Probability-Based Multi-objective Optimization for Material Selection by Maosheng Zheng & Haipeng Teng & Jie Yu & Ying Cui & Yi Wang

Author:Maosheng Zheng & Haipeng Teng & Jie Yu & Ying Cui & Yi Wang
Language: eng
Format: epub
ISBN: 9789811933516
Publisher: Springer Nature Singapore

6.1 Introduction

Usually in many industrial processes and experiments, quality improvement or optimization is conducted by using experimental design, such as orthogonal experimental design, response surface design and uniform experimental design. Optimization for one individual objective separately could not give the appropriate consequence of the optimization for several objectives simultaneously in general, and the simultaneous optimization of the multi-objectives doesn’t equal to any form of “superposition” of individual objective optimization.

Up to now, though several multi-objective optimization approaches have been proposed [1–5], the general mathematical treatment in these approaches is “additive” algorithm for the normalized evaluation indexes, and some methods even include personal factors. In the viewpoint of probability theory, “additive” algorithm is not consistent with the essence of “simultaneous optimization of multiple indexes” [6]. In fact, if different normalization algorithms are applied, considerable differences in the results of these methods could be produced [7]. So, above discussion indicates that approach relying on any type of “additive” algorithm is at most semi-quantitative methods in some sense.

As to optimization of multi-objective orthogonal experimental test design, Taguchi developed analysis methods, both “analysis of signal to noise ratio (SNR)” and “grey relational analysis (GRA)” are combined to solve the optimal problem [8]. The scaling factors, the insufficiency of SNR for assessing beneficial and unbeneficial indicators, and target best type indicators as well, the “additive” algorithm and the personal factor in grey relational coefficient, etc., are all included in the treatment, which leads to the inevitable inherent shortcomings of this approach. Besides, the “comprehensive balance method” and “comprehensive scoring method” are also used to conduct the assessment of optimization of multi-objective orthogonal experimental design [8–10], which are not fully quantitative, but empirical ones instead.

Response surface methodology (RSM) is an integration of both statistical and mathematical technique, which is a useful optimal method. It is widely used in both formulation of new products and design improvement of existing product [11]. Pareto algorithm is usually used in response surface design for optimization of multi-objective problem, but the inherent feature of “additive” algorithm remains [11].

Derringer et al. and Jorge et al. once proposed desirability function to transfer each response variable into a desirability value [1, 2], but this kind of approach is not coincident with the original idea of simultaneous optimization of multi-objective at all in the viewpoint of probability theory.

Uniform experimental design methodology (UEDM) was developed by Fang and Wang, which is a novel experimental design method to meet the demand of very few amount of experiment number for valuable experiment, such as in missile design [12]. It has now been utilized in many fields with fruitful consequences and huge benefits. Similar to the optimization of multi-objective orthogonal test design, some treatments with “additive” algorithm and the personal factors are used to deal with its optimization of multiple objectives [13].

In the viewpoint of probability theory, “simultaneous optimization of multiple indexes” should adopt the form of “multiplication” algorithm for the partial probability of each independent event to get the joint probability of the “overall (integrated) event” appropriately [6]. Thus,

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