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

inwhich 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.