We consider the optimal scheduling of hydropower plants in a hydrothermal interconnected system. This problem, of outmost importance for large-scale power systems with a high proportion of hydraulic generation, requir...
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We consider the optimal scheduling of hydropower plants in a hydrothermal interconnected system. This problem, of outmost importance for large-scale power systems with a high proportion of hydraulic generation, requires a detailed description of the so-called hydro unit production function. In our model, we relate the amount of generated hydropower to nonlinear tailrace levels;we also take into account hydraulic losses, turbine-generator efficiencies, as well as multiple 0-1 states associated with forbidden operation zones. Forbidden zones are crucial to avoid nasty phenomena such as mechanical vibrations in the turbine, cavitation, and low efficiency levels. The minimization of operating costs subject to such detailed constraints results in a large-scale mixed-integer nonlinear programming problem. By means of Lagrangian Relaxation, the original problem is split into a sequence of smaller and easy-to-solve subproblems, coordinated by a dual master program. In order to deal better with the combinatorial aspect introduced by the forbidden zones, we derive three different decomposition strategies, applicable to various configurations of hydro plants (with few or many units, which can be identical or different). We use a sequential quadratic programming algorithm to solve nonlinear subproblems. We assess our approach on a real-life hydroelectric configuration extracted from the south sub region of the Brazilian hydrothermal power system.
Robotic flat-end milling of complex surfaces offers advantages such as high flexibility and high machining efficiency. In the process of planning the toolpath based on the cutter contact path, the robot functional red...
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Robotic flat-end milling of complex surfaces offers advantages such as high flexibility and high machining efficiency. In the process of planning the toolpath based on the cutter contact path, the robot functional redundancy and the tool orientation need to be solved carefully. This paper presents a posture optimization method for robotic flat-end milling. Taking the weighted sum of the machining width and the toolpath smoothness performance criterion as the objective function, an optimization model considering the joint limits and gouging avoidance is established. An efficient algorithm based on sequential quadratic programming is proposed to solve this nonconvex problem. During the execution of the algorithm, the machining width is efficiently calculated by an iterative method based on conformal geometric algebra, while its derivatives are approximated analytically. Simulations and experiments demonstrate that the presented technique can resolve the tool axis direction and the robot redundancy effectively to increase the machining width and improve the toolpath smoothness, thus reducing the time for machining and improving the surface quality.
A sequential quadratic programming algorithm for solving nonlinear programming problems is presented. The new feature of the algorithm is related to the definition of the merit function. Instead of using one penalty p...
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A sequential quadratic programming algorithm for solving nonlinear programming problems is presented. The new feature of the algorithm is related to the definition of the merit function. Instead of using one penalty parameter per iteration and increasing it as the algorithm progresses, we suggest that a new point is to be accepted if it stays sufficiently below the piecewise linear function defined by some previous iterates on the (f, parallel to C parallel to(2)(2))-space. Therefore, the penalty parameter is allowed to decrease between successive iterations. Besides, one need not to decide how to update the penalty parameter. This approach resembles the filter method introduced by Fletcher and Leyffer [Math. Program., 91 (2001), pp. 239-269], but it is less tolerant since a merit function is still used. Numerical comparison with standard methods shows that this strategy is promising.
The sintering mold imposes strict requirements for temperature uniformity. The mold geometric parameters and the power configuration of heating elements exert substantial influence. In this paper, we introduce an opti...
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The sintering mold imposes strict requirements for temperature uniformity. The mold geometric parameters and the power configuration of heating elements exert substantial influence. In this paper, we introduce an optimization approach that combines response surface models with the sequential quadratic programming algorithm to optimize the geometric parameters and heating power configuration of a heating system for sintering mold. The response surface models of the maximum temperature difference, maximum temperature, and minimum temperature of the sintering area are constructed utilizing the central composite design method. The model ' s reliability is rigorously confirmed through variance analysis, residual analysis, and generalization capability validation. The models demonstrate remarkable predictive accuracy within the design space. A nonlinear constrained optimization model is established based on the response surface models, and the optimal parameters are obtained after 9 iterations using the sequential quadratic programming algorithm. Under the optimal parameters, the maximum temperature difference is maintained at less than 5 degrees C, confirming exceptional temperature uniformity. We conduct parameter analysis based on standardized effects to determine the main influencing factors of temperature uniformity, revealing that the distance between adjacent heating rods and the power density of the inner heating rods exert significant influence. Enhanced temperature uniformity can be achieved by adopting a larger distance between heating rods and configuring the power density of the heating rods to a relatively modest level. This work introduces a practical approach to optimize the heating systems for sintering molds, with potential applications in various industrial mold optimization.
