There is increasing evidence of the shortage of solver-based models for solving logically-constrained AC optimal power flow problem (LCOPF). Although in the literature the heuristic-based models have been widely used ...
详细信息
There is increasing evidence of the shortage of solver-based models for solving logically-constrained AC optimal power flow problem (LCOPF). Although in the literature the heuristic-based models have been widely used to handle the LCOPF problems with logical terms such as conditional statements, logical-and, logical-or, etc., their requirement of several trials and adjustments plagues finding a trustworthy solution. On the other hand, a well-defined solver-based model is of much interest in practice, due to rapidity and precision in finding an optimal solution. To remedy this shortcoming, in this paper we provide a solver-friendly procedure to recast the logical constraints to solver-based mixed-integer nonlinear programming (MINLP) terms. We specifically investigate the recasting of logical constraints into the terms of the objective function, so it facilitates the pre-solving and probing techniques of commercial solvers and consequently results in a higher computational efficiency. By applying this recast method to the problem, two sub-power- and sub-function-based MINLP models, namely SP-MINLP and SF-MINLP, respectively, are proposed. Results not only show the superiority of the proposed models in finding a better optimal solution, compared to the existing approaches in the literature, but also the effectiveness and computational tractability in solving large-scale power systems under different configurations.
This paper presents the application of MINLP (mixed-integer nonlinear programming) approach for scheduling of a CHP (combined heat and power) plant in the day-ahead wholesale energy markets. This work employs first pr...
详细信息
This paper presents the application of MINLP (mixed-integer nonlinear programming) approach for scheduling of a CHP (combined heat and power) plant in the day-ahead wholesale energy markets. This work employs first principles models to describe the nonlinear dynamics of a CHP plant and its individual components. The MINLP framework includes practical constraints such as minimum/maximum power output and steam flow restrictions, minimum up/down times, start-up and shut-down procedures, and fuel limits. Special care is given to the explicit modeling of the unit start-up types (hot, warm, and cold), which depend on the component's prior reservation time, resulting in the differences in the time-dependent start-up costs of generating units. The model also accounts for the different operating modes (synchronization, soak, dispatch, and desynchronization) during start-up and shut-down of each unit. We provide case studies involving the Hal C. Weaver power plant complex at the University of Texas at Austin to demonstrate the effectiveness of the proposed methodology. The results show that the optimized operating strategies can yield substantial net incomes from electricity sales. (C) 2014 Elsevier Ltd. All rights reserved.
In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic cla...
详细信息
In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.
We present a mixed-integer nonlinear programming (MINLP) formulation to achieve minimum-cost designs for reinforced concrete (RC) structures that satisfy building code requirements. The objective function includes mat...
详细信息
We present a mixed-integer nonlinear programming (MINLP) formulation to achieve minimum-cost designs for reinforced concrete (RC) structures that satisfy building code requirements. The objective function includes material and labor costs for concrete, steel reinforcing bars, and formwork according to typical contractor methods. Restrictions enforce correct geometry of the cross-section dimensions for each element and relative sizes of cross-section dimensions of elements within the structure. Other restrictions define a stiffness and displacement correlation among all structural elements via finite element analysis. The design of minimum cost RC structures introduces a new class of optimization problems, namely, mixed-integernonlinear programs with complementarity constraints. The complementarity constraints are used to model RC element strength and American Concrete Institute code-required safety factors. We reformulate the complementarity constraints as nonlinear equations and show that the resulting ill-conditioned MINLPs can be solved by using an off-the-shelf MINLP solver. Our work provides discrete-valued design solutions for an explicit representation of a process most often performed implicitly with iterative calculations. We demonstrate the capabilities of a mixed-integernonlinear algorithm, MINLPBB, to find optimal sizing and reinforcing for cast-in-place beam and column elements in multistory RC structures. Problem instances contain up to 678 variables, of which 214 are integer, and 844 constraints, of which 582 are nonlinear. We solve problems to local optimality within a reasonable amount of computational time, and we find an average cost savings over typical-practice design solutions of 13 percent.
The increasing complexity of building energy systems integrated with renewable energy systems requires essentially more intelligent scheduling strategy. The energy systems often have strong nonlinear characteristics a...
详细信息
The increasing complexity of building energy systems integrated with renewable energy systems requires essentially more intelligent scheduling strategy. The energy systems often have strong nonlinear characteristics and have discrete working ranges. The mixed-integer nonlinear programming approach is used to solve their optimal scheduling problems of energy systems in building integrated with energy generation and thermal energy storage in this study. The optimal scheduling strategy minimizes the overall operation cost day-ahead, including operation energy cost and cost concerning the plant on/off penalty. A case study is conducted to validate the proposed strategy based on the Hong Kong Zero Carbon Building. Four scenarios are investigated and compared to exam the performance of the optimal scheduling. Results show that the strategy can reduce operation energy cost greatly (about 25%) compared with a rule-based strategy and the reduction is even increased to about 47% when a thermal energy storage system is used. The strategy can also reduce the on/off frequency of chillers significantly. (C) 2015 Elsevier Ltd. All rights reserved.
A large number of heat flows at various temperature and pressure levels exist in a polygeneration plant which co-produces electricity and chemical products. Integration of these external heat flows in a heat recovery ...
