| Many real-world problems can be solved as multi-objective optimization problems,among which some require a large number of physical experiments or simulations to evaluate the objective values of a solution.The optimization of such problems is time-consuming.The offline data-driven optimization algorithms are proposed to solve these time-consuming problems by introducing computational cheap surrogate models to replace the expensive objective evaluations and saving the expensive objective evaluations in the optimization process.Therefore,this paper proposes two different offline data-driven optimization algorithms to solve the computationally expensive multi-objective optimization problems.The main work is given as follows:First,an offline multi-objective optimization with association approximation to reference vectors(AARV)is proposed.In the proposed method,the ideal point is used to guide the population evolution,and a surrogate model is trained to approximate the distance between a candidate solution and the ideal point,which is used as the indicator to measure the convergence performance.The diversity of the population is ensured by the uniformly distributed reference vectors.Inspired by the K-nearest neighbor algorithm,this paper proposes to use the nearest neighbor samples to estimate the association relation between a candidate solution and the reference vector.In the experiment,the DTLZ test set is used to verify the performance of the proposed algorithm.The proposed algorithm is compared with the offline data-driven optimization algorithm called MS-RV and three classic online data-driven optimization algorithms.Experimental results show that the proposed algorithm can reduce the number of real evaluations on the premise of ensuring performance.Second,a performance indicator based surrogates for offline data-driven multi-objective optimization(PIS-ODEMO)is proposed.To further improve the accuracy of the association relation between candidate solutions and reference vector,the proposed algorithm trains an offline surrogate model for each reference vector to estimate the angle of a candidate solution to the reference vector.The method is used to reduce the error accumulation on the angle resulting from the approximation of objective functions.The proposed algorithm improves the evolution process that is based on a reference vector.In the experiment,DTLZ and WFG test sets are used to verify the performance of the proposed algorithm.The proposed algorithm is compared with the offline data-driven optimization algorithm called MS-RV and four classic online data-driven optimization algorithms.The experimental results show that the proposed algorithm can effectively solve computationally expensive multi-objective optimization problems. |
