Intelligent interactive multiobjective optimization method and its application to reliability optimization

In most practical situations involving reliability optimization, there are several mutually conflicting goals such as maximizing the system reliability and minimizing the cost, weight and volume. This paper develops an effective multiobjective optimization method, the Intelligent Interactive Multiobjective Optimization Method (IIMOM). In IIMOM, the general concept of the model parameter vector is proposed. From a practical point of view, a designer's preference structure model is built using Artificial Neural Networks (ANNs) with the model parameter vector as the input and the preference information articulated by the designer over representative samples from the Pareto frontier as the desired output. Then with the ANN model of the designer's preference structure as the objective, an optimization problem is solved to search for improved solutions and guide the interactive optimization process intelligently. IIMOM is applied to the reliability optimization problem of a multi-stage mixed system with five different value functions simulating the designer in the solution evaluation process. The results illustrate that IIMOM is effective in capturing different kinds of preference structures of the designer, and it provides a complete and effective solution for medium- and small-scale multiobjective optimization problems.     

An optimization method for multiplexer locations

Summary In order to reduce the costs of using (or leasing) a data telecommunication network, a subscriber can lease multiplexers from the network carrier. These multiplexers are placed between the subscriber terminals and the corresponding exchange, several multiplexers being able to be connected in series. An optimization method for the location of such multiplexers is presented here.

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Zusammenfassung Um die Kosten eines gemieteten Datennetzes zu senken, kann ein Teilnehmer Multiplexer vom Netzeigner mieten. Diese liegen zwischen den Terminals und der zugehörigen Vermittlungsstelle und können in Serie geschaltet sein. Ein Verfahren zur Optimierung der Standorte solcher Multiplexer wird hier dargestellt.

     

An interactive method for multiple objective linear fractional programming problems

Multiple objective linear fractional programming (MOLFP) is an important field of research. Using some branch and bound techniques, we have developed a new interactive method for MOLFP that drastically reduces the computational effort needed, while providing guidance for the decision maker in the choice of his/her preferred solutions. The basic idea of the computation phase of the algorithm is to optimize one of the fractional objective functions while constraining the others. Several linear programming problems, organized in a tree structure, are generated as the search evolves. The whole idea is simple and it results in a fast and very intuitive approach to exploring the non-dominated set of solutions in MOLFP, and eventually to finding the preferred solution.This work was supported by the Fundação para a Ciência e Tecnologia and FEDER, project POCTI/32405/GES/2000.     

Global formulation for interactive multiobjective optimization

Interactive methods are useful and realistic multiobjective optimization techniques and, thus, many such methods exist. However, they have two important drawbacks when using them in real applications. Firstly, the question of which method should be chosen is not trivial. Secondly, there are rather few practical implementations of the methods. We introduce a general formulation that can accommodate several interactive methods. This provides a comfortable implementation framework for a general interactive system. Besides, this implementation allows the decision maker to choose how to give preference information to the system, and enables changing it anytime during the solution process. This change-of-method option provides a very flexible framework for the decision maker.     

An interactive on-line multi-objective optimization approach with application to metal cutting turning operation

An on-line supervisory computer control model for optimization of multiple objective programming problems is developed and applied to machining problems. Specifically, the turning operation is formulated and solved by the approach. For the first time, the characteristics of on-line multi-objective problems are described and an approach for solving such problems is developed. The proposed system maintains feasibility of operations and optimizes objectives based on the machine performance and on-line interactions with the decision-maker (DM). The model is hierarchical and consists of two levets: level 1 is designed to protect automated machinery and the workpiece by monitoring the process outputs; and level 2 is designed to optimize the on-line multi-objective problem. The tasks of both levels are accomplished by on-line monitoring and control of changes in process outputs via real-time information provided by sensors. The recommended parameters, obtainable from the multi-objective optimization approach, are used to create and update a database for machinability problems for future use. An example is discussed.     

