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

AGGLOMERATION DURING FLUIDIZED-BED COMBUSTION OF BIOMASS

Wheat stalk is tested to investigate the formation of bed agglomeration. The results show that defluidization time decreases with the combustion temperature increasing. The minimum fluidization velocity of the bed material after the test increases. The K, Ca and Si elements play the most important role in bed defluidization

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

Extension of Intersection Method for Multi-Objective Optimization in Case of Interval Number and its Application

This paper aims to develop the extension of intersection method for multi-objective optimization under condition of interval number. Based on the linear correlation of partial favourable probability and the corresponding performance indicator, and the assumption of uniform distribution of the actual value of performance indicator within the range of its lower and upper limits in case of interval number, it derives that the actual partial favourable probability of a performance indicator is the arithmetic mean value of the partial favourable probabilities of the arithmetic mean value and the variation value of the interval index of the corresponding performance indicator for each candidate, or their desired sum. Furthermore, according to the rule of algorithm for the total favourable probability quantitatively, all candidates are ranked according to their total favourable probabilities to complete the multi- objective optimization in case of interval number. As applications, the quantitative assessments of multi-criteria selections for effective dwelling house walls, project managers and contractor for construction works are given in detail, satisfied results are obtained

Error Analysis for Designed Test and Numerical Integral by Using UED in Material Research

In this article, the error analysis for designed test and definite integral in employing uniform experimental design is analogically developed on basis of midpoint rule in rectangle method for assessing definite integral through conducting discretized sampling approximately. It concluded that the discrete sampling-point by means of good lattice point in the evaluations of definite integral and maximum value of a function is promised with higher accuracy, and the predicted entire error of this uniform sampling point method for above problems decreases with the number of sampling points significantly

Application of Probability-based Multi-objective Optimization in Portfolio Investment and Engineering Management Problems

Markowitz\u27s approach could not deal with the overall optimization of both minimizing variance of return rate and maximizing return rate simultaneously due to its short of rational method for handling multi-objective optimization. In this article, a hybrid of the probability-based multi-objective optimization with the uniform design for experiments of mixtures is performed to solve the portfolio investment problem of concurrent optimization of both maximizing return rate and minimizing variance of return rate. The probability-based multi-objective optimization is employed to transfer the bi-objective problem of portfolio investment into a mono-objective one with total preferable probability as the goal for the overall optimization of the system in spirit of probability theory, the uniform design for experiments of mixtures is used to perform the subsequent discretization. Project management problem is rather a multi-objective to conduct naturally. The analysis shows the rationality of the hybrid solution

Design and Operation of Biomass Circulating Fluidized Bed Boiler with High Steam Parameter

Two circulating fluidized bed(CFB) boilers with capacity of 12 MWe and 25 MWe, respectively, with biomass as fuel, adopting the basic technology independently developed by Institute of Engineering Thermophysics (IET), Chinese Academy of Sciences, have been in commercial operation since March 2010 in China. This paper focuses on the design principles, the design specifications and operating results of the two CFB boilers

Status of Muon Collider Research and Development and Future Plans

The status of the research on muon colliders is discussed and plans are outlined for future theoretical and experimental studies. Besides continued work on the parameters of a 3-4 and 0.5 TeV center-of-mass (CoM) energy collider, many studies are now concentrating on a machine near 0.1 TeV (CoM) that could be a factory for the s-channel production of Higgs particles. We discuss the research on the various components in such muon colliders, starting from the proton accelerator needed to generate pions from a heavy-Z target and proceeding through the phase rotation and decay ($\pi \to \mu \nu_{\mu}$) channel, muon cooling, acceleration, storage in a collider ring and the collider detector. We also present theoretical and experimental R & D plans for the next several years that should lead to a better understanding of the design and feasibility issues for all of the components. This report is an update of the progress on the R & D since the Feasibility Study of Muon Colliders presented at the Snowmass'96 Workshop [R. B. Palmer, A. Sessler and A. Tollestrup, Proceedings of the 1996 DPF/DPB Summer Study on High-Energy Physics (Stanford Linear Accelerator Center, Menlo Park, CA, 1997)].Comment: 95 pages, 75 figures. Submitted to Physical Review Special Topics, Accelerators and Beam