Dynamic Multi-objective Evolutionary Optimization Based On Kernel Extreme Learning Machine Predictions

Multi-objective problems(MOPs)are widely used in engineering practice and scientific research.Dynamic multi-objective optimization problems(DMOPs)are a class of MOPs in which the objective function,constraints and parameters vary with time,and have a higher complexity and universality than static multi-objective problems.Therefore,the study of dynamic multi-objective optimization problems has important real-life and production applications.Existing dynamic multi-objective evolutionary optimization algorithms typically model the dynamic process of DMOPs as a simple linear correlation model,which in turn solves the problem using a linear predictive model.However,in practical scenarios,the modelling process is often difficult to satisfy and may lead to the failure of the relevant algorithm.Therefore,to improve the robustness and applicability of the algorithm,this thesis proposes a dynamic multi-objective evolutionary approach based on Kernel Extreme Learning Machine(KELM)prediction,which exploits the fast and efficient fitting ability of KELM to non-linear models to improve the prediction accuracy and solution performance of the algorithm in the face of non-linearly varying patterns of DMOPs,the details of the study are as follows:1.In this thesis,a decomposition-based time series construction method is designed.Firstly,the decomposition of the target space is achieved by constructing reference points and reference vectors in the target space;secondly,the projection distance between the individuals of the optimal solution set and different reference vectors at previous moments is calculated,and the individuals are associated with the reference vectors closest to them;finally,the historical individuals associated to each reference vector are constructed as a time series,and multiple time series are output according to the number of reference vectors.Based on this,it can be seen that the individuals of the historical solution set associated to the same reference vector have strong time correlation and can be used to extract and fit the dynamic change pattern of the problem.2.A dynamic multi-objective algorithm based on the KELM prediction is designed.The KELM is a single hidden layer feedforward neural network,and the output layer weights can be directly calculated by matrix inversion or pseudo-inversion methods,so it has fast and efficient non-linear learning capability;at the same time,the introduction of the kernel function can map multiple non-linear time series from low-dimensional space to high-dimensional space,and achieve linear regression of non-linear time series in high-dimensional space to find the evolutionary trend of solutions.Using the constructed multiple time series as training samples and inputs,the KELM is used to fit and learn the dynamic change patterns implied in the historical solution set,and finally achieve accurate prediction of the location of individuals in the population in the new environment,generate the predicted initial population,and then use the decomposition-based multi-objective evolutionary algorithm to obtain the optimal solution set in the new environment.3.The effectiveness of the studied algorithm is verified through simulation experiments on 14 dynamic multi-objective benchmark test problems.The performance of the proposed method is compared with six popular dynamic multi-objective optimization algorithms and the results are analyzed by selecting three evaluation metrics on 14 DF series benchmark problems under the premise of ensuring fairness.The experimental results show that the proposed algorithm is able to respond quickly to environmental changes and exhibits better prediction and solution performance.In addition,the robustness of the proposed algorithm and the basis of parameter selection are verified through experimental analysis of the sensitivity of the hyperparameters and the length of the time series of the KELM predictor.The experimental results demonstrate that the proposed kernel limit learning machine predictor combined with evolutionary multi-objective optimization to solve DMOPs is efficient and accurate in tracking Pareto optimal solutions.The KELM based predictor is able to quickly and efficiently predict the location of the optimal solution set in a new environment in the face of non-linear changing patterns,improving the adaptive capability and solution performance of the algorithm for complex dynamic multi-objective problems.