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Introduction/purpose: Cutting is a typical material process. However, an appropriate solution for simultaneous optimization of material machinability and tool life in material cutting processes has not been obtained yet. In this article, probabilistic multi-objective robust design (PMORD) is expounded and the robust design problem in the simultaneous optimization of material machinability and tool life is analyzed by taking the machining of ferrite-bainite dual-phase steel as an example. Methods: According to PMORD, the arithmetic mean and its deviation of various performance and utility indexes of alternative schemes are evaluated as twin independent responses, which respectively contribute a part of the partial preferable probability to the performance indexes. In the evaluation, the arithmetic average of the utility index is taken as the representative of the utility attribute, and the evaluation is made in accordance with the function or preference of the utility index. However, the deviation term is generally used as an unbeneficial type of the index (that is, the smaller the better) to participate in the evaluation. The product of the two parts of partial preferable probability is the actual partial preferable probability of the corresponding performance index. The product of the partial preferable probability of all performance utility indexes gives the total preferable probability of the corresponding scheme, which is the only index for each scheme to participate in the competition in robust design. Results: The optimization result of this example is that the tool life is 1297.3333 s (standard deviation is 2.0817 s) and the surface roughness is 2.22μm (standard deviation is 0.2μm), while the corresponding working conditions are that the heat treatment temperature of the material is 790°C, the cutting speed is 150m/min, the feed speed is 0.15mm/rev, and the cutting depth is 0.2mm. Conclusion: The example of the parameter optimization of cutting of ferrite-bainite dual-phase steel by means of PMORD indicates the rationality of the appropriate solution. [ABSTRACT FROM AUTHOR]

Introduction/purpose: Turning is a typical machining process. However, an appropriate solution for a concurrent optimization of minimizing surface roughness, minimizing cutting forces and vibrations, and maximizing the material removal rate in turning processes has not been found yet. This article formulates the rule of separating an independent attribute from multiple attributes by using the linear correlation coefficient in the spirit of the cluster analysis first. Moreover, the evaluation of the concurrent optimization of steel turning by means of probability - based multi - objective optimization (PMOO) is taken as an example to show the procedure including the separation of an independent attribute from multiple attributes by using PMOO. Methods: PMOO is a promising solution for turning processes. It is necessary to have an independent attribute in the evaluation of PMOO to be analogical as an independent event in the view of the probability theory. The separation of an independent attribute from multiple attributes by using the linear correlation coefficient is conducted in the spirit of the cluster analysis. It further assumes that if the linear correlation coefficient of two attributes in the cluster analysis is higher than 0.8, i.e., in case of very strong correlation, then they could be put into one category, and only one of them could be taken as an independent attribute to join the evaluation of PMOO. Results: The formulation reflects the essence of PMOO and its application in material machining rationally, which opens a new way for solving the relevant problem. The example of the parameter optimization of steel turning by means of PMOO indicates the rationality of the appropriate solution. Conclusion: This innovative study has practical significance of making the utilization of PMOO method reasonable by providing a rational rule of separating independent attributes from multiple attributes of PMOO. [ABSTRACT FROM AUTHOR]

Introduction/purpose: In this paper, a new approach to solving the portfolio investment problem is formulated to handle simultaneous optimization of both maximizing the rate of return and minimizing the variance of the rate of return. Probability - based multi – objective optimization is combined with uniform design for experiments with mixtures to conduct processing. Methods: Preliminarily, probability - based multi – objective optimization is employed to synthesize the bi-objective problem of simultaneous optimization of both maximizing the rate of return and minimizing the variance of the rate of return into a single objective one of the total preferable probability of each alternative scenario. The total preferable probability is the product of all partial preferable probabilities of each performance utility; subsequently, the method of uniform design for experiments with mixtures is used to create a set of effective sampling points for the portfolio investment problem to provide discretization in data processing and simplifying treatment, of which the proportion xi follows the constraint condition of xl + x2 + x3．．．+ xs = 1 with the total number of variables s for xi. Results: The new approach is used to deal with the portfolio Investment problem that is, in essence, simultaneous optimization of both maximizing the rate of return and minimizing the variance of the rate of return, which leads to reasonable consequences. The results are with the quality of rationality from the respect of the probability theory for simultaneous optimization of multiple objectives. [ABSTRACT FROM AUTHOR]

Introduction/purpose: In this paper, probability based multi - objective optimization (PMOO) is employed to objectively study the optimization problems of the drug encapsulation of water-soluble chitosan (WSC) / poly - gama - glutamic acid (γ-PGA) - tanshinone IIA (TA) with a response surface design and glycerosome - triptolide with an orthogonal experimental design. Methods: In PMOO, a concept of preferable probability has been introduced to describe a preference degree of the performance utility. Each beneficial and unbeneficial utility index contributes a partial preferable probability in a linear manner, positively and negatively, respectively and all the performance utility indicators are simultaneously and equally treated. The total preferable probability of a candidate is the product of all partial preferable probabilities, which thus transfers a multi- objective problem into a single-objective one. Results: 1. The optimal encapsulation of WSC /γ-PGA - TA is for WSCof 5.755 mg.ml-1, TA of 1.0275 mg.ml-1, when the ratio of TA to the carrier material is 1: 4.9, and the reaction time is 1.302h. 2. The optimal preparation conditions of glycerosomes - triptolide are a glycerol concentration of 20%, the phospholipid to cholesterol mass ratio of 30:1 and the phospholipid to triptolide mass ratio of 5:1. C 8 onclusion: The results show the applicability of PMOO in the optimization of encapsulation composites with designed tests. [ABSTRACT FROM AUTHOR]

