Large-scale multi-objective optimization problems(LSMOPs)pose challenges to existing optimizers since a set of well-converged and diverse solutions should be found in huge search spaces.While evolutionary algorithms are good at solving small-scale multi-objective optimization problems,they are criti-cized for low efficiency in converging to the optimums of LSMOPs.By contrast,mathematical programming methods offer fast convergence speed on large-scale single-objective optimiza-tion problems,but they have difficulties in finding diverse solu-tions for LSMOPs.Currently,how to integrate evolutionary algo-rithms 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 gradi-ents and differential evolution are used to update different deci-sion 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 strat-egy of evolutionary multi-objective optimization is used to differ-entiate 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 state-of-the-art evolutionary algorithms,mathematical pro-gramming methods,and hybrid algorithms,the proposed algo-rithm exhibits better convergence and diversity performance on a variety of benchmark and real-world LSMOPs.

Ye Tian;Haowen Chen;Haiping Ma;Xingyi Zhang;Kay Chen Tan;Yaochu Jin

Information Materials and Intelligent Sensing Laboratory of Anhui Province,Institutes of Physical Science and Information Technology,Anhui University,and also with the Institute of Artificial Intelligence,Hefei Comprehensive National Science Center,Hefei 230601,China;Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education,School of Artificial Intelligence,Anhui University,Hefei 230601,China;Department of Computing,The Hong Kong Poly-technic University,Hong Kong SAR,China;Faculty of Technology,Bielefeld University,Bielefeld 33619,Germany

自动化学报（英文版）

[1]Ye Tian;Haowen Chen;Haiping Ma;Xingyi Zhang;Kay Chen Tan;Yaochu Jin-.Integrating Conjugate Gradients Into Evolutionary Algorithms for Large-Scale Continuous Multi-Objective Optimization)[J].自动化学报（英文版）,2022(10):1801-1817

LSMOPs,cized,optimums,entiate

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