Strategy Of Expensive Interval Multi-objective Optimization Based On Data Mining

In practical applications, the interval multi-objective optimization problems are prevalent and complex. Because of the subjective and objective factors, The accurate function expressions of optimization problems are often unknown, and the cost of the assessment test for the optimization object is often very expensive. Such issues are summed up as "the problem of expensive interval multi-objective optimization with unknown optimization functions", for this problem, two solutions are proposed based on the adequacy of the modeling data.For the case that the modeling data are sufficient, a kind of Gaussian modeling approach based on interval midpoint and uncertainty is proposed. In this method, genetic algorithm is used to minimize model prediction error functions, therefore the interval midpoint and uncertainty Gaussian modeling of objective functions and constraint functions are got. So that the modeling problem of lacking correlation between upper and lower bounds in the traditional interval function identification is solved. Then those models are used as surrogate models of the optimization objects and are applied to the interval multi-objective NSGA-II algorithm. For the improved NSGA-II algorithm, the precondition of algorithm converging to the theory Pareto front in probability is indicated and proved by random process theory.For the case that the modeling data are not sufficient, a kind of NSGA-II is proposed based on data mining technology in decision space which includes nearest neighbor and PCA. Firstly, candidate solutions in the solution set are divided into feasible solutions and non-feasible solutions according to constraints. And nearest neighbor is used to distinguish the solutions which meet constraints through computing similarity between candidate solutions and sample solutions. Secondly, nearest neighbor is also applied to distinguish dominance relationship and non-dominance relationship for Pareto dominance relationship of two solutions. Finally, because of the absence of the crowding distance in objective space, in order to compare the solutions with same sequence, the solution set is clustered by K-means clustering, then the dimensions of the solutions of each category are reduced by PCA, thus the closest solutions before and after candidate solutions can be found. So that the solutions with same sequence are screened by crowding distance in decision space. Therefore, the NSGA-II is improved. The convergence of the improved algorithm is also proved by random process theory.