Many-objective optimization problems are common and important in real-world applications

previous theories and methods suitable for them

however

are few so far.We presented a set-based many-objective evolutionary optimization algorithm with integrating a decision-maker's preferences to effectively solve the problems above in this study.In the proposed method

each objective function of the original optimization problem was first transformed into a desirability function based on preference areas given by the decision-maker over it;thereafter

the optimization problem was further transformed into a bi-objective optimization one by taking such indicators as hyper-volume and the decision-maker's satisfaction as two new objectives in which a set formed by multiple solutions of the original optimization problem is as the new decision variable;finally

the transformed bi-objective optimization problem was solved by using a set-based evolutionary optimization algorithm to obtain a Pareto optimal set which meets the decision-maker's preferences and balances the convergence and the distribution.The proposed method was applied to four benchmark many-objective optimization problems and compared with the other methods.The experimental results showed its advantages.