Simulation based optimization of stochastic systems with integer design variables by sequential multipoint linear approximation

Optimization problems are considered for which objective function and constraints are defined as expected values of stochastic functions that can only be evaluated at integer design variable levels via a computationally expensive computer simulation. Design sensitivities are assumed not to be available. An optimization approach is proposed based on a sequence of linear approximate optimization subproblems. Within each search subregion a linear approximate optimization subproblem is built using response surface model building. To this end, N simulation experiments are carried out in the search subregion according to a D-optimal experimental design. The linear approximate optimization problem is solved by integer linear programming using corrected constraint bounds to account for any uncertainty due to the stochasticity. Each approximate optimum is evaluated on the basis of M simulation replications with respect to objective function change and feasibility of the design. The performance of the optimization approach and the influence of parameters N and M is illustrated via two analytical test problems. A third example shows the application to a production flow line simulation model. Received April 28, 2000     

Performance measurement and lumped parameter modeling of single server flow lines subject to blocking: An effective process time approach

The present paper extends the so-called effective process time (EPT) approach to single server flow lines with finite buffers and blocking. The power of the EPT-approach is that it quantifies variability in workstation process times without the need to identify each of the contributing disturbances, and that it directly provides an algorithm for the actual computation of EPTs. It is shown that EPT-realizations can be simply obtained from arrival and departure times of lots, by using sample path equations. The measured EPTs can be used for bottleneck analysis and for lumped parameter modeling. Simulation experiments show that for lumped parameter modeling of flow lines with finite buffers, in addition to the mean and variance, offset is also a relevant parameter of the process time distribution. A case from the automotive industry illustrates the approach.     

Influence of some organic compounds on the corrosion mechanism of carbon steel (XC 38) in 3% NaCl I. dodecyl sodium phosphonate (C10H21PO3Na2) and n-undecylimidazole (C14H26N2) surfactants

The electrochemical behaviour of carbon steel (XC38) in stirred and aerated 3% NaCl solution has been investigated using a rotating disc electrode. Steady-state and transient measurements have been carried out. The influence of surfactant additives on the corrosion process is reported.     

Chemical and electrochemical inhibition studies of corrosion and hydrogen surface embrittlement. I. Fe0.78B0.13Si0.09 amorphous alloy in molar HCl

Diorthoaminophenoldisulfane (DOAPD) was synthesized for use as a corrosion inhibitor and in order to test its effect on the hydrogen surface embrittlement of Fe_0.78B_0.13Si_0.09 alloy. Results of electrochemical and gravimetric measurements were consistent and confirmed the beneficial role of this inhibitor. The amorphous state of the alloy was confirmed by X-ray measurements and differential thermal analysis. The maximum inhibition of corrosion was attained in the presence of 10^–4 M DOAPD. This inhibitor concentration also gave rise to a diminution of metal hydrogenation. A mechanism explaining the mixed role of the disulfane was confirmed.     

An augmented Lagrangian decomposition method for quasi-separable problems in MDO

Several decomposition methods have been proposed for the distributed optimal design of quasi-separable problems encountered in Multidisciplinary Design Optimization (MDO). Some of these methods are known to have numerical convergence difficulties that can be explained theoretically. We propose a new decomposition algorithm for quasi-separable MDO problems. In particular, we propose a decomposed problem formulation based on the augmented Lagrangian penalty function and the block coordinate descent algorithm. The proposed solution algorithm consists of inner and outer loops. In the outer loop, the augmented Lagrangian penalty parameters are updated. In the inner loop, our method alternates between solving an optimization master problem and solving disciplinary optimization subproblems. The coordinating master problem can be solved analytically; the disciplinary subproblems can be solved using commonly available gradient-based optimization algorithms. The augmented Lagrangian decomposition method is derived such that existing proofs can be used to show convergence of the decomposition algorithm to Karush–Kuhn–Tucker points of the original problem under mild assumptions. We investigate the numerical performance of the proposed method on two example problems.     

Photoelectrochemical study of the layered compound In23Pse3

The layered compound $\text{In}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{PSe}{}_3$ is studied by photoelectrochemical technique. Two modes of transition, indirect ～ 1.55 eV, and direct ～ 1.80 eV are evidenced. An estimation of the hole diffusion length is given through the use of Gärtner model ($\text{L}\text{? 4 μ}\text{m}$). The flat band positions of the junction $\text{In}{}_{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{PSe}{}_3\text{-}\text{electrolyte}$ at different pH values are determined in an electrochemical scale.     

Chemical and electrochemical inhibition studies of corrosion and hydrogen surface embrittlement. II. Fe0.81B0.13Si0.04C0.02 amorphous alloy in molar HCl

The effect of diorthoaminophenoldisulfane (DOAPD) on the corrosion and hydrogen embrittlement of Fe_0.81B_0.13Si_0.04C_0.02 amorphous alloy has been studied. The amorphous state of the alloy was confirmed by X-ray analysis. Inhibitor efficiency in 1m HCl was estimated from electrochemical and gravimetric measurements. Reproducible results obtained from both techniques are consistent. DOAPD at 10^–4 m gave a maximum corrosion inhibition of the alloy in 1m HCl and evidence for a cathodic inhibition mechanism is presented. Hydrogenation of the alloy was reduced by the addition of 10^–4 m DOAPD.     

Crash worthiness design optimization using multipoint sequential linear programming

A design optimization tool has been developed for the crash victim simulation software MADYMO. The crash worthiness optimization problem is characterized by a noisy behaviour of objective function and constraints. Additionally, objective function and constraint values follow from a computationally expensive numerical analysis. Sequential approximate optimization is used to deal with both the noisy functional behaviour and the high computational costs. By means of multipoint approximations, a sequence of linear programming problems is generated that can be easily solved. The optimization approach is illustrated for an analytical test problem and an industrial crash worthiness design problem.     

Multi-modality in augmented Lagrangian coordination for distributed optimal design

This paper presents an empirical study of the convergence characteristics of augmented Lagrangian coordination (ALC) for solving multi-modal optimization problems in a distributed fashion. A number of test problems that do not satisfy all assumptions of the convergence proof for ALC are selected to demonstrate the convergence characteristics of ALC algorithms. When only a local search is employed at the subproblems, local solutions to the original problem are often attained. When a global search is performed at subproblems, global solutions to the original, non-decomposed problem are found for many of the examples. Although these findings are promising, ALC with a global subproblem search may yield only local solutions in the case of non-convex coupling functions or disconnected feasible domains. Results indicate that for these examples both the starting point and the sequence in which subproblems are solved determines which solution is obtained. We illustrate that the main cause for this behavior lies in the alternating minimization inner loop, which is inherently of a local nature.     

A novel surrogate-based approach for optimal design of electromagnetic-based circuits

A new geometric design centring approach for optimal design of central processing unit-intensive electromagnetic (EM)-based circuits is introduced. The approach uses norms related to the probability distribution of the circuit parameters to find distances from a point to the feasible region boundaries by solving nonlinear optimization problems. Based on these normed distances, the design centring problem is formulated as a max–min optimization problem. A convergent iterative boundary search technique is exploited to find the normed distances. To alleviate the computation cost associated with the EM-based circuits design cycle, space-mapping (SM) surrogates are used to create a sequence of iteratively updated feasible region approximations. In each SM feasible region approximation, the centring process using normed distances is implemented, leading to a better centre point. The process is repeated until a final design centre is attained. Practical examples are given to show the effectiveness of the new design centring method for EM-based circuits.