A method for finding all roots of a system of nonlinear equations is described. Our method makes use of C-GRASP, a recently proposed continuous global optimization heuristic. Given a nonlinear system, we solve a corre...
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A method for finding all roots of a system of nonlinear equations is described. Our method makes use of C-GRASP, a recently proposed continuous global optimization heuristic. Given a nonlinear system, we solve a corresponding adaptively modified global optimization problem multiple times, each time using C-GRASP, with areas of repulsion around roots that have already been found. The heuristic makes no use of derivative information. We illustrate the approach using systems found in the literature. (C) 2008 Elsevier Ltd. All rights reserved.
In this work, we address the simultaneous design and control of a binary distillation column. The problem is first formulated as a mixed-integer dynamic optimization problem that is then transformed into a mixed-integ...
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In this work, we address the simultaneous design and control of a binary distillation column. The problem is first formulated as a mixed-integer dynamic optimization problem that is then transformed into a mixed-integer nonlinear programming problem using the simultaneous dynamic optimization approach (i.e., full discretization). This formulation is capable of designing the optimal feed tray location, tray sizing, optimal operating steady states, the optimal open-loop trajectory between them, and also the best controller paring and parameters that does the best tracking of the open-loop trajectory. For solving the complex mixed-integer dynamic optimization problem, an optimization decomposition strategy is proposed. The solution strategy is based on solving relaxed versions of the optimization problem and using the results to initialize complex problem versions. The full space problem was solved with the Bonmin solver. Two cases were analyzed, and in both the solver and the proposed decomposition strategy were capable of solving the problems successfully.
This paper presents a strategy for the solution of nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP) problems. based oil the coupling of the equation-oriented simulator ASCEND IV with the sto...
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This paper presents a strategy for the solution of nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP) problems. based oil the coupling of the equation-oriented simulator ASCEND IV with the stochastic optimizers MSGA and MSIMPSA. Both NLP and MINLP formulations of a reactive distillation example were explored. The results show that the connection between the two software blocks was successfully established. Despite the highly nonlinear behavior of the proposed example, the results presented generally agree with those previously obtained for the same case study using other approaches, namely, SIMOP, which is a FORTRAN 77-based NLP simulation tool developed for optimization problems Increasing the column dimension or switching the vapor-liquid equilibrium (VLE) description to a nonideal Situation, which produces nonlinear models with a much larger number of equations that must be solved simultaneously, show that the results deteriorate. This is attributed to the lack of user control over the subsystems' structures (viz, tearing variables). This problem was partially circumvented through the application of a more elaborate scheme initialization for the column variables.
In the face of shorter product life cycles, designing products with modular component parts can shorten product development time and speed up the introduction of new products in the market. Utilizing stylized models, ...
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In the face of shorter product life cycles, designing products with modular component parts can shorten product development time and speed up the introduction of new products in the market. Utilizing stylized models, we examine the reuse/redesign, quality, speed-to-market, and marketing decisions for two consecutive generations of a multicomponent modular product. With modularity that assumes a stable product architecture, each component can be improved by incurring a design cost that is convex increasing in the level of quality. Our study generates the following insights. When development start-up (fixed) cost is negligible, it is profitable to upgrade every component part;otherwise, it is beneficial to reuse some of the existing parts without making any design improvements in order to save on development cost. In an effort to reduce product development time while maximizing profit, we found solid evidence that the productivity level in developing every component part can be a key driver of speed-to-market. Individually, a new product launch time postponement and an R&D budget increase can lead to improvements in component part quality and overall product quality, but our models show that better improvement in quality can be achieved from launch time postponement (budget increase) when product design teams have low (high) product development productivity. Finally, when the marginal cost of producing the new product is equal to that of the old product, it is optimal to remove the old product from the market and sell only the new product.
The class of generalized pattern search (GPS) algorithms for mixed variable optimization is extended to problems with stochastic objective functions. Because random noise in the objective function makes it more diffic...
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The class of generalized pattern search (GPS) algorithms for mixed variable optimization is extended to problems with stochastic objective functions. Because random noise in the objective function makes it more difficult to compare trial points and ascertain which points are truly better than others, replications are needed to generate sufficient statistical power to draw conclusions. Rather than comparing pairs of points, the approach taken here augments pattern search with a ranking and selection (R&S) procedure, which allows for comparing many function values simultaneously. Asymptotic convergence for the algorithm is established, numerical issues are discussed, and performance of the algorithm is studied on a set of test problems. Published by Elsevier B.V.
This paper deals with the synthesis of optimal trajectories for acrobatic air races. A typical example of all air race event is the Red Bull Air Race World Series, where high-performance aerobatic aircraft fly a presc...
