minimize salary expenditure with skilled labor, a single maintenance team is considered which is unavailable during certain periods of time. Other challenging constraints involve constant minimum and variable maximum power demands. The objective is to maximize the revenue from electricity sales assuming seasonal variations in electricity pricing by reducing idle times and shutdowns in high-tariff periods. By first developing a generalized disjunctive programming model and then applying both big-M and hull reformulation techniques, we reduce the burden of finding the appropriate set of mixed-integer linear constraints. Through the solution of a real-life problem, we show that the proposed formulations are very efficient computationally, while gaining valuable insights about the system.
- Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problemsPublication . Castro, Pedro; Grossmann, Ignacio E.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).
- Rolling-horizon algorithm for scheduling under time-dependent utility pricing and availabilityPublication . Castro, Pedro; Harjunkoski, Iiro; Grossmann, Ignacio E.This work addresses the scheduling of continuous single-stage multiproduct plants with energy intensive processing tasks and time-dependent electricity cost and power supply. A new rolling horizon algorithm is proposed that consists of a planning model to predict the production levels and a continuous-time model for detailed scheduling. The results from a set of test problems from the literature show that the algorithm can generate global optimal solutions much more rapidly than standalone discrete or continuous-time formulations in problems involving unlimited power availability.
- Scope for industrial applications of production scheduling models and solution methodsPublication . Harjunkoski, Iiro; Maravelias, Christos T.; Bongers, Peter; Castro, Pedro; Engell, Sebastian; Grossmann, Ignacio E.; Hooker, John; Mendez, Carlos A.; Sand, Guido; Wassick, JohnThis paper gives a review on existing scheduling methodologies developed for process industries. Above all, the aim of the paper is to focus on the industrial aspects of scheduling and discuss the main characteristics, including strengths and weaknesses of the presented approaches. It is claimed that optimization tools of today can effectively support the plant level production. However there is still clear potential for improvements, especially in transferring academic results into industry. For instance, usability, interfacing and integration are some aspects discussed in the paper. After the introduction and problem classification, the paper discusses some lessons learned from industry, provides an overview of models and methods and concludes with general guidelines and examples on the modeling and solution of industrial problems.