使用支持向量机的微处理器验证向量优化方法

为了解决微处理器仿真验证中随机验证向量质量不高的问题,提出了一种基于支持向量机(SVM)的验证向量优化方法。该方法将已仿真运行的验证向量及其覆盖率信息作为支持向量机的样本进行有监督学习,得到验证向量关于功能覆盖点的分类器。利用训练后的分类器对于新产生的验证向量进行预测,并丢弃预测中不能提高覆盖率的冗余验证向量。实验数据表明该方法能准确地过滤冗余验证向量,提高仿真运行的验证向量的质量。和完全随机的验证向量生成方法相比,该方法达到相同的功能覆盖率仅需要前者1/3的验证向量。     

An updated interactive boundary layer method for high Reynolds number flows

The quasi‐simultaneous interactive boundary layer (IBL) method is improved with the iterative correction of an inviscid operator. The updated interactive boundary layer method (UIBL) presented in this work, uses the Hess–Smith panel method (HSPM) as an inviscid operator to update the outer flow calculation and the inviscid velocity in the interaction law (IL). The discretization of the Hilbert integral (HI) from the original method is modified to reduce the error introduced by the calculation of the HI in a restricted domain. The method is tested on a flat plate with a small indentation for two‐dimensional, steady, incompressible and laminar flow. The UIBL method is capable to predict the flow separation and reattachment with good accuracy. The accuracy of the results is competitive with the numerical solution of the Navier–Stokes equations (NSE). Copyright © 2005 John Wiley & Sons, Ltd.     

An optimization method for quantitative impedance tomography

A near-field ultrasonic tomography method providing high resolution imaging for soft tissue in the reflection mode is reported. When the Born approximation is valid, the main limitation of this method is that it requires an incident pulse with infinite bandwidth, whereas the incident pulses used in practice have a limited bandwidth, which makes quantitative reconstruction impossible. The reconstructed image is qualitative in the sense that it is a band-pass filtered reconstruction of the impedance distribution. An optimization method based on the use of the geometrical information provided by the tomographic reconstruction is developed to obtain the quantitative information required. The object was approximated locally by an equivalent canonical body, on the basis of the previous global estimation. The inversion procedure is then carried out using the minimization of a cost function, which is the average over frequency of the difference between the measured field scattered by the object and the estimated field scattered by the equivalent canonical body. Assuming the object to be homogeneous by regions, the last step consists of assigning the estimated local impedance value to the region of interest. When the geometry of the real body is almost canonical, the optimization method yields accurate impedance assessments.     

A method for simulation based optimization using radial basis functions

We propose an algorithm for the global optimization of expensive and noisy black box functions using a surrogate model based on radial basis functions (RBFs). A method for RBF-based approximation is introduced in order to handle noise. New points are selected to minimize the total model uncertainty weighted against the surrogate function value. The algorithm is extended to multiple objective functions by instead weighting against the distance to the surrogate Pareto front; it therefore constitutes the first algorithm for expensive, noisy and multiobjective problems in the literature. Numerical results on analytical test functions show promise in comparison to other (commercial) algorithms, as well as results from a simulation based optimization problem.     

Pareto navigator for interactive nonlinear multiobjective optimization

We describe a new interactive learning-oriented method called Pareto navigator for nonlinear multiobjective optimization. In the method, first a polyhedral approximation of the Pareto optimal set is formed in the objective function space using a relatively small set of Pareto optimal solutions representing the Pareto optimal set. Then the decision maker can navigate around the polyhedral approximation and direct the search for promising regions where the most preferred solution could be located. In this way, the decision maker can learn about the interdependencies between the conflicting objectives and possibly adjust one’s preferences. Once an interesting region has been identified, the polyhedral approximation can be made more accurate in that region or the decision maker can ask for the closest counterpart in the actual Pareto optimal set. If desired, (s)he can continue with another interactive method from the solution obtained. Pareto navigator can be seen as a nonlinear extension of the linear Pareto race method. After the representative set of Pareto optimal solutions has been generated, Pareto navigator is computationally efficient because the computations are performed in the polyhedral approximation and for that reason function evaluations of the actual objective functions are not needed. Thus, the method is well suited especially for problems with computationally costly functions. Furthermore, thanks to the visualization technique used, the method is applicable also for problems with three or more objective functions, and in fact it is best suited for such problems. After introducing the method in more detail, we illustrate it and the underlying ideas with an example.     