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This paper deals with the synthesis of optimal trajectories for acrobatic air races. A typical example of all air race event is the Red Bull Air Race World Series, where high-performance aerobatic aircraft fly a prescribed slalom course consisting of specially designed inflatable pylons, known as 'air gates', in the fastest possible time. The trajectory that we seek to optimise is based on Such a course. The air race problem is formulated as a minimum-time optimal control problem and solved in open-loop form using a direct numerical multi-phase trajectory optimisation approach based oil collocation and non-linear programming. The multiphase feature of the employed collocation algorithm is used to enable a Receding-Horizon optimisation approach, in which only a limited number of manoeuvres in sequence is considered. It is shown that the Receding-Horizon control approach provides a near-optimal solution at a significantly reduced computational cost relative to trajectory optimisation over the entire course. To avoid the path inclination singularity in the equations of motion based on Euler angles, a point-mass model formulation is used that is based on quaternions. Numerical results are presented for an Extra 300S, a purpose-designed acrobatic aircraft.
The article focuses on a study on the development of a linear feedback guidance scheme for-low thrust Earth-orbit transfers that involve many orbital revolutions. The key concept of the proposed guidance scheme is cit...
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The article focuses on a study on the development of a linear feedback guidance scheme for-low thrust Earth-orbit transfers that involve many orbital revolutions. The key concept of the proposed guidance scheme is cited. It notes that the study used the parameterized control law in both optimization and guidance. According to the author, the scheme possesses near-optimal performance because the optimal trajectory and control can tracked by means of space vehicles.
A new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach is presented. The objective minimises power losses, balancing...
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A new and efficient methodology for distribution network reconfiguration integrated with optimal power flow (OPF) based on a Benders decomposition approach is presented. The objective minimises power losses, balancing load among feeders and subject to constraints such as capacity limit of branches, minimum and maximum power limits of substations or distributed generators, minimum deviation of bus voltages and radial optimal operation of networks. A variant of the generalised Benders decomposition algorithm is applied to solve the problem. The formulation can be embedded under two stages;the first one is the master problem and is formulated as a mixed integer non-linear programming problem. This stage determines the radial topology of the distribution network. The second stage is the slave problem and is formulated as a non-linear programming problem. This stage is used to determine the feasibility of the master problem solution by means of an OPF and provides information to formulate the linear Benders cuts that connect both problems. The model is programmed in GAMS mathematical modelling language. The effectiveness of the proposal is demonstrated through two examples extracted from the specialised literature.
In this paper we present a multi-layer approach for motion planning in obstacle rich environments. The approach is built on the principle of separation of concern which partitions the motion planning problem into mult...
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In this paper we present a multi-layer approach for motion planning in obstacle rich environments. The approach is built on the principle of separation of concern which partitions the motion planning problem into multiple independent layers. This enables design space exploration at each layer. We partition the motion planning algorithm into a roadmap layer and an optimal control layer. Elements of computational geometry are used to process the obstacle rich environment and generate a set of convex feasible regions, which is then used by the optimal control layer to generate trajectories while satisfying dynamics of the vehicle. The roadmap layer ignores the dynamics of the system, and plans paths at a global level using coarse representation of the environment. The optimal control layer ignores the complexity of the environment and plans paths at a mid-level using fine representation of the dynamics and the environment. In this manner a separation of concern is achieved. This decomposition enables computationally tractable methods to be developed for addressing motion planning in complex environments.
The operational airspace of aerospace vehicles, including airplanes and unmanned aerial vehicles, is often restricted so that constraints on three-dimensional climbs, descents, and other maneuvers are necessary. In th...
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The operational airspace of aerospace vehicles, including airplanes and unmanned aerial vehicles, is often restricted so that constraints on three-dimensional climbs, descents, and other maneuvers are necessary. In this paper, the problem of determining constrained, three-dimensional, minimum time-to-climb, and minimum fuel-to-climb trajectories for an aircraft in an airspace defined by a rectangular prism of arbitrary height is considered. The optimal control problem is transformed to a parameter optimization problem. Because a helical geometry appears to be a natural choice for climbing and descending trajectories subject to horizontal constraints, helical curves are chosen as starting trajectories. A procedure for solving the minimum time-to-climb and minimum fuel-to-climb problems by using the direct collocation and nonlinear programming methods including Chebyshev pseudospectral and Gauss pseudospectral discretization is discussed. Results obtained when different constraints are placed on airspace and state variables are presented to show their effect on the performance index. The question or "optimality" of the numerical results is also considered.
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