With the development of drone technology, unmanned aerial vehicle (UAV)-based edge computing has emerged as a promising computing paradigm with broad application prospects. However, the limited endurance of UAVs makes...
详细信息
Focusing on smooth constrained optimization problems, and inspired by the complementary approximate Karush-Kuhn-Tucker (CAKKT) conditions, this work introduces the weighted complementary approximate Karush-Kuhn-Tucker...
详细信息
Focusing on smooth constrained optimization problems, and inspired by the complementary approximate Karush-Kuhn-Tucker (CAKKT) conditions, this work introduces the weighted complementary approximate Karush-Kuhn-Tucker (WCAKKT) conditions. They are shown to be verified by limit points generated not only by safeguarded augmented Lagrangian methods, but also by inexact restoration methods, inverse and logarithmic barrier methods, and a penalized algorithm for constrained nonsmooth optimization. Under the analyticity of the feasible set description, and resting upon a desingularization result, the new conditions are proved to be equivalent to the CAKKT conditions. The WCAKKT conditions capture the algebraic elements of the desingularization result needed to characterize CAKKT sequences using a weighted complementarity condition that asymptotically sums zero. Due to its generality and strength, the new condition may help to enlighten the practical performance of algorithms in generating CAKKT sequences.
Concentrating solar power (CSP) plants present a promising path towards utility-scale renewable energy. The power tower, or central receiver, configuration can achieve higher operating temperatures than other forms of...
详细信息
Concentrating solar power (CSP) plants present a promising path towards utility-scale renewable energy. The power tower, or central receiver, configuration can achieve higher operating temperatures than other forms of CSP, and, like all forms of CSP, naturally pairs with comparatively inexpensive thermal energy storage, which allows CSP plants to dispatch electricity according to market price incentives and outside the hours of solar resource availability. Currently, CSP plants commonly include a steam Rankine power cycle and several heat exchange components to generate high-pressure steam using stored thermal energy. The efficiency of the steam Rankine cycle depends on the temperature of the plant's operating fluid, and so is a main concern of plant operators. However, the variable nature of the solar resource and the conservatism with which the receiver is operated prevent perfect control over the receiver outlet temperature. Therefore, during periods of solar variability, collection occurs at lower-than-design temperature. To support operator decisions in a real-time setting, we develop a revenue-maximizing non-convex mixed-integer, quadradically-constrained program which determines a dispatch schedule with sub-hourly time fidelity and considers temperature-dependent power cycle efficiency. The exact nonlinear formulation proves intractable for real-time decision support. We present exact and inexact techniques to improve problem tractability that include a hybrid nonlinear and linear formulation. Our approach admits solutions within approximately 3% of optimality, on average, within a five-minute time limit, demonstrating its usability for decision support in a real-time setting.
The finite Fourier series shape-based approach for fast initial trajectory design satisfies the equations of motion and other problem constraints at discrete points by using a nonlinear programming solver to design th...
详细信息
The finite Fourier series shape-based approach for fast initial trajectory design satisfies the equations of motion and other problem constraints at discrete points by using a nonlinear programming solver to design the Fourier coefficients. In this paper, the finite Fourier series approach is extended to account for the necessary conditions for optimality during the Fourier coefficient design. The proposed method uses the approximate trajectories to analytically estimate the costates at these discrete points by employing a finite difference technique on the adjoint differential equations. Lagrange multipliers associated with any terminal state constraints are determined using an auxiliary function. Residual errors in the stationarity condition are reduced through the objective function, with the Legendre-Clebsch condition enforced as a nonlinear inequality constraint;applying these two conditions finds suboptimal solutions without an excessive loss of computational efficiency. Test cases use steering angle and thrust acceleration magnitude controls and span Earth-escape spirals, geostationary spacecraft rendezvous, and phasing maneuvers. The presented results demonstrate the proposed method's ability to achieve trajectories closer to the optimal solution.
A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. On...
详细信息
A central goal for multi-objective optimization problems is to compute their nondominated sets. In most cases these sets consist of infinitely many points and it is not a practical approach to compute them exactly. One solution to overcome this problem is to compute an enclosure, a special kind of coverage, of the nondominated set. For that computation one often makes use of so-called local upper bounds. In this paper we present a generalization of this concept. For the first time, this allows to apply a warm start strategy to the computation of an enclosure. We also show how this generalized concept allows to remove empty areas of an enclosure by deleting certain parts of the lower and upper bound sets which has not been possible in the past. We demonstrate how to apply our ideas to the box approximation algorithm, a general framework to compute an enclosure, as recently used in the solver called BAMOP. We show how that framework can be simplified and improved significantly, especially concerning its practical numerical use. In fact, we show for selected numerical instances that our new approach is up to eight times faster than the original one. Hence, our new framework is not only of theoretical but also of practical use, for instance for continuous convex or mixed-integer quadratic optimization problems.(c) 2023 Elsevier B.V. All rights reserved.
