Research On Expensive Multi-Objective Optimization Algorithm Based On R2 Indicator

Multi-objective optimization problems are common in practical engineering,such as the car robust design problem,water resources management,portfolio planning and many other optimization problems.The traditional multi-objective optimization algorithms usually require tens of thousands of evaluation times,and it is only suitable for solving general multi-objective optimization problems.Because each evaluation takes a high time or economic cost,the traditional multi-objective optimization algorithms are not suitable for solving expensive multi-objective optimization problems.At the same time,the gaussian model can well predict the original model and provide uncertain information,which is of great help to solve the expensive optimization problem in practical application.Therefore,more and more attention has been paid to the study of expensive multi-objective optimization algorithm.Aiming at the problem that multi-objective optimization algorithm can not solve the expensive multi-objective optimization problem,this thesis proposes an expensive multi-objective particle swarm optimization algorithm based on R2.The algorithm mainly consists of three parts:In order to tackle the problem that the traditional weight generation method is difficult to generate any weight uniformly distributed in the objective space,the weight vector generation method based on directional Angle is adopted;By introducing elite selection strategy based on R2 indicator,selection mechanism and Gaussian learning strategy and Elitist learning strategy assistance algorithm in the conventional particle swarm optimization algorithm,particle swarm optimization algorithm can conduct global search effectively.On the basis of the original expected improvement algorithm,it is optimized to select calibration points for primitive function evaluation.Refering to the problem of low efficiency and model management difficulty,this thesis propose an expensive multi-objective evolutionary algorithms by contacting R2 indicator with gaussian model.The algorithm consists of three parts:A new utility function of R2 indicator is designed,which calculates the R2 indicator based on the output of gaussian model.When selecting evaluation points,R2 indicator with new utility function not only take into account the convergence and diversity of the individual population,but also the expected value and mean square error of the individual population,which increases the exploration ability of the individual population in the objective space.An adaptive selection strategy is proposed.According to the expected improvement of each individual,an adaptive selection strategy is proposed,which can accelerates the population convergence and ensures the diversity of the algorithm.A double-archive management strategy is carried out and updated in each iteration.One is used to store the non-dominated individuals and the other is used to build the gaussian model,which can guarantee the outstanding individual to be preserved and improve the convergence of the algorithm and the quality of the model.To verify the rationality and validity of algorithms,the expensive multi-objective particle swarm optimization algorithm based on R2 and the expensive multi-objective evolutionary algorithm based on R2 are experimented on benchmark test functions.