Collaborative Training in Sensor Networks: A graphical model approach

Graphical models have been widely applied in solving distributed inference problems in sensor networks. In this paper, the problem of coordinating a network of sensors to train a unique ensemble estimator under communication constraints is discussed. The information structure of graphical models with specific potential functions is employed, and this thus converts the collaborative training task into a problem of local training plus global inference. Two important classes of algorithms of graphical model inference, message-passing algorithm and sampling algorithm, are employed to tackle low-dimensional, parametrized and high-dimensional, non-parametrized problems respectively. The efficacy of this approach is demonstrated by concrete examples

A New "Intersection" Method for Multi-Objective Optimization in Material Selection

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

Hybrids of Uniform Test and Sequential Uniform Designs with "Intersection" Method for Multi- objective Optimization

For multi-objective optimization under condition of complicated objective function, the data processing in the evaluation is sometime tediously long, special algorithm is needed to be adopted. Since the remarkable features of uniform distribution of test points within the test domain and the small number of tests, fully representative of each point, and easy to perform regression analysis, the uniform test design method is hybrid with the “intersection” method for multi-objective optimization to simplify the complicated data process in evaluation first. Furthermore, the "intersection" multi-objective optimization methodology is combined with sequential uniform design so as to get a more precise approximation for solving multi-objective optimization problem, the procedure for searching optimum of the “intersection“ multi-objective optimization methodology with sequential uniform design algorithm is put forward. A multi-objective optimization of linear programming problem with three variables is taken as our example, which involves a maximum for one objective and a minimum for another objective. The result for applying the novel approach to the example indicates the effectiveness of current hybrids

Hybrid of "Intersection" Algorithm for Multi-Objective Optimization with Response Surface Methodology and its Application

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

Approach of Solving Multi-objective Programming Problem by Means of Probability Theory and Uniform Experimental Design

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 multi-objective 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