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    A Hopfield neural network approach to the dual response problem
    (JOHN WILEY & SONS LTD, 2005) Koksoy, O; Yalcinoz, T
    The application of neural networks to optimization problems has been an active research area since the early 1980s. Unconstrained optimization, constrained optimization and combinatorial optimization problems have been solved using neural networks. This study presents a new approach using Hopfield neural networks (HNNs) for solving the dual response system (DRS) problems. The major aim of the proposed method is to produce a string of solutions, rather than a 'one-shot' optimum solution, to make the trade-offs available between the mean and standard deviation responses. This gives more flexibility to the decision-maker in exploring alternative solutions. The proposed method has been tested on two examples. The HNN results are very close to those obtained by using the NIMBUS (Nondifferentiable Interactive Multiobjective Bundle-based Optimization System) algorithm. Choosing an appropriate solution method for a certain multi-objective optimization problem is not easy, as has been made abundantly clear. Unlike the NIMBUS method, the HNN approach does not set any specific assumptions on the behaviour or the preference structure of the decision maker. As a result, the proposed method will still work and generate alternative solutions whether or not the decision maker has enough time and capabilities for co-operation. Copyright (c) 2005 John Wiley & Sons, Ltd.
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    Dual response optimization: The desirability approach
    (UNIV CINCINNATI INDUSTRIAL ENGINEERING, 2005) Koksoy, O
    Designing high-quality products and processes at low cost is an economic and technological challenge to the engineer. Recent advances in quality technology have resulted from considering the variation of a quality characteristic as well as its mean value. In the 1990s, much attention was given to the optimization of dual response systems as an important response surface methodology tool for quality improvement. The most recent articles have all relied on nonlinear programming techniques to obtain the actual solution. While these techniques certainly work, it is also possible to solve the dual response problems using the more familiar technique of multiple response optimization. We demonstrate this using the desirability function approach. The proposed approach allows to specify minimum and maximum acceptable values for each response in addition to specifying certain parameters to be chosen so that this gives more flexibility to the decision maker in exploring alternative solutions and the trade-offs between the mean and standard deviation responses. A numerical example illustrates the methodology. Comparisons with other existing methods were also discussed.
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    Joint optimization of mean and standard deviation using response surface methods
    (AMER SOC QUALITY CONTROL-ASQC, 2003) Koksoy, O
    Taguchi's robust parameter design calls for simultaneous optimization of the mean and standard deviation responses. The dual response optimization procedures have been adapted to achieve this goal by taking into account both the mean and standard deviation response functions. The popular formulations of the dual response problem typically impose a restriction on the value of the secondary response (i.e., keeping the standard deviation below a specified value) and optimize the primary response function (i.e., maximize or minimize the mean). Restrictions on the secondary response, however, may rule out better conditions, since an acceptable value for the secondary response is usually unknown. In fact, process conditons that result in a smaller standard deviation are often preferable. A more flexible formulation of the problem can be achieved by considering the secondary response as another primary response. The proposed method will generate more alternative solutions, called Pareto optimal solutions. This gives more flexibility to the decision-maker in exploring alternative solutions. It is also insightful to examine graphically how the controllable variables simultaneously impact the mean and standard deviation. The procedure is illustrated with three examples, using both the NIMBUS software for nonlinear multiobjective programming and the Solver in the Excel spreadsheet.
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    Mean square error criteria to multiresponse process optimization by a new genetic algorithm
    (ELSEVIER SCIENCE INC, 2006) Koksoy, O; Yalcinoz, T
    The recent push for quality in industry has brought response surface methodology to the attention of many users. Most of the published literature on robust design methodology is basically concerned with optimization of a single response or quality characteristic which is often most critical to consumers. For most products, however, quality is multidimensional, so it is common to observe multiple responses in an experimental situation. In this paper, we present a methodology for analyzing several quality characteristics simultaneously using the mean square error (MSE) criterion when data are collected from a combined array. Problems with highly nonlinear, or multimodal, objective functions are extremely difficult to solve and are further complicated by the presence of multiple objectives. An alternative approach is to use a heuristic search procedure such as a genetic algorithm (GA). The GA generates a string of solutions using genetics-like operators such as selection, crossover and mutation. In this paper, a genetic algorithm based on arithmetic crossover for the multiresponse problem is proposed. The string of solutions highlight the trade-offs that one needs to consider in order to obtain a compromise solution. A numerical example has been presented to illustrate the performance and the applicability of the proposed method. (c) 2005 Elsevier Inc. All rights reserved.
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    Multiresponse robust design: Mean square error (MSE) criterion
    (ELSEVIER SCIENCE INC, 2006) Koksoy, O
    Most of the published literature on robust design methodology is basically concerned with optimization of a single response or quality characteristic which is often most critical to consumers. However, manufactured products are typically characterized by numerous quality characteristics. In this paper we present a general framework for the multivariate problem when data are collected from a combined array. Within the framework, a mean square error (MSE) criterion is utilized and a non-linear multiobjective programming problem based on the individual MSE functions of each response is proposed for quality improvement. We adapted a suitable non-linear optimization algorithm to solve the proposed formulation. The optimization method used in this paper generates a string of solutions, called Pareto optimal solutions, rather than a "one shot" optimum solution to make selections and evaluate the trade-offs. The paper also presents an example and comparative results in order to demonstrate the potentials of the proposed approach. (c) 2005 Elsevier Inc. All rights reserved.