Choosing proper locations for urban transit hubs has always been a critical concern facing urban transportation planning agencies in China. This study proposes a mixed integer optimal location model for urban transit ...
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Choosing proper locations for urban transit hubs has always been a critical concern facing urban transportation planning agencies in China. This study proposes a mixed integer optimal location model for urban transit hubs, with the objective to minimize the demand-weighted total travel time, when explicitly taking into account traffic analysis zones as demand origins or destinations in a target urban area. An integer non-linear programming (INLP) reformulation was developed to reduce the number of variables significantly. Bilinear constraints in the proposed INLP formulation were then remodeled into linear functions to ensure that global optimal solutions were obtained. The model was successfully applied to optimize the hub locations in Suzhou Industrial Park, China, with the result of significantly improved system performance. The effects of several critical factors, such as the number of hubs and the travel time discount coefficient on the system performance, were also investigated.
This paper presents a canonical duality theory and optimal solutions to a class of global optimization problems subjected to linear inequality constraints. By using the canonical dual transformation developed recently...
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This paper presents a canonical duality theory and optimal solutions to a class of global optimization problems subjected to linear inequality constraints. By using the canonical dual transformation developed recently, a canonical dual problem is formulated, which is perfectly dual to the primal problem. The global minmizer can be identified by the triality theory. Results show that if the global extrema of the original problem are located on the boundary of the primal feasible space, the dual solution should be interior point of the dual feasible set. Several examples are illustrated to show how this theory works. (c) 2008 Elsevier Inc. All rights reserved.
We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interior-point method developed by Stein [O. Stei...
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We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interior-point method developed by Stein [O. Stein, Bi-level Strategies in Semi-infinite programming, Kluwer Academic Publishers, Boston, 2003]. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on real-world data are also presented. (C) 2007 Elsevier B.V. All rights reserved.
This paper presents a nonlinear, multi-phase and stochastic dynamical system according to engineering background. We show that the stochastic dynamical system exists a unique solution for every initial state. A stocha...
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This paper presents a nonlinear, multi-phase and stochastic dynamical system according to engineering background. We show that the stochastic dynamical system exists a unique solution for every initial state. A stochastic optimal control model is constructed and the sufficient and necessary conditions for optimality are proved via dynamic programming principle. This model can be converted into a parametric nonlinear stochastic programming by integrating the state equation. It is discussed here that the local optimal solution depends in a continuous way on the parameters. A revised Hooke-Jeeves algorithm based on this property has been developed. Computer simulation is used for this paper, and the numerical results illustrate the validity and efficiency of the algorithm. (C) 2007 Elsevier B.V. All rights reserved.
Based on an augmented Lagrangian line search function, a sequential quadratically constrained quadratic programming method is proposed for solving nonlinearly constrained optimization problems. Compared to quadratic p...
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Based on an augmented Lagrangian line search function, a sequential quadratically constrained quadratic programming method is proposed for solving nonlinearly constrained optimization problems. Compared to quadratic programming solved in the traditional SQP methods, a convex quadratically constrained quadratic programming is solved here to obtain a search direction, and the Maratos effect does not occur without any other corrections. The "active set" strategy used in this subproblem can avoid recalculating the unnecessary gradients and (approximate) Hessian matrices of the constraints. Under certain assumptions, the proposed method is proved to be globally, superlinearly, and quadratically convergent. As an extension, general problems with inequality and equality constraints as well as nonmonotone line search are also considered. (c) 2007 Published by Elsevier B.V.
Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function....
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Our problem of interest consists of minimizing a separable, convex and differentiable function over a convex set, defined by bounds on the variables and an explicit constraint described by a separable convex function. Applications are abundant, and vary from equilibrium problems in the engineering and economic sciences, through resource allocation and balancing problems in manufacturing, statistics, military operations research and production and financial economics, to subproblems in algorithms for a variety of more complex optimization models. This paper surveys the history and applications of the problem, as well as algorithmic approaches to its solution. The most common techniques are based on finding the optimal value of the Lagrange multiplier for the explicit constraint, most often through the use of a type of line search procedure. We analyze the most relevant references, especially regarding their originality and numerical findings, summarizing with remarks on possible extensions and future research. (c) 2006 Elsevier B.V. All rights reserved.
