Semidefinite programming (SDP) relaxation offers a tight relaxation to nonconvex alternating current optimal power flow (AC OPF) problems. When the solution obtained from SDP relaxation of AC OPF is a rank-1 positive ...
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Semidefinite programming (SDP) relaxation offers a tight relaxation to nonconvex alternating current optimal power flow (AC OPF) problems. When the solution obtained from SDP relaxation of AC OPF is a rank-1 positive semidefinite (PSD) matrix, this solution is exact to the original problem. Research efforts have been devoted to find a rank-1 PSD matrix. In this paper, a nonlinear programming formulation with the PSD matrix as the decision variable is proposed. The rank-1 PSD matrix constraint is equivalent to all 2x2 minors of the PSD matrix being zero. The main challenge of the proposed formulation is the large number of the quadratic equality constraints. For a system of N buses, there are CN2CN2 minor related constraints (For a 10-node system, this number is 2025). Graph decomposition-based approach is then implemented in this research to decompose a power grid into radial lines and three-node cycles. Enforcing the related submatrices PSD and rank-1 guarantees a full PSD rank-1 matrix. Case study results demonstrate that the proposed formulation can provide similar quality results with the original AC OPF formulation.
One of the most important factors that bring success in modern warfare is to show air superiority. Unmanned aerial vehicles (UAVs) have now become an essential component of military air operations. UAVs can be operate...
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One of the most important factors that bring success in modern warfare is to show air superiority. Unmanned aerial vehicles (UAVs) have now become an essential component of military air operations. UAVs can be operated in two ways: by pilots from remote control stations or by flying autonomously. Under the condition of disconnection from the control station, UAVs have trouble maintaining navigation and maneuverability. By applying multisensor data fusion, an escape path prediction algorithm was developed and presented as an engagement escape method in this study. To develop the algorithm for prediction of the optimal escape route, data from various sensors are collected and processed under the influence of noise. The data from the distance and angle sensors are interpreted in the Extended Kalman Filter and estimations are made. The instant optimal escape route is created by applying the constrained optimization method on the estimations made. The main motivation of this study is developing a deterministic-based method to get the certification of it in aviation. Therefore, instead of stochastic-based learning approaches, a deterministic approach is preferred. nonlinear programming is used as the constraint optimization method because the constraints and objective function are nonlinear. In the selected scenarios, it can be seen in the simulation results that the proposed method shows a promising result in terms of escape from engagement.
This contribution presents a heuristic approach for solving nonconvex mixed-integer nonlinear programming (MINLP) problems with highly constrained discontinuous domains. A new fuzzy penalty strategy is proposed to mak...
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This contribution presents a heuristic approach for solving nonconvex mixed-integer nonlinear programming (MINLP) problems with highly constrained discontinuous domains. A new fuzzy penalty strategy is proposed to make stochastic algorithms capable of solving optimization problems with a large number of difficult-to-satisfy constraints. The method consists of a dynamic penalty formulation based on the magnitude and frequency of the constraint violation, applied according to a hierarchical classification of the constraints. The new strategy is introduced to a multi-objective optimization algorithm based on evolutionary strategies. The performance of the proposed methodology is investigated on the basis of a multi-enterprise supply chain optimization problem.
In this paper, we consider the task to start the operation of an industrial evaporation system. Rigorous modelling gives rise to a hybrid automaton with large nonlinear DAE-models that describe the continuous evolutio...
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In this paper, we consider the task to start the operation of an industrial evaporation system. Rigorous modelling gives rise to a hybrid automaton with large nonlinear DAE-models that describe the continuous evolution in the discrete locations. The optimization problem is solved by a hierarchical procedure that consists of a branch-and-bound algorithm with embedded nonlinear dynamic optimization over a finite look-ahead horizon. Important elements of the algorithm are the introduction of a dynamic choice of the time intervals over which the controls are constant and of tailored penalty functions in order to obtain solutions which are close to infeasible trajectories.
Based on the systems approach to mathematical modeling, the paper shows the method for selecting the optimum design features of boiler drums with a given structure for minimum mass. The optimization problem is reduced...
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Based on the systems approach to mathematical modeling, the paper shows the method for selecting the optimum design features of boiler drums with a given structure for minimum mass. The optimization problem is reduced to finding the minimum of the objective function in a 10-dimensional space bounded by 11 constraints. The numerical example has been presented.
