Softmax Regression and Particle Swarm Optimization with Taboos and a Heuristic Strategy for Dose-effect Data Fitting

The fitting of the dose-effect data of traditional Chinese medicine is of important meaning in the research of the dose-effect relationship of traditional Chinese medicine. Aiming at the problem that the dose-effect data of traditional Chinese medicine are of multi-dimensional structure and the problem that standard particle swarm optimization (PSO) method may fall into a radical or still state, in this paper, the authors apply softmax regression to the modeling of the fitting of the dose-effect data of traditional Chinese medicine, and suggest a novel method for the data fitting based on a hybrid particle swarm optimization algorithm with taboos and a heuristic strategy. In this study, Min-Max normalization method is used to normalize independent variables and dependent variables. Then the authors conduct a fast dimensional transformation by multiplying a transformation matrix on the right side of independent variable matrix. After that, a mathematic model for the fitting of dose-effect data is built in accordance with softmax regression including a regression formula and an evaluation function. In the end, the authors apply a novel hybrid PSO algorithm with taboos and a heuristic strategy to the fitting of the dose-effect data of traditional Chinese medicine. In the comparative experiments, the authors implemented hill climbing algorithm, conventional genetic algorithm, standard PSO algorithm and our method, and utilized these methods to conduct the fitting of the dose-effect data. Experimental results on the problem of dose-effect data fitting demonstrate that the proposed method significantly outperforms the 3 classic methods with respect to accuracy in the conducted experiments. And our method is more efficient than hill climbing algorithm and conventional genetic algorithm in comparative experiments.