Initial bubbles in flowing liquid from a nozzle were observed from two mutually perpendicular directions. Two nozzles of 0.086 cm and 0.305 cm in diameter were used. The gas flow rate and the superficial liquid velocity ranged from 0.33 cm3/s to 36.2 cm3/s and from 0 cm/s to 154.9 cm/s, respectively.
The bubble size formed in flowing liquid decreased with decreasing gas flow rate and with increasing superficial liquid velocity. Three types of bubble formation, i.e. single bubbles, coalescent bubbles and gas jets, were observed depending upon the gas rate and the liquid velocity. Two empirical equations of the bubble sizes are given.
Abstract. One of the major issues in applying multi-objective genetic algorithms to real-world problems is how to reduce the large number of evaluations. The simplest approach is a search with a small population size. However, the diversity of solutions is often lost with such a search. To overcome this difficulty, this paper proposes a diversity maintenance mechanism using clustering and Network Inversion that is capable of preserving diversity by relocating solutions. In addition, the proposed mechanism adopts clustering of training data sets to improve the accuracy of relocation. The results of numerical experiments on test functions and diesel engine emission and fuel economy problems showed that the proposed mechanism provided solutions with high diversity even when the search was performed with a small number of solutions.
Abstract. In multi-objective optimization, it is important that the obtained solutions are high quality regarding accuracy, uniform distribution, and broadness. Of these qualities, we focused on accuracy and broadness of the solutions and proposed a search strategy. Since it is difficult to improve both convergence and broadness of the solutions at the same time in a multi-objective GA search, we considered to converge the solutions first and then broaden them in the proposed search strategy by dividing the search into two search stages. The first stage is to improve convergence of the solutions, and a reference point specified by a decision maker is adopted in this search. In the second stage, the solutions are broadened using the Distributed Cooperation Scheme. From the results of the numerical experiment, we found that the proposed search strategy is capable of deriving broader solutions than conventional multi-objective GA with equivalent accuracy.
Abstract. When training Support Vector Machine (SVM), selection of a training data set becomes an important issue, since the problem of overfitting exists with a large number of training data. A user must decide how much training data to use in the training, and then select the data to be used from a given data set. We considered to handle this SVM training data selection as a multi-objective optimization problem and applied our proposed MOGA search strategy to it. It is essential for a broad set of Pareto solutions to be obtained for the purpose of understanding the characteristics of the problem, and we considered the proposed search strategy to be suitable. The results of the experiment indicated that selection of the training data set by MOGA is effective for SVM training.
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