By combining the finite element method with dynamic programming, the dynamic finite element & nonlinear programming method (the dynamic FE&NLP method, i.e. the finite element & dynamic programming method (...
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By combining the finite element method with dynamic programming, the dynamic finite element & nonlinear programming method (the dynamic FE&NLP method, i.e. the finite element & dynamic programming method (the FE&DP method) is developed and systematized in order to control transient differential equation systems with both equality or inequality constraints and a nonlinear objective function. Such systems are frequently encountered in various engineering and scientific problems of control and optimal design. The dynamic FE&NLP method (the FE&DP method) is applied to optimal control in thermal diffusion phenomena. The tractability in the initial or final condition, the boundary conditions and the equality or inequality constraints makes sure that the method becomes a powerful technique for several new types of boundary value problems with nonlinear objective function.
Algorithms solving optimal control problems for linear discrete systems and linear continuous systems (without discretization) are discussed. The algorithms are based on a new approach to solving linear programming pr...
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Algorithms solving optimal control problems for linear discrete systems and linear continuous systems (without discretization) are discussed. The algorithms are based on a new approach to solving linear programming problems worked out in Minsk. (USSR). A new method for solving nonlinear programming problems is justified. It uses the network interpretation of nonlinear functions and special network operations. Results of numerical experiment (on geometric programming problems) are given. In conclusion an algorithm of solving optimal control problem for the system with nonlinear input is described.
Coal chemical industry plays a critical role in China’s economic growth and energy security. However, its carbon-intensity characteristics cause a large number of CO 2 emissions during coal chemicals production. Faci...
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Coal chemical industry plays a critical role in China’s economic growth and energy security. However, its carbon-intensity characteristics cause a large number of CO 2 emissions during coal chemicals production. Facing intense pressure to reduce CO 2 emissions, it is urgent to seek synergistic development between CO 2 emissions reduction and coal chemical engineering. A nonlinear programming (NLP) approach is proposed to optimize the deployment of China’s coal chemical industry under carbon constraints. The NLP model is pursuing the minimum CO 2 emission per unit value of gross output of coal to chemicals sector (CPUVGC) with simultaneously satisfying economic growth. Twelve main categories coal chemical products and six measures or technologies of CO 2 emission reduction are taken into consideration in the NLP model, based on which a short-term (2020), mid-term (2030) and long-term (2050) deployment of coal chemical industry under restriction of CO 2 emissions are investigated, and sensitivity or uncertainty analysis of effects of crude oil price (COP), which have a significant impact on coal chemicals price, on CO 2 emission reduction target also is performed. Three scenarios involved 100% (positive), 50% (moderate) and 25% (conservative) of the predicted target of CO 2 emissions reduction from different technologies or measures of CO 2 emissions reduction are analyzed in different periods. At the end, the development roadmap (2020-2030-2050) of coal chemical industry under carbon constraints is plotted and some specific suggestions and safeguard measures are also provided to guarantee implement of the planning.
Optimization techniques based on nonlinear programming are used to compute the constant, optimal output feedback gains, for linear multivariable control systems. The computation of these feedback gains provides a usef...
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Optimization techniques based on nonlinear programming are used to compute the constant, optimal output feedback gains, for linear multivariable control systems. The computation of these feedback gains provides a useful design tool in the development of aircraft active control systems. Broyden-Fletcher-Goldfarb-Shanno (BFGS), Davidon-Fletcher-Powell (DFP), and Newton methods are used in conjunction with appropriate starting values to compute the optimal gains; and a comparison of the effectiveness of the techniques is given. Also a modification of the DFP Method in which an analytical approximation of the inverse Hessian is used as a priming value is developed and evaluated. An example problem, the optimal control of a flexible aircraft, is used to evaluate the techniques. Results indicate that the methods provide an efficient and cost effective solution of the optimal output feedback problem.
The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a CAD package where both design objective and constraints are quadratic cost functions. This formul...
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The familiar suboptimal regulator design approach is recast as a constrained optimization problem and incorporated in a CAD package where both design objective and constraints are quadratic cost functions. This formulation permits the separate consideration of, for example, modelfollowing errors, sensitivity measures and control energy as objectives to be minimized or limits to be observed. Efficient techniques for computing the interrelated cost functions and their gradients are utilized in conjunction with a nonlinear programming algorithm. The effectiveness of the approach and the degree of insight into the problem which it affords is illustrated in a helicopter regulation design example.
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