Introduction/purpose: An approximation for assessing a definite integral is continuously an attractive topic owing to its practical needs in scientific and engineering areas. An efficient approach for preliminarily calculating a definite integral with a small number of sampling points was newly developed to get an approximate value for a numerical integral with a complicated integrand. In the present paper, an efficient approach with a small number of sampling points is combined to the novel probability– based multi–objective optimization (PMOO) by means of uniform experimental design so as to simplify the complicated definite integral in the PMOO preliminarily. Methods: The distribution of sampling points within its single peak domain is deterministic and uniform, which follows the rules of the uniform design method and good lattice points; the total preferable probability is the unique and deterministic index in the PMOO. Results: The applications of the efficient approach with finite sampling points in solving typical problems of PMOO indicate its rationality and convenience in the operation. Conclusion: The efficient approach with finite sampling points for assessing a definite integral is successfully combined with PMOO by means of the uniform design method and good lattice points. [ABSTRACT FROM AUTHOR]

Introduction/purpose: An approximate approach to definite integral calculation has been an attractive problem continuously since the creation of integration due to practical needs in scientific and engineering areas. In most practical cases, the integrand is complex, which leads to a difficulty of obtaining an exact value of integration, so an approximate value of the definite integral with certain accuracy is satisfactory for practical applications. In this paper, an efficient approach for calculating a definite integral with a small number of sampling points is proposed based on the uniform design method from the viewpoint of practical application. Methods: The distribution of sampling points in its single peak domain is deterministic and uniform, which follows the rule of the uniform design method and good lattice points. [ABSTRACT FROM AUTHOR]

Introduction/purpose: The newly developed probability-based multi – objective optimization (MOO) has introduced a novel concept of preferable probability to represent a preferability degree of a candidate in optimization in order to overcome the inherent shortcomings of subjective and “additive” factors in the previous MOO methods. In this paper, the new method is extended to include robust optimization for material engineering. Furthermore, energy consumption in a melting process with orthogonal array design and the robust optimization of four different process schemes in machining an electric globe valve body are taken as examples. Methods: The arithmetic mean value of each performance utility indicator of the candidate contributes to one part of the partial preferable probability, while the deviation of each performance utility indicator from its arithmetic mean value of the candidate contributes to the other part of the partial preferable probability quantitatively. Furthermore, following the procedures of the newly developed probability-based multi–objective optimization (PMOO), the total preferable probability of a candidate is obtained, which thus transfers a multi–objective optimization problem into a single– objective optimization problem. Results: The optimal control factors of lower electric energy consumption with robustness are bundled steel, loose steel, and uncleaned steel of 12.5%, 50% and 37.5% by weight, respectively, in this steel melting process. This case is closely followed by the scenario of 50 wt% bundled steel, 50 wt% loose steel, and 0 wt% uncleaned steel. The robust optimization of four different process schemes for machining an electric globe valve body is scheme No. 1. Conclusion: The extension of probability-based multi-objective optimization while considering robustness is successful, which can be easily used to deal with the optimal problem with dispersion of data to get objectively an optimal result with robustness in material engineering. The extension of probability-based multi-objective optimization while considering robustness will be beneficial to relevant research and process optimization. [ABSTRACT FROM AUTHOR]

Introduction/purpose: Althought many methods have been proposed to deal with the problem of material selection, there are inherent defects of additive algorithms and subjective factors in such methods. Recently, a probability-based multi–objective optimization was developed to solve the inherent shortcomings of the previous methods, which introduces a novel concept of preferable probability to reflect the preference degree of the candidate in the optimization. In this paper, the new method is utilized to conduct an optimal scheme of the switching material of the RF-MEMS shunt capacitive switch, the sintering parameters of natural hydroxyapatite and the optimal design of the connecting claw jig. Methods: All performance utility indicators of candidate materials are divided into two groups, i.e., beneficial or unbeneficial types for the selection process; each performance utility indicator contributes quantitatively to a partial preferable probability and the product of all partial preferable probabilities makes the total preferable probability of a candidate, which transfers a multi–objective optimization problem into a single–objective optimization one and represents a uniquely decisive index in the competitive selection process. Results: Cu is the appropriate material in the material selection for RF - MEMS shunt capacitive switches; the optimal sintering parameters of natural hydroxyapatite are at 1100°C and 0 compaction pressure; and the optimal scheme is scheme No 1 for the optimal design of a connecting claw jig. Conclusion: The probability-based multi-objective optimization can be easily used to deal with an optimal problem objectively in material engineering. [ABSTRACT FROM AUTHOR]