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- Resource-task network formulations for industrial demand side management of a steel plantPublication . Castro, Pedro; Sun, Lige; Harjunkoski, IiroIn today’s energy markets, there is a growing effort toward the alignment of the industrial sector and the power grid for the sake of efficient energy distribution and consumption. In this paper, the resource-task network is used to provide a generic modeling framework for production scheduling under energy constraints. Three alternative process models for the energy-intensive melt shop of a steel plant are proposed and linked to a discrete-time formulation. The results show a trade-off between accurate representation of problem data and computational performance. By keeping track of the total energy and power consumption through time, we study the impact of fluctuating energy prices on the scheduling of operations and the economic benefits that can be obtained from the plant’s participation in the price- and incentive-based industrial demand side management programs.
- Comparison of global optimization algorithms for the design of water-using networksPublication . Castro, Pedro; Teles, João P.We address a special class of bilinear process network problems with global optimization algorithms iterating between a lower bound provided by a mixed-integer linear programming (MILP) formulation and an upper bound given by the solution of the original nonlinear problem (NLP) with a local solver. Two conceptually different relaxation approaches are tested, piecewise McCormick envelopes and multiparametric disaggregation, each considered in two variants according to the choice of variables to partition/parameterize. The four complete MILP formulations are derived from disjunctive programming models followed by convex hull reformulations. The results on a set of test problems from the literature show that the algorithm relying on multiparametric disaggregation with parameterization of the concentrations is the best performer, primarily due to a logarithmic as opposed to linear increase in problem size with the number of partitions. The algorithms are also compared to the commercial solvers BARON and GloMIQO through performance profiles.
- Assessing micro-generation’s and non-linear loads’ impact in the power quality of low voltage distribution networksPublication . Bonifácio, Paulo; Viana, Susana; Rodrigues, L.; Estanqueiro, AnaDistribution networks face an increasing penetration of solar PV (photovoltaic) and small WTG (wind turbine generator) as well as other forms of micro-generation. To this scenario, one must add the dissemination of non-linear loads such as EV (electric vehicles). There is something in common between those loads and sources: the extensive use of power electronic converters with commutated switches. These devices may be a source of medium-to-high frequency harmonic distortion and their impact on the local distribution grid must be carefully assessed in order to evaluate their negative impacts on the network, on the existing conventional loads and also on other active devices. In this paper, methodologies to characterize effects such as: harmonics, network unbalances, damaging power line resonance conditions, and over/under voltages are described and applied to a real local grid configuration.
- Univariate parameterization for global optimization of mixed-integer polynomial problemsPublication . Teles, João P.; Castro, Pedro; Matos, Henrique A.This paper presents a new relaxation technique to globally optimize mixed-integer polynomial programming problems that arise in many engineering and management contexts. Using a bilinear term as the basic building block, the underlying idea involves the discretization of one of the variables up to a chosen accuracy level (Teles, J.P., Castro, P.M., Matos, H.A. (2013). Multiparametric disaggregation technique for global optimization of polynomial programming problems. J. Glob. Optim. 55, 227–251), by means of a radix-based numeric representation system, coupled with a residual variable to effectively make its domain continuous. Binary variables are added to the formulation to choose the appropriate digit for each position together with new sets of continuous variables and constraints leading to the transformation of the original mixed-integer non-linear problem into a larger one of the mixed-integer linear programming type. The new underestimation approach can be made as tight as desired and is shown capable of providing considerably better lower bounds than a widely used global optimization solver for a specific class of design problems involving bilinear terms.
- Multi-parametric disaggregation technique for global optimization of polynomial programming problemsPublication . Teles, João P.; Castro, Pedro; Matos, Henrique A.This paper discusses a power-based transformation technique that is especially useful when solving polynomial optimization problems, frequently occurring in science and engineering. The polynomial nonlinear problem is primarily transformed into a suitable reformulated problem containing new sets of discrete and continuous variables. By applying a term-wise disaggregation scheme combined with multi-parametric elements, an upper/lower bounding mixed-integer linear program can be derived for minimization/maximization problems. It can then be solved to global optimality through standard methods, with the original problem being approximated to a certain precision level, which can be as tight as desired. Furthermore, this technique can also be applied to signomial problems with rational exponents, after a few effortless algebraic transformations. Numerical examples taken from the literature are used to illustrate the effectiveness of the proposed approach.
- Reactive scheduling in a make-to-order flexible job shop with re-entrant process and assembly: a mathematical programming approachPublication . Gomes, Marta C.; Barbosa-Póvoa, Ana Paula; Novais, Augusto Q.A mixed-integer linear programming model is presented for the scheduling of flexible job shops, a production mode characteristic of make-to-order industries. Re-entrant process (multiple visits to the same machine group) and a final assembly stage are simultaneously considered in the model. The formulation uses a continuous time representation and optimises an objective function that is a weighted sum of order earliness, order tardiness and in-process inventory. An algorithm for predictive-reactive scheduling is derived from the proposed model to deal with the arrival of new orders. This is illustrated with a realistic example based on data from the mould making industry. Different reactive scheduling scenarios, ranging from unchanged schedule to full re-scheduling, are optimally generated for order insertion in a predictive schedule. Since choosing the most suitable scenario requires balancing criteria of scheduling efficiency and stability, measures of schedule changes were computed for each re-scheduling solution. The short computational times obtained are promising regarding future application of this approach in the manufacturing environment studied.
- 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.
- 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.
- 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).
- Building innovation networks in science-based young firms: the selection of knowledge sourcesPublication . Sousa, Cristina; Fontes, MargaridaThe paper investigates the strategic choices made by young science-based firms regarding the selection of knowledge sources. Data collected on Portuguese biotechnology firms are analysed with a view to answer to two research questions: whether, to what extent and in which conditions science-based entrepreneurs activate their social capital and/or build new knowledge relationships at start-up; whether and to what extent the knowledge relationships established at start-up persist and/or the firm builds relationships with new organisations. The results confirm the importance attributed to tie persistence but they also show that science-based firms need to search for new knowledge sources from the very early stages. Thus, their start-up behaviour departs from the one often depicted by the entrepreneurship literature, that emphasises the mobilisation of the entrepreneurs' social capital. Results also show that persistence of ties established at start-up is lower than would be expected.