This paper develops a campaign-level space logistics optimization framework that simultaneously considers mission planning and spacecraft design using mixed-integer nonlinear programming. In the mission planning part ...
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This paper develops a campaign-level space logistics optimization framework that simultaneously considers mission planning and spacecraft design using mixed-integer nonlinear programming. In the mission planning part of the framework, deployment and utilization of in-orbit infrastructures, such as in-orbit propellant depots or in situ resource utilization plants, are also taken into account. Two methods are proposed: First, the mixed-integer nonlinear programming problem is converted into a mixed-integer linear programming problem after approximating the nonlinear model with a piecewise linear function and linearizing quadratic terms. In addition, another optimization framework is provided, based on simulated annealing, which separates the spacecraft model from mission planning formulation. An example mission scenario based on multiple Apollo missions is considered, and the results show a significant improvement in the initial mass in low Earth orbit by campaign-level design as compared with the traditional mission-level design. It is also shown that the mixed-integer linear programming-based method gives better-quality solutions than the simulated annealing-based method, although the simulated annealing method is more flexible for extension to a higher-fidelity spacecraft model.
Integration of real-time optimization and control with higher level decision-making (scheduling and planning) is an essential goal for profitable operation in a highly competitive environment. While integrated large-s...
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Integration of real-time optimization and control with higher level decision-making (scheduling and planning) is an essential goal for profitable operation in a highly competitive environment. While integrated large-scale optimization models have been formulated for this task, their size and complexity remains a challenge to many available optimization solvers. On the other hand, recent development of powerful, large-scale solvers leads to a reconsideration of these formulations, in particular, through development of efficient large-scale barrier methods for nonlinear programming (NLP). As a result, it is now realistic to solve NLPs on the order of a million variables, for instance, with the IPOPT algorithm. Moreover, the recent NLP sensitivity extension to IPOPT quickly computes approximate solutions of perturbed NLPs. This allows on-line computations to be drastically reduced, even when large nonlinear optimization models are considered. These developments are demonstrated on dynamic real-time optimization strategies that can be used to merge and replace the tasks of (steady-state) real-time optimization and (linear) model predictive control. We consider a recent case study of a low density polyethylene (LDPE) process to illustrate these concepts. (C) 2008 Elsevier Ltd. All rights reserved.
This paper addresses the local convergence properties of the affine-scaling interior-point algorithm for nonlinear programming. The analysis of local convergence is developed in terms of parameters that control the in...
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This paper addresses the local convergence properties of the affine-scaling interior-point algorithm for nonlinear programming. The analysis of local convergence is developed in terms of parameters that control the interior-point scheme and the size of the residual of the linear system that provides the step direction. The analysis follows the classical theory for quasi-Newton methods and addresses q-linear, q-superlinear, and q-quadratic rates of convergence.
In this paper, we describe how to reformulate a problem that has second-order cone and/or semi-definiteness constraints in order to solve it using a general-purpose interior-point algorithm for nonlinear programming. ...
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In this paper, we describe how to reformulate a problem that has second-order cone and/or semi-definiteness constraints in order to solve it using a general-purpose interior-point algorithm for nonlinear programming. The resulting problems are smooth and convex, and numerical results from the DIMACS Implementation Challenge problems and SDPLib are provided.
A nonlinear programming approach, along with finite element implementation, has been developed to perform plastic limit analysis for materials under non-associated plastic flow, so the plastic stability condition of n...
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A nonlinear programming approach, along with finite element implementation, has been developed to perform plastic limit analysis for materials under non-associated plastic flow, so the plastic stability condition of non-standard materials can be directly calculated. In the framework of Radenkovic's theorems, a decoupled material model with non-associated plastic flow was introduced into kinematic limit analysis so that the classic limit theorems were extended for non-standard plastic flow materials, such as cohesive-frictional materials. A non-associated plastic dissipation power is derived, and a purely kinematic formulation is obtained for limit analysis. Based on the mathematical programming theory and the finite element method, the numerical implementation of kinematic limit analysis is formulated as a nonlinear programming problem subject only to one equality constraint. An extended direct iterative algorithm is proposed to solve the resulting programming problem. The developed method has a wide applicability for limit analysis. The effectiveness and efficiency of the proposed method are validated through numerical examples and the influence of non-associated plastic flow on stability conditions of structures is numerically investigated.
We consider a smooth nonlinear program subject to perturbations in the right-hand side of the constraints. We do not assume that the unique solution of the original problem satisfies any qualification hypothesis. We s...
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We consider a smooth nonlinear program subject to perturbations in the right-hand side of the constraints. We do not assume that the unique solution of the original problem satisfies any qualification hypothesis. We suppose instead that the direction of perturbation satisfies the hypothesis of Gollan. We study the variation of the cost and, with the help of some second-order sufficiency conditions, obtain some conditions satisfied by the first term of the expansion of the solution. These conditions may vary depending on the existence of a Lagrange multiplier for the original problem.