Avalanche forecast with the method of nearest neighbours: An interactive approach

Avalanche forecasting by statistical methods is seldom practiced, because the forecaster does not know how to apply the results. The method of nearest neighbours is introduced to visualize these results, e.g. ten days most similar to a given situation are selected from a period of 20 years. These ten days serve as a basis for decisions, as well as enabling a control of the accuracy of past avalanche records. Some examples are given. The results of three methods (Obled and Good, 1980) are compared and examples of the computer outputs given. A suggestion is made for improving the model by evaluating an a posteriori probability.     

Parallelism in interactive operations in finite-element simulation

The parallelizing of interactive operations that are part of the finite-element simulation of electromagnetic fields is examined. The total solution time in finite-element analysis is the time assigned to (1) preprocessing, (2) assembling and solving the matrix equation, and (3) postprocessing the solution. In the analysis the tasks of pre- and postprocessing are interactive, with the user sitting at a terminal and specifying various parameters. Two computer routines are identified as the most frequently used in an interactive setting: one identifies a triangle pointed out by a user, and the other identifies a node pointed out by a user. Procedures for parallelizing them are given. A way of parallelizing the plotting of equipotentials and drawing the device, which are frequently required in interactive use, is also presented. It is shown that this method may have more to offer in reducing the nuisance of waiting for certain computer responses compared with the more commonly adopted approach of parallelizing the solver section of a finite-element program     

An adaptive response surface method for crashworthiness optimization

Response surface-based design optimization has been commonly used for optimizing large-scale design problems in the automotive industry. However, most response surface models are built by a limited number of design points without considering data uncertainty. In addition, the selection of a response surface in the literature is often arbitrary. This article uses a Bayesian metric to systematically select the best available response surface among several candidates in a library while considering data uncertainty. An adaptive, efficient response surface strategy, which minimizes the number of computationally intensive simulations, was developed for design optimization of large-scale complex problems. This methodology was demonstrated by a crashworthiness optimization example.     

Trade-off analysis approach for interactive nonlinear multiobjective optimization

When solving multiobjective optimization problems, there is typically a decision maker (DM) who is responsible for determining the most preferred Pareto optimal solution based on his preferences. To gain confidence that the decisions to be made are the right ones for the DM, it is important to understand the trade-offs related to different Pareto optimal solutions. We first propose a trade-off analysis approach that can be connected to various multiobjective optimization methods utilizing a certain type of scalarization to produce Pareto optimal solutions. With this approach, the DM can conveniently learn about local trade-offs between the conflicting objectives and judge whether they are acceptable. The approach is based on an idea where the DM is able to make small changes in the components of a selected Pareto optimal objective vector. The resulting vector is treated as a reference point which is then projected to the tangent hyperplane of the Pareto optimal set located at the Pareto optimal solution selected. The obtained approximate Pareto optimal solutions can be used to study trade-off information. The approach is especially useful when trade-off analysis must be carried out without increasing computation workload. We demonstrate the usage of the approach through an academic example problem.     

Applying the approximation method PAINT and the interactive method NIMBUS to the multiobjective optimization of operating a wastewater treatment plant

Using an interactive multiobjective optimization method called NIMBUS and an approximation method called PAINT, preferable solutions to a five-objective problem of operating a wastewater treatment plant are found. The decision maker giving preference information is an expert in wastewater treatment plant design at the engineering company Pöyry Finland Ltd. The wastewater treatment problem is computationally expensive and requires running a simulator to evaluate the values of the objective functions. This often leads to problems with interactive methods as the decision maker may get frustrated while waiting for new solutions to be computed. Thus, a newly developed PAINT method is used to speed up the iterations of the NIMBUS method. The PAINT method interpolates between a given set of Pareto optimal outcomes and constructs a computationally inexpensive mixed integer linear surrogate problem for the original wastewater treatment problem. With the mixed integer surrogate problem, the time required from the decision maker is comparatively short. In addition, a new IND-NIMBUS^® PAINT module is developed to allow the smooth interoperability of the NIMBUS method and the PAINT method.     

