| Multi-objective evolutionary algorithms have attracted a lot of attention from researchers in the past 20 years,and more and more multi-objective evolutionary algorithms have been applied to many optimization problems of complex industrial process successfully.Now,most multi-objective evolutionary algorithms assume that there exist explicit analytic functions to evaluate the candidate solutions obtained during the optimization process.However,in real-world applications,it is usually very difficult to build up precise mathematical models to describe complex industrial processes due to lack of clear mechanisms.Iron ore beneficiation process is a typical complex industrial process full of physical and chemical changes which are beyond description,so there is no one mathematical model which can illustrate the relationship between the operational indices and the production indices.By using surrogates instead real performance functions to evaluate the individuals during the evaluation process,and the surrogates are updated by using efficient management strategy,which ensure that the algorithm can obtain high quality solutions with a limited number of real performance function evaluation.Most of the existing algorithms do not meet the requirements of the optimization of the beneficiation operational process in diversity and efficiency.To address the problems above,supported by the National Natural Science Foundation project "Data-driven industrial complex system operational optimization control and its application(61525302)",the research on surrogate-assisted multi-objective evolutionary algorithm has been carried out.The main work of this paper is list as follows:(1)The analysis of the operational optimization of iron ore beneficiation process is presented.First,the detailed description of iron ore beneficiation process and the decision-making of operational indices for beneficiation process are given.Then the performance indices of the optimal decision-making of operational indices are carried out.Finally,the decision variables and the constraints are conducted.(2)An improved surrogate-assisted multi-objective evolutionary algorithm based on RVEA,called RVEA-GP,has been proposed.A Gaussian process model is brought in evolution process as a surrogate and then a reference vector based model management strategy which improve the diversity by clustering the reference vector is proposed.The proposed algorithm is tested on benchmark functions compared with typical algorithm RVEA and ParEGO.The results show that the candidate solutions obtained by proposed algorithm distribute more uniformly around the real Pareto front than compared algorithms with limited real function evaluation.(3)The ensemble model assist RVEA,named En-RVEA,is proposed.The neural network model,Gaussian process model and polynomial model are integrated by proposed adaptive model integration method.And then,in order to improve the diversity of the algorithm,an ensemble model management strategy based on the reference vector changing information is proposed.Finally,we test the proposed method En-RVEA on benchmark functions and compare with RVEA-GP.The results demonstrate that En-RVEA has more competitive performance in diversity than RVEA-GP.(4)The surrogates of optimization of the beneficiation operational process are constructed,in addition,the proposed two algorithms have been applied to the optimization of the beneficiation operational process which eight typical working conditions have been selected based the actual production condition.The proposed algorithms are compared with ParEGO and RVEA on the optimization of beneficiation operational process.It can be clearly observed from the results that the quality of the solutions obtained by proposed En-RVEA and RVEA-GP are significantly better than RVEA and ParEGO in both diversity and convergence.It also demonstrate the proposed algorithms are reasonable and effective for optimization of the beneficiation operational process. |
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