The problem of time-optimal de-tumbling control (TODTC) of a rigid spacecraft moving between two attitudes is studied in this article. Unlike conventional approaches, which involve solving a set of differential equati...
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The problem of time-optimal de-tumbling control (TODTC) of a rigid spacecraft moving between two attitudes is studied in this article. Unlike conventional approaches, which involve solving a set of differential equations, a novel numerical method is introduced. In the proposed method, by fixing the count of control steps and treating the sampling period as a variable, the TODTC problem is formulated as a nonlinear programming ( NLP) problem by utilizing an iterative procedure. Generating initial feasible solutions systematically is also discussed, since these are usually needed in solving a NLP problem. In this manner, the optimization process of the NLP problem can be started from many different points when searching for the optimal solution. Simulation results are included, to show the feasibility of the proposed method.
We describe an asynchronous parallel derivative-free algorithm for linearly constrained optimization. Generating set search (GSS) is the basis of our method. At each iteration, a GSS algorithm computes a set of search...
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We describe an asynchronous parallel derivative-free algorithm for linearly constrained optimization. Generating set search (GSS) is the basis of our method. At each iteration, a GSS algorithm computes a set of search directions and corresponding trial points and then evaluates the objective function value at each trial point. Asynchronous versions of the algorithm have been developed in the unconstrained and bound-constrained cases which allow the iterations to continue (and new trial points to be generated and evaluated) as soon as any other trial point completes. This enables better utilization of parallel resources and a reduction in overall run time, especially for problems where the objective function takes minutes or hours to compute. For linearly constrained GSS, the convergence theory requires that the set of search directions conforms to the nearby boundary. This creates an immediate obstacle for asynchronous methods where the definition of nearby is not well defined. In this paper, we develop an asynchronous linearly constrained GSS method that overcomes this difficulty and maintains the original convergence theory. We describe our implementation in detail, including how to avoid function evaluations by caching function values and using approximate lookups. We test our implementation on every CUTEr test problem with general linear constraints and up to 1000 variables. Without tuning to individual problems, our implementation was able to solve 95% of the test problems with 10 or fewer variables, 73% of the problems with 11-100 variables, and nearly half of the problems with 100-1000 variables. To the best of our knowledge, these are the best results that have ever been achieved with a derivative-free method for linearly constrained optimization. Our asynchronous parallel implementation is freely available as part of the APPSPACK software.
Binary integrators are an important part of the receiver in many operating radar systems. The optimisation of a binary integrator is not a simple task, because it requires the solution of a (k x n)-dimensional nonline...
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Binary integrators are an important part of the receiver in many operating radar systems. The optimisation of a binary integrator is not a simple task, because it requires the solution of a (k x n)-dimensional nonlinear optimisation problem, where n is the number of integrated bits (or the number of sensors in a distributed radar or sensor network) and k is the number of the design parameters of the single-pulse detector. An algorithm that converts the multi-dimensional optimisation problem into a one-dimensional problem, so reducing considerably the computational complexity, is developed. This reduction in computational complexity makes the real-time optimisation possible and practical, so it is very helpful for mobile sites in which the optimisation should be performed continually. The proposed algorithm can be applied when either the 'AND' or the 'OR' integration rule is adopted. The results are illustrated by means of two study cases. In the first case, the binary integrator of a constant false alarm rate radar detector is optimised;in the second one a decentralised detection system composed by n similar sensors is considered and the decision rules are jointly optimised according to the Neyman-Pearson criterion.
uv-decomposition method for solving a mathematical program with equilibrium constraints （MPEC） problem with linear complementarity constraints is presented. The problem is first converted into a nonlinear programmin...
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uv-decomposition method for solving a mathematical program with equilibrium constraints （MPEC） problem with linear complementarity constraints is presented. The problem is first converted into a nonlinear programming one. The structure of subdifferential a corresponding penalty function and results of its uv-decomposition are given. A conceptual algorithm for solving this problem with a superUnear convergence rate is then constructed in terms of the obtained results.
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