An Approach to Continuous Approximation of Pareto Front Using Geometric Support Vector Regression for Multi-objective Optimization of Fermentation Process

The approaches to discrete approximation of Pareto front using multi-objective evolutionary algorithms have the problems of heavy computation burden, long running time and missing Pareto optimal points. In order to overcome these problems, an approach to continuous approximation of Pareto front using geometric support vector regression is presented. The regression model of the small size approximate discrete Pareto front is constructed by geometric support vector regression modeling and is described as the approximate continuous Pareto front. In the process of geometric support vector regression modeling, considering the distribution characteristic of Pareto optimal points, the separable augmented training sample sets are constructed by shifting original training sample points along multiple coordinated axes. Besides, an interactive decision-making (DM) procedure, in which the continuous approximation of Pareto front and decision-making is performed interactively, is designed for improving the accuracy of the preferred Pareto optimal point. The correctness of the continuous approximation of Pareto front is demonstrated with a typical multi-objective optimization problem. In addition, combined with the interactive decision-making procedure, the continuous approximation of Pareto front is applied in the multi-objective optimization for an industrial fed-batch yeast fermentation process. The experimental results show that the generated approximate continuous Pareto front has good accuracy and completeness. Compared with the multi-objective evolutionary algorithm with large size population, a more accurate preferred Pareto optimal point can be obtained from the approximate continuous Pareto front with less computation and shorter running time. The operation strategy corresponding to the final preferred Pareto optimal point generated by the interactive DM procedure can improve the production indexes of the fermentation process effectively.

Graphical AbstractBasic principle for continuous approximation of Pareto front and interactive decision-making.This figure shows the basic principle for continuous approximation of Pareto front and interactive decision-making. The regression model of small size approximate discrete Pareto front is constructed by geometric SVR modeling and is described as the approximate continuous Pareto front. In order to improve the accuracy of the preferred Pareto optimal point, an interactive decision-making procedure is presented. Specifically, the continuous approximation of Pareto front and DM will be performed interactively in the dynamic interested region. As the contraction of interested region, the accuracy of the approximate continuous Pareto front and the preferred Pareto optimal point will be improved. As shown in the graphic, the final preferred Pareto optimal point is closer to the original point than all Pareto optimal points generated by SEC-MOPSO with large size population, which means the preferred Pareto optimal point has better accuracy in terms of the values of the objective functions.Figure optionsDownload full-size imageDownload as PowerPoint slide