The Design Space Root Finding method for efficient risk optimization by simulation

Reliability-Based Design Optimization (RBDO) is computationally expensive due to the nested optimization and reliability loops. Several shortcuts have been proposed in the literature to solve RBDO problems. However, these shortcuts only apply when failure probability is a design constraint. When failure probabilities are incorporated in the objective function, such as in total life-cycle cost or risk optimization, no shortcuts were available to this date, to the best of the authors knowledge. In this paper, a novel method is proposed for the solution of risk optimization problems. Risk optimization allows one to address the apparently conflicting goals of safety and economy in structural design. In the conventional solution of risk optimization by Monte Carlo simulation, information concerning limit state function behavior over the design space is usually disregarded. The method proposed herein consists in finding the roots of the limit state function in the design space, for all Monte Carlo samples of random variables. The proposed method is compared to the usual method in application to one and n-dimensional optimization problems, considering various degrees of limit state and cost function nonlinearities. Results show that the proposed method is almost twenty times more efficient than the usual method, when applied to one-dimensional problems. Efficiency is reduced for higher dimensional problems, but the proposed method is still at least two times more efficient than the usual method for twenty design variables. As the efficiency of the proposed method for higher-dimensional problems is directly related to derivative evaluations, further investigation is necessary to improve its efficiency in application to multi-dimensional problems.     

An adaptive direct multisearch method for black-box multi-objective optimization

Optimization and Engineering - At present, black-box and simulation-based optimization problems with multiple objective functions are becoming increasingly common in the engineering context. In...     

盾构机动态交互仿真系统的研究与实现

盾构机是用于开挖隧道等地下施工的专用工程机械,有着广阔的应用前景。但因掘进装备等的高度复杂性,以及地质条件、工况的不确定性等导致的安全问题,对盾构机的学习和研究带来一定难度。鉴于此,利用VRML、Cult3D、HTML等开发了一个基于网络的交互装配、运动仿真和虚拟漫游系统,具有导航漫游、交互操作虚拟对象、信息查询等功能,形象直观地展示了盾构机的构造和原理,为盾构机的学习和研究提供了一个很好的平台。     

An optimality criterion method for dynamic optimization of structures

This paper presents an optimality criterion method for the determination of the least weight design of a structural system which satisfies a specific frequency requirement plus upper and lower bounds on the design variables. The design algorithm is an iterative solution of the Kuhn–Tucker optimality criterion based on choosing a single value of the Lagrange multiplier which minimizes the sum of the squares of residuals. The method has been applied to a variety of structures. Results assert that the method is capable of locating the optimal design in a small number of redesign cycles. The method avoids the scaling of design variables. It can treat non-structural masses and is applicable to. structural elements with a wide variety of size-stiffness. The procedure has been completely automated in a computer program on an IBM-PC microcomputer.     

Reliability-based design optimization using a generalized subset simulation method and posterior approximation

The evaluation of the probabilistic constraints in reliability-based design optimization (RBDO) problems has always been significant and challenging work, which strongly affects the performance of RBDO methods. This article deals with RBDO problems using a recently developed generalized subset simulation (GSS) method and a posterior approximation approach. The posterior approximation approach is used to transform all the probabilistic constraints into ordinary constraints as in deterministic optimization. The assessment of multiple failure probabilities required by the posterior approximation approach is achieved by GSS in a single run at all supporting points, which are selected by a proper experimental design scheme combining Sobol’ sequences and Bucher’s design. Sequentially, the transformed deterministic design optimization problem can be solved by optimization algorithms, for example, the sequential quadratic programming method. Three optimization problems are used to demonstrate the efficiency and accuracy of the proposed method.