For the sequential quadratic programming method (SQP), we show that close to a solution satisfying the same assumptions that are required for its local quadratic convergence (namely uniqueness of the Lagrange multipli...
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For the sequential quadratic programming method (SQP), we show that close to a solution satisfying the same assumptions that are required for its local quadratic convergence (namely uniqueness of the Lagrange multipliers and the second-order sufficient optimality condition), the direction given by the SQP subproblem using the Hessian of the Lagrangian is a descent direction for the standard l(1)-penalty function. We emphasize that this property is not straightforward at all, because the Hessian of the Lagrangian need not be positive definite under these assumptions or, in fact, under any other reasonable set of assumptions. In particular, this descent property was not known previously, under any assumptions (even including the stronger linear independence constraint qualification, strict complementarity, etc.). We also check the property in question by experiments on nonconvex problems from the Hock-Schittkowski test collection for a model algorithm. While to propose any new and complete SQP algorithm is not our goal here, our experiments confirm that the descent condition, and a model method based on it, work as expected. This indicates that the new theoretical findings that we report might be useful for full/practical SQP implementations which employ second derivatives and linesearch for the l(1)-penalty function. In particular, our results imply that in SQP methods where using subproblems without Hessian modifications is an option, this option has a solid theoretical justification at least on late iterations.
In this paper, the potential-stream function method, a very efficient computational method for the inverse design of two-dimensional compressor blades in transonic flow conditions is presented. By investigating the in...
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In this paper, the potential-stream function method, a very efficient computational method for the inverse design of two-dimensional compressor blades in transonic flow conditions is presented. By investigating the influence of the prescribed velocity coefficient distribution on the blade surface, it is found that the non-physical solution usually obtained by the general inverse method could be effectively avoided by adjusting the local velocity coefficient distribution. The objective functions were set-up for the leading edge, trailing edge closing problems, and outlet flow angle, respectively, for the numerical optimization on the basis of sequential quadratic programming. The optimum blade profiles with satisfactory performance and reasonable geometric shape can be obtained by this improved optimization method.
In this study, an efficient soft computing paradigm is presented for solving Bagley-Torvik systems of fractional order arising in fluid dynamic model for the motion of a rigid plate immersed in a Newtonian fluid using...
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In this study, an efficient soft computing paradigm is presented for solving Bagley-Torvik systems of fractional order arising in fluid dynamic model for the motion of a rigid plate immersed in a Newtonian fluid using feed-forward fractional artificial neural networks (FrANNs) and sequential quadratic programming (SQP) algorithm. The strength of FrANNs has been utilized to construct an accurate modeling of the equation using approximation theory in mean square error sense. Training of weights of FrANNs is performed with SQP techniques. The designed scheme has been examined on different variants of the systems. The comparative studies of the proposed solutions with available exact as well as reference numerical results demonstrate the worth and effectiveness of the solver. The accuracy, consistency, and complexity are evaluated in depth through results of statistics.
For systems with nonlinear dynamics, Dynamic programming for control is commonly considered in the framework of integrated plant and control system design. Despite its popularity, this control strategy can run into so...
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For systems with nonlinear dynamics, Dynamic programming for control is commonly considered in the framework of integrated plant and control system design. Despite its popularity, this control strategy can run into some computational issues as the performance is dependent on the state and input discretization. In this paper, we propose a sequential quadratic programming-based control optimization strategy for integrated system design, where both the plant and control are optimized for the case study of a continuously variable transmission. The proposed plant and control design problem will be solved using a nested strategy.
In this paper, a sequential quadratic programming method is presented for largescale nonlinear and possibly non-convex model predictive control (MPC) optimization problem which is often set up with a separable objecti...
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In this paper, a sequential quadratic programming method is presented for largescale nonlinear and possibly non-convex model predictive control (MPC) optimization problem which is often set up with a separable objective function. By introducing the so-call consensus constraints to separate the couplings among the subsystems. The resulting QP subproblem is formulated in a separable form, which makes it possible to use the existing alternating direction methods, like ADMM, to efficiently compute Newton steps for the overall system in a distributed way. In order to enforce the convergence rate of the distributed computation, a distributed line search with local merit functions is also proposed.
In this paper a numerical method for the solution of state constrained optimal control problems is presented. The method is derived from an infinite dimensional analogue of sequential quadratic programming. The main p...
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In this paper a numerical method for the solution of state constrained optimal control problems is presented. The method is derived from an infinite dimensional analogue of sequential quadratic programming. The main purpose of the paper is to present some theoretical aspects of the method. An experimental numerical implementation of the method is discussed.
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