Multi-reservoir ESN-based prediction strategy for dynamic multi-objective optimization

Dynamic multi-objective optimization problems (DMOPs) have several conflicting and time-varying objectives or constraints. To quickly follow the dynamical Pareto optimal front (POF) of DMOPs, prediction model-based optimization algorithms have been widely studied. However, in most existing prediction-based methods, only the linear relationship of historical solutions is studied, and complex correlations among the decision variables are always ignored. To address this issue, the multi-reservoir ESN (MRESN) based predictor is designed and integrated with the multi-objective evolutionary algorithm based on decomposition (MOEA/D), which is called MRESN-MOEA/D in short. The comprehensive relationship among the previous solutions is derived using the MRESN predictor, whose multi-reservoir structure projects the inputs into the complex echo-state space and enhances the information sharing among the decision variables. To overcome the limitation caused by insufficient training solutions, the fractal interpolation technique is implemented before MRESN training. Then, the trained MRESN predictor is applied to produce the original population for the new environment. Finally, MRESN-MOEA/D is applied in both simulated benchmarks and an actual dynamical wastewater treatment system. The experiment results illustrate that the proposed algorithm outperforms other state-of-the-art methods with better convergence and diversity.