详细信息
A large number of heat flows at various temperature and pressure levels exist in a polygeneration plant which co-produces electricity and chemical products. Integration of these external heat flows in a heat recovery steam generator (HRSG) has great potential to further enhance energy efficiency of such a plant;however, it is a challenging problem arising from the large design space of heat exchanger network. In this paper, a mixed-integer nonlinear programming model is developed for the design optimization of a HRSG with consideration of all alternative matches between the HRSG and external heat flows. This model is applied to four polygeneration cases with different HRSG types, and results indicate that the optimized heat network mainly depends on the HRSG type and the model specification. (C) 2013 Elsevier Ltd. All rights reserved.
This paper addresses the efficient solution of computer aided molecular design (CAMD) problems, which have been posed as mixed-integer nonlinear programming models. The models of interest are those in which the number...
详细信息
This paper addresses the efficient solution of computer aided molecular design (CAMD) problems, which have been posed as mixed-integer nonlinear programming models. The models of interest are those in which the number of linear constraints far exceeds the number of nonlinear constraints, and with most variables participating in the nonconvex terms. As a result global optimization methods are needed. A branch-and-bound algorithm (BB) is proposed that is specifically tailored to solving such problems. In a conventional BB algorithm, branching is performed on all the search variables that appear in the nonlinear terms. This translates to a large number of node traversals. To overcome this problem, we have proposed a new strategy for branching on a set of linear branching functions, which depend linearly on the search variables. This leads to a significant reduction in the dimensionality of the search space. The construction of linear underestimators for a class of functions is also presented. The CAMD problem that is considered is the design of optimal solvents to be used as cleaning agents in lithographic printing. (C) 2002 Elsevier Science Ltd. All rights reserved.
In this paper, a new finite element model updating (FEMU) method is proposed based on mixed-integer nonlinear programming (MINLP) to deal with model-form uncertainty in FE models. Depending on modelers' preference...
详细信息
In this paper, a new finite element model updating (FEMU) method is proposed based on mixed-integer nonlinear programming (MINLP) to deal with model-form uncertainty in FE models. Depending on modelers' preference and experience, various FE models can be constructed for a specific structure in practice. However, no one can guarantee that a specific model representation is always best (Model-form uncertainty). Conventional method should perform model updating for each FE model independently and select a best one among them, so that it becomes computationally intensive with many candidate FE models. To handle model-form uncertainty, this study formulates FEMU as the MINLP problem. The proposed method assigns an integer variable for model choice, while continuous real variables are used for the updating parameters. With this formulation, the optimization algorithm can explore both model and parameter space simultaneously to deal with the model-form uncertainty in FE models. Firstly, three numerical experiments were explored to evaluate the performance of the proposed method by considering possible situations in reality as follows: (1) a true FE model exists in model space with an admissible FE model;(2) only admissible FE model exists in model space;and (3) no true and admissible FE models exist in model space. Then, the proposed method was experimentally validated through a real bridge. The results show that the proposed method can find a best FE model with optimal estimates of the updating parameters with much less computational efforts against the conventional FEMU.
We propose a modified sequential quadratic programming method for solving mixed-integer nonlinear programming problems. Under the assumption that integer variables have a smooth influence on the model functions, i.e.,...
详细信息
We propose a modified sequential quadratic programming method for solving mixed-integer nonlinear programming problems. Under the assumption that integer variables have a smooth influence on the model functions, i.e., that function values do not change drastically when in-or decrementing an integer value, successive quadratic approximations are applied. The algorithm is stabilized by a trust region method with Yuan's second order corrections. It is not assumed that the mixed-integer program is relaxable or, in other words, function values are evaluated only at integer points. The Hessian of the Lagrangian function is approximated by a quasi-Newton update formula subject to the continuous and integer variables. Numerical results are presented for a set of 80 mixed-integer test problems taken from the literature. The surprising result is that the number of function evaluations, the most important performance criterion in practice, is less than the number of function calls needed for solving the corresponding relaxed problem without integer variables.
Given urban data derived from a geographical information system (GIS), we consider the problem of constructing an estimate of the electrical distribution system of an urban area. We employ the image data to obtain an ...
详细信息
Given urban data derived from a geographical information system (GIS), we consider the problem of constructing an estimate of the electrical distribution system of an urban area. We employ the image data to obtain an approximate electrical load distribution over a network of a prespecificed discretization. Together with partial information about existing substations, we determine the optimal placement of electrical substations to sustain such a load that minimizes the cost of capital and losses. This requires solving large-scale quadratic programs with discrete variables for which we present a novel penalization-smoothing scheme. The choice of locations allows one to determine the optimal flows in this network, as required by physical requirements which provide us with an approximation of the distribution network. Furthermore, the scheme allows for approximating systems in the presence of no-go areas, such as lakes and fields. We examine the performance of our algorithm on the solution of a set of location problems and observe that the scheme is capable of solving large-scale instances, well beyond the realm of existing mixed-integer nonlinear programming solvers. We conclude with a case study in which a stage-wise extension of this scheme is developed to reflect the temporal evolution of load. (C) 2010 Elsevier Ltd. All rights reserved.
暂无评论