Solving nonlinear integer programs with large-scale optimization software

This paper describes recent experience in tackling large nonlinear integer programming problems using the MINOS large-scale optimization software. A technique is presented for extending the constrained search approach used in MINOS to exploring integer-feasible solutions once a continuous optimal solution is obtained. Computational experience with this approach is described for two classes of problems: quadratic assignment problems and pipeline network design problems.     

Optimal sequencing in the presence of setup times for tow/barge traffic through a river lock

Queues of tow/barges form when a river lock is rendered inoperable due to lock malfunction, a tow/barge accident or adverse lock operating conditions. In this paper, we develop model formulations that allow the queue to be cleared using a number of differing objectives. Of particular interest is the presence of different setup times between successive passages of tow/barges through the lock. Dependent on the objective chosen, we are able to show that certain ordering protocols may be used to markedly reduce the sequencing search space for N tow/barges from the order of N! to 2^N. We present accompanying linear and nonlinear integer programming formulations and carry out computational experiments on a representative set of problems.     

A Smoothing-Type Algorithm for Solving Linear Complementarity Problems with Strong Convergence Properties

In this paper, we construct an augmented system of the standard monotone linear complementarity problem (LCP), and establish the relations between the augmented system and the LCP. We present a smoothing-type algorithm for solving the augmented system. The algorithm is shown to be globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, if the LCP has a solution, then the algorithm either generates a maximal complementary solution of the LCP or detects correctly solvability of the LCP, and in the latter case, an existing smoothing-type algorithm can be directly applied to solve the LCP without any additional assumption and it generates a maximal complementary solution of the LCP; and that if the LCP is infeasible, then the algorithm detect correctly infeasibility of the LCP. To the best of our knowledge, such properties have not appeared in the existing literature for smoothing-type algorithms. This work was partially supported by the National Natural Science Foundation of China (Grant No. 10571134), the Natural Science Foundation of Tianjin (Grant No. 07JCYBJC05200), and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry.     

MONOTONIZATION IN GLOBAL OPTIMIZATION

A general monotonization method is proposed for converting a constrained programming problem with non-monotone objective function and monotone constraint functions into a monotone programming problem. An equivalent monotone programming problem with only inequality constraints is obtained via this monotonization method. Then the existing convexification and concavefication methods can be used to convert the monotone programming problem into an equivalent better-structured optimization problem.     

Topology optimization of microfluidic mixers

This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering the layout of flow/non‐flow regions subject to a constraint on the pressure drop between inlet and outlet. For a square cross‐sectioned pipe the mixing is increased by 70% compared with a straight pipe at the cost of a 2.5 fold increase in pressure drop. Another example where only the bottom profile of the channel is a design domain results in intricate herring bone patterns that confirm findings from the literature. Copyright © 2008 John Wiley & Sons, Ltd.     

反相液相色谱二元流动相组成的计算机统计试验全局最佳化

本文用一类非线性规划形式表述的分离模型作为最优化标准,用统计试验全局最佳化方法寻求二元流动相的最佳组成。实验证明:至多5个试验和10分钟左右的计算时间即可找到全局最佳点。     

Identification and control of nonlinear systems by a dissimilation particle swarm optimization-based Elman neural network

In this paper, we first present a learning algorithm for dynamic recurrent Elman neural networks based on a dissimilation particle swarm optimization. The proposed algorithm computes concurrently both the evolution of network structure, weights, initial inputs of the context units, and self-feedback coefficient of the modified Elman network. Thereafter, we introduce and discuss a novel control method based on the proposed algorithm. More specifically, a dynamic identifier is constructed to perform speed identification and a controller is designed to perform speed control for Ultrasonic Motors (USM). Numerical experiments show that the novel identifier and controller based on the proposed algorithm can both achieve higher convergence precision and speed than other state-of-the-art algorithms. In particular, our experiments show that the identifier can approximate the USM's nonlinear input–output mapping accurately. The effectiveness of the controller is verified using different kinds of speeds of constant, step, and sinusoidal types. Besides, a preliminary examination on a randomly perturbation also shows the robust characteristics of the two proposed models.     

Sample average approximation of expected value constrained stochastic programs

We propose a sample average approximation (SAA) method for stochastic programming problems with expected value constraints. Such problems arise, for example, in portfolio selection with constraints on conditional value-at-risk (CVaR). We provide a convergence analysis and a statistical validation scheme for the proposed method.     

The apolar bilinear form in geometric modeling

Some recent methods of Computer Aided Geometric Design are related to the apolar bilinear form, an inner product on the space of homogeneous multivariate polynomials of a fixed degree, already known in 19th century invariant theory. Using a generalized version of this inner product, we derive in a straightforward way some of the recent results in CAGD, like Marsden's identity, the expression for the de Boor-Fix functionals, and recursion schemes for the computation of B-patches and their derivatives.

     

半无限规划的一阶最优性条件和牛顿型算法

在Fischer-Burmeister非线性互补函数的基础上,得到了半无限规划问题的一个新的一阶必要条件,并将半无限规划问题转化成一个光滑的无约束优化问题,给出了适合该问题的一个Damp-Newton算法,数值例子表明:算法结构简单,数值计算有效.