IEEE/CAA Journal of Automatica Sinica
Citation:  Y. Tian, H. W. Chen, H. P. Ma, X. Y. Zhang, K. C. Tan, and Y. C. Jin, “Integrating conjugate gradients into evolutionary algorithms for largescale continuous multiobjective optimization,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 10, pp. 1801–1817, Oct. 2022. doi: 10.1109/JAS.2022.105875 
Largescale multiobjective optimization problems (LSMOPs) pose challenges to existing optimizers since a set of wellconverged and diverse solutions should be found in huge search spaces. While evolutionary algorithms are good at solving smallscale multiobjective optimization problems, they are criticized for low efficiency in converging to the optimums of LSMOPs. By contrast, mathematical programming methods offer fast convergence speed on largescale singleobjective optimization problems, but they have difficulties in finding diverse solutions for LSMOPs. Currently, how to integrate evolutionary algorithms with mathematical programming methods to solve LSMOPs remains unexplored. In this paper, a hybrid algorithm is tailored for LSMOPs by coupling differential evolution and a conjugate gradient method. On the one hand, conjugate gradients and differential evolution are used to update different decision variables of a set of solutions, where the former drives the solutions to quickly converge towards the Pareto front and the latter promotes the diversity of the solutions to cover the whole Pareto front. On the other hand, objective decomposition strategy of evolutionary multiobjective optimization is used to differentiate the conjugate gradients of solutions, and the line search strategy of mathematical programming is used to ensure the higher quality of each offspring than its parent. In comparison with stateoftheart evolutionary algorithms, mathematical programming methods, and hybrid algorithms, the proposed algorithm exhibits better convergence and diversity performance on a variety of benchmark and realworld LSMOPs.
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