This study presents a method for form-finding and analysis of hyperelastic tensegrity structures based on a special strut finite element and unconstrained nonlinear programming. The strut element can function as a hyp...
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This study presents a method for form-finding and analysis of hyperelastic tensegrity structures based on a special strut finite element and unconstrained nonlinear programming. The strut element can function as a hyperelastic truss element with an initial cut in its undeformed length or as a strut element that shows constant force irrespectively of its nodal displacements. For the hyperelastic strut element, the invariants of the Right Cauchy-Green deformation tensor are written in terms of the element's nodal displacements and the cut in the element's undeformed length. The structure's total potential energy is expressed as function of its nodal displacements and the cuts in the elements' undeformed lengths. The minimization of this function is a nonlinear programming problem where the displacements are the unknowns. The form-finding procedure is performed by a static analysis where the stiffness matrix maybe singular along the path to equilibrium without causing convergence problems. The mathematical model includes the element's cross-sectional deformation while the element moves in space, fully modelling its three-dimensional character. The constraint for incompressibility is satisfied exactly, eliminating the need for a penalty or augmented Lagrangian method.
In this paper, we present an interior point method for nonlinear programming that avoids the use of penalty function or filter. We use an adaptively perturbed primal dual interior point framework to computer trial ste...
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In this paper, we present an interior point method for nonlinear programming that avoids the use of penalty function or filter. We use an adaptively perturbed primal dual interior point framework to computer trial steps and a central path technique is used to keep the iterate bounded away from 0 and not to deviate too much from the central path. A trust-funnel-like strategy is adopted to drive convergence. We also use second-order correction (SOC) steps to achieve fast local convergence by avoiding Maratos effect. Furthermore, the presented algorithm can avoid the blocking effect. It also does not suffer the blocking of productive steps that other trust-funnel-like algorithm may suffer. We show that, under second-order sufficient conditions and strict complementarity, the full Newton step (combined with an SOC step) will be accepted by the algorithm near the solution, and hence the algorithm is superlinearly local convergent. Numerical experiments results, which are encouraging, are reported.
In this paper we present a method for converting general nonlinear programming (NLP) problems into separable programming (SP) problems by using feedforward neural networks (FNNs). The basic idea behind the method is t...
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In this paper we present a method for converting general nonlinear programming (NLP) problems into separable programming (SP) problems by using feedforward neural networks (FNNs). The basic idea behind the method is to use two useful features of FNNs: their ability to approximate arbitrary continuous nonlinear functions with a desired degree of accuracy and their ability to express nonlinear functions in terms of parameterized compositions of functions of single variables. According to these two features, any nonseparable objective functions and/or constraints in NLP problems can be approximately expressed as separable functions with FNNs. Therefore, any NLP problems can be converted into SP problems. The proposed method has three prominent features. (a) It is more general than existing transformation techniques: (b) it can be used to formulate optimization problems as SP problems even when their precise analytic objective function and/or constraints are unknown;(c) the SP problems obtained by the proposed method may highly facilitate the selection of grid points for piecewise linear approximation of nonlinear functions. We analyze the computational complexity of the proposed method and compare it with an existing transformation approach. We also present several examples to demonstrate the method and the performance of the simplex method with the restricted basis entry rule for solving SP problems. (C) 2003 Elsevier Science Ltd. All rights reserved.
In this paper, a mixed integer nonlinear programming model is proposed to concurrently design two segments (i.e., upstream and midstream) of crudel oil supply chain. The network includes all entities and their connect...
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In this paper, a mixed integer nonlinear programming model is proposed to concurrently design two segments (i.e., upstream and midstream) of crudel oil supply chain. The network includes all entities and their connections from oil wells to product depots. Furthermore, a real world example is applied to show the improved model application. Furthermore, a sensitivity analysis in which +/- 20% deviations at a time were placed on two parameters is presented. Also, model performance is analyzed with GAMS 22.6. The proposed multiperiod and multiproduct model consists of several decisions (i.e., oil field development, transformation, transportation, and distribution). The main contributions of this work are inclusion of all entities related to upstream and midstream segments and both oil field development and transformation planning, simultaneously. Finally, it is shown that a decrease in production cost of refinery products will lead to more net profit given all refinery production capacity are used. Also, increase in refinery production capacity will improve network net profit given new fixed cost investment is not applied (e.g., refineries and transportation modes). This is the first study that simultaneously considers and optimizes upstream and midstream of crude oil supply chain. Second, it presents a unique mathematical model. Third, all features and parameters are included. Fourth, it is practical and may be used for other crude oil supply chain.
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