The dislocation hyperbolic augmented Lagrangian algorithm (DHALA) solves the nonconvex programming problem considering an update rule for its penalty parameter and considering a condition to ensure the complementarity...
详细信息
The dislocation hyperbolic augmented Lagrangian algorithm (DHALA) solves the nonconvex programming problem considering an update rule for its penalty parameter and considering a condition to ensure the complementarity condition. in this work, we ensure that the sequence generated by DHALA converges to a Karush-Kuhn-Tucker (KKT) point, and we present computational experiments to demonstrate the performance of our proposed algorithm.
Many applications arising in control theory, nonlinear networks, generalized Leontief input-output model and economics lead to a broad range of optimization and equilibrium problems. Under suitable convexity assumptio...
详细信息
Many applications arising in control theory, nonlinear networks, generalized Leontief input-output model and economics lead to a broad range of optimization and equilibrium problems. Under suitable convexity assumptions, the equilibrium conditions of such problems may be compactly stated as the vertical nonlinear complementarity problem (VNCP). In this paper, based on modulus-based formulation of the VNCP, we present a variety of modulus-based matrix splitting methods for solving the VNCP. Under some mild conditions, we establish the convergence of the proposed method. Numerical experiments indicate that the proposed method is effective.
An effective approach is proposed for optimal control problems in aerospace engineering. First, several interval lengths are treated as optimization variables directly to localize the switching points accurately. Seco...
详细信息
An effective approach is proposed for optimal control problems in aerospace engineering. First, several interval lengths are treated as optimization variables directly to localize the switching points accurately. Second, the variable intervals are usually refined into more subintervals homogeneously to obtain the trajectories with high accuracy. To reduce the number of optimization variables and improve the efficiency, the control and the state vectors are parameterized using different meshes in this paper such that the control can be approximated asynchronously by fewer parameters where the trajectories change slowly. Then, the variables are departed as independent variables and dependent variables, the gradient formulae, based on the partial derivatives of dependent parameters with respect to independent parameters, are computed to solve nonlinear programming problems. Finally, the proposed approach is applied to the classic moon lander and hang glider problems. For the moon lander problem, the proposed approach is compared with CVP, Fast-CVP and GPM methods, respectively. For the hang glider problem, the proposed approach is compared with trapezoidal discretization and stopping criteria methods, respectively. The numerical results validate the effectiveness of the proposed approach.& COPY;2023 Published by Elsevier Inc. on behalf of The Franklin Institute.
The resource allocation problem is among the classical problems in operations research, and has been studied extensively for decades. However, current solution approaches are not able to efficiently handle problems wi...
详细信息
The resource allocation problem is among the classical problems in operations research, and has been studied extensively for decades. However, current solution approaches are not able to efficiently handle problems with expensive function evaluations, which can occur in a variety of applications. We study the integer resource allocation problem with expensive function evaluations, for both convex and non-convex separable cost functions. We present several solution methods, both heuristics and exact methods, that aim to limit the number of function evaluations. The methods are compared in numerical experiments using both randomly generated instances and instances from two resource allocation problems occur-ring in radiation therapy planning. Results show that the presented solution methods compare favorably against existing derivative free optimization solvers. (c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://***/licenses/by/4.0/ )
In the framework of data envelopment analysis (DEA), Tone (Eur J Oper Res 130(3):498-509, 2001) introduced the slacks-based measure (SBM) of efficiency, which is a nonradial model that incorporates all the slacks of t...
详细信息
In the framework of data envelopment analysis (DEA), Tone (Eur J Oper Res 130(3):498-509, 2001) introduced the slacks-based measure (SBM) of efficiency, which is a nonradial model that incorporates all the slacks of the evaluated decision-making units (DMUs) into their efficiency scores, unlike classical radial efficiency models. Next, Tone (Eur J Oper Res 143(1):32-41, 2002) developed the SBM super-efficiency model in order to differentiate and rank efficient DMUs, whose SBM efficiency scores are always 1. However, as pointed out by Chen (Eur J Oper Res 226(2):258-267, 2013), some interpretation problems arise when the so-called super-efficiency projections are weakly efficient, leading to an overestimation of the SBM super-efficiency score. Moreover, this overestimation is closely related to discontinuity issues when implementing SBM super-efficiency in conjunction with SBM efficiency. Chen (Eur J Oper Res 226(2):258-267, 2013) and Chen et al. (Ann Oper Res 278(1):101-121, 2019) treated these problems, but they did not arrive to a fully satisfactory solution. In this paper, we review these papers and propose a new complementary score, called composite SBM, that actually fixes the discontinuity problems by counteracting the overestimation of the SBM super-efficiency score. Moreover, we extend the composite SBM model to different orientations and variable returns to scale, and propose additive versions. Finally, we give examples and state some open problems.
暂无评论