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Transportation process or activity can be considered as a multi-objective problem reasonably. However, it is difficult to obtain an absolute shortest path with optimizing the multiple objectives at the same time by means of Pareto approach. In this paper, a novel method for solving multi-objective shortest path problem in respect of probability theory is developed, which aims to get the rational solution of multi-objective shortest path problem. Analogically, each objective of the shortest path problem is taken as an individual event, thus the concurrent optimization of many objectives equals to the joint event of simultaneous occurrence of the multiple events, and therefore the simultaneous optimization of multiple objectives can be solved on basis of probability theory rationally. The partial favorable probability of each objective of every scheme (routine) is evaluated according to the actual preference degree of the utility indicator of the objective. Moreover, the product of all partial favorable probabilities of the utility of objective of each scheme (routine) casts the total favorable probability of the corresponding scheme (routine), which results in the decisively unique indicator of the scheme (routine) in the multi-objective shortest path problem in the point of view of system theory. Thus, the optimum solution of the multi-objective shortest path problem is the scheme (routine) with highest total favorable probability. Finally, an application example is given to illuminate the approach. [ABSTRACT FROM AUTHOR]

In this paper, an approach to deal with the multi-objective programming problem is regulated by means of probability-based multi-objective optimization, discrete uniform experimental design, and sequential algorithm for optimization. The probability-based method for multi-objective optimization is used to conduct conversion of the multi-objective optimization problem into a single-objective optimization one in the viewpoint of probability theory. The discrete uniform experimental design is used to supply an efficient sampling to simplify the conversion. The sequential algorithm for optimization is employed to carry out further optimization. The corresponding treatments reveal the essence of the multiobjective programming, and consideration of the simultaneous optimization of each objective of multi-objective programming problem rationally. Two examples are conducted to illuminate the rationality of the approach. [ABSTRACT FROM AUTHOR]

This paper regulates a rational approach of robust design in material machining process on basis of the probability method for multi-objective optimization. As an expansion, it takes the arithmetic mean value of the performance index of the alternative and its deviation as twin independent responses to make contributions of two parts of the partial favorable probability individually; the arithmetic mean value of the performance index represents the performance index according to its function and preference in the assessment, and the deviation exhibits an index with the characteristic of the smaller the better in general. Furthermore, the product of the above twin parts of partial favorable probability forms the actual favorable probability of the performance index of each alternative in the treatment, which is the unique indicator of the performance index of the alternative in the robust optimum. Moreover, examples are given to illustrate the application of the approach. [ABSTRACT FROM AUTHOR]

Recently, a new "intersection" method for multi-objective optimization was developed in the points of view set theory and probability theory, which introduces a new idea of favorable probability to reflect the favorable degree of the utility of performance indicator in multi-objective optimization, and the product of all partial favorable probabilities of entire utilities of performance indicators makes the overall / total favorable probability of the candidate. Here, in this paper, the new "intersection" algorithm for multi-objective optimization is combined effectively with response surface methodology (RSM) by taking each response as one objective, which transfers the multi-response optimization problem into a single response one with the help of the overall / total favorable probability of each scheme. The overall / total favorable probability is the uniquely decisive index of the scheme in the optimization. Applications of the hybrid approach with two examples in material technology are given, proper predictions are obtained.

In the present paper, a new concept of favorable probability is proposed first, and a simplified approach for multi-criteria decision-making is developed on basis of probability theory. It assumes that all the performance indexes of all alternatives can be divided into beneficial and unbeneficial types in the multi-criteria decision-making, and each performance index of all alternative makes its contribution to a partial favorable probability in positively or negatively correlative manners linearly upon its type of beneficial or unbeneficial; the partial favorable probability of each performance index with the same physical meaning is normalized in the alternative group; the product of all partial favorable probability of an alternative makes the total favorable probability of the alternative. As a consequence, all the alternatives can be ranked according to their total favorable probability comparatively in the multi-criteria decision-making. As application examples of the new method, the quantitative assessment of multi-criteria selection for effective dwelling house walls, project managers and contractor for construction works are given in detail, satisfied results are obtained. First published online 10 January 2023

A novel approach for material selection is developed on basis of probability theory. The novel concept of favorable probability is formed to express the favorable degree of a candidate material in the selection. It assumes that all utility indexes of material performance indicators can be attributed to beneficial or unbeneficial type, and each utility index of material performance indicator devotes to one partial favorable probability in the selection; a partial favorable probability is linearly correlative to the corresponding utility index of material performance indicator in positive or negative manners upon its nature of whether beneficial or unbeneficial type; the product of all the partial favorable probabilities forge the overall / global favorable probability of a candidate material. Finally, all the candidate materials can be ranked according to their overall favorable probability comparatively in the material selection. As application examples, the quantitative material selections of cylindrical shaft, stamping of titanium bipolar plates for fuel cell and tribological coatings are given; furthermore, the novel approach is combined with the orthogonal and uniform experiment designs to conduct their optimizations under multi‐object conditions. [ABSTRACT FROM AUTHOR]

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.