Abstract
Till now the previous methods for multi-objective optimization adopt the "additive" algorithm for the normalized evaluation indexes, which has the inherent shortcoming of taking the form of "union" in the viewpoint of set theory. In fact, "simultaneous optimization of multiple indexes" should be more appropriate to take the form of "intersection" for the normalized evaluation indexes in the respects of set theory and "joint probability" in probability theory. In this paper, a new concept of favorable probability is proposed to reflect the favorable degree of the candidate material in the selection; All material property indicators are divided into beneficial or unbeneficial types to the material selection; Each material property indicator correlates to a partial favorable probability quantitatively, and the total favorable probability of a candidate material is the product of all partial favorable probabilities in the viewpoints of "intersection" of set theory and "joint probability" in probability theory, which is the sole decisive index in the competitive selection process. Results of the application examples indicate the validity of the new method.
Highlights
INTRODUCTIONThere are more than 40,000 useful metal alloys and non-metal engineering materials in the world [1]
At present, there are more than 40,000 useful metal alloys and non-metal engineering materials in the world [1]
Tab. 2 shows the results of partial favorable probability Pij and the total favorable probabilities Pi assessed for each material property indicators for the four candidate materials
Summary
There are more than 40,000 useful metal alloys and non-metal engineering materials in the world [1]. I.e. benefit - cost analysis, is used to select the optimum design - material combination for the initial screening of materials. This method is lacking of quantitative comparison of other attributes, such as difficulty of manufacturing and processing technique, environment, etc. In order to conduct the scaling process, the denominator is subjectively selected, which affects the value of each decision matrix element and determines the final result of the comparison. Maosheng Zheng, et al.: A New "Intersection" Method for Multi-Objective Optimization in Material Selection negative ideal solution. A new "intersection" method for multi-objective optimization in material selection is developed on basis of set theory and probability theory. The total favorable probability of a candidate material is the decisive index for the material to get victory in the selection process
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