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.     

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。     

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.     

Fundamental error analysis and geometric interpretation for block truncation coding techniques

Various variants and hybrid approaches evolved from the origin of Delp and Mitchell's block truncation coding (BTC) or moment preserving quantizer (MPQ) have formed a niche as an effective and simple image compression methodology with attractive coding performance achieved at moderate bitrates. As BTC is still lacking a fundamental error analysis, in this paper we present some fundamental insights regarding one-bit (or two-level) BTC's truncation error by providing mathematical analysis as well as novel geometric interpretation. We further show that the mean-square error (MSE) of Lema and Mitchell's absolute moment block truncation coding (AMBTC) is always bounded below (i.e., less than or equal to) that of BTC. Therefore, with additional advantages in computation and implementation, AMBTC is always superior. Furthermore, we developed a new adaptive equal sign position optimization (ESPO) algorithm for optimum pixel classification. Our quantization error analysis shows that incorporating the ESPO algorithm into conventional AMBTC or BTC achieves minimum MSE in either case.     

Extending a class of continuous estimation of distribution algorithms to dynamic problems

In this paper, a class of continuous Estimation of Distribution Algorithms (EDAs) based on Gaussian models is analyzed to investigate their potential for solving dynamic optimization problems where the global optima may change dramatically during time. Experimental results on a number of dynamic problems show that the proposed strategy for dynamic optimization can significantly improve the performance of the original EDAs and the optimal solutions can be consistently located.     

Computer-assisted multifactor optimization of selectivity in gas chromatography

Summary A computer-assisted method is presented for the simultaneous multifactor optimization (stationary phase loading, column temperature and carrier gas flow rate) of the analytical conditions for the optimum separation of multicomponent samples in gas chromatography. The optimization of the separation over the experimental region is based on a special polynomial from twelve preliminary experiments using the resolution as the selection criterion. Computer scanning technique was used for optimum selection in three dimensions. Excellent agreement was obtained between the predicted data and the experimental results.     

Stochastic approximation algorithm for minimax problems

A stochastic approximation algorithm for minimax optimization problems is analyzed. At each iterate, it performs one random experiment, based on which it computes a direction vector. It is shown that, under suitable conditions, it a.s. converges to the set of points satisfying necessary optimality conditions. The algorithm and its analysis bring together ideas from stochastic approximation and nondifferentiable optimization.     

Concurrent stochastic methods for global optimization

The global optimization problem, finding the lowest minimizer of a nonlinear function of several variables that has multiple local minimizers, appears well suited to concurrent computation. This paper presents a new parallel algorithm for the global optimization problem. The algorithm is a stochastic method related to the multi-level single-linkage methods of Rinnooy Kan and Timmer for sequential computers. Concurrency is achieved by partitioning the work of each of the three main parts of the algorithm, sampling, local minimization start point selection, and multiple local minimizations, among the processors. This parallelism is of a coarse grain type and is especially well suited to a local memory multiprocessing environment. The paper presents test results of a distributed implementation of this algorithm on a local area network of computer workstations. It also summarizes the theoretical properties of the algorithm.Research supported by AFOSR grant AFOSR-85-0251, ARO contract DAAG 29-84-K-0140, NSF grant DCR-8403483, and NSF cooperative agreement DCR-8420944.