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Volume 10 Issue 5
May  2023

IEEE/CAA Journal of Automatica Sinica

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L. Zhang, Q. Kang, Q. Deng, L. Y. Xu, and  Q. D. Wu,  “A line complex-based evolutionary algorithm for many-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 5, pp. 1150–1167, May 2023. doi: 10.1109/JAS.2023.123495
Citation: L. Zhang, Q. Kang, Q. Deng, L. Y. Xu, and  Q. D. Wu,  “A line complex-based evolutionary algorithm for many-objective optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 5, pp. 1150–1167, May 2023. doi: 10.1109/JAS.2023.123495

A Line Complex-Based Evolutionary Algorithm for Many-Objective Optimization

doi: 10.1109/JAS.2023.123495
Funds:  This work was supported in part by the National Natural Science Foundation of China (51775385), the Natural Science Foundation of Shanghai (23ZR1466000), the Shanghai Industrial Collaborative Science and Technology Innovation Project (2021-cyxt2-kj10), the Innovation Program of Shanghai Municipal Education Commission (202101070007E00098), the Innovation Project of Engineering Research Center of Integration and Application of Digital Learning Technology of MOE (1221046), and the Program to Cultivate Middle-Aged and Young Cadre Teacher of Jiangsu Province
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  • In solving many-objective optimization problems (MaOPs), existing nondominated sorting-based multi-objective evolutionary algorithms suffer from the fast loss of selection pressure. Most candidate solutions become nondominated during the evolutionary process, thus leading to the failure of producing offspring toward Pareto-optimal front with diversity. Can we find a more effective way to select nondominated solutions and resolve this issue? To answer this critical question, this work proposes to evolve solutions through line complex rather than solution points in Euclidean space. First, Plücker coordinates are used to project solution points to line complex composed of position vectors and momentum ones. Besides position vectors of the solution points, momentum vectors are used to extend the comparability of nondominated solutions and enhance selection pressure. Then, a new distance function designed for high-dimensional space is proposed to replace Euclidean distance as a more effective distance-based estimator. Based on them, a novel many-objective evolutionary algorithm (MaOEA) is proposed by integrating a line complex-based environmental selection strategy into the NSGA-III framework. The proposed algorithm is compared with the state of the art on widely used benchmark problems with up to 15 objectives. Experimental results demonstrate its superior competitiveness in solving MaOPs.

     

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    Highlights

    • This work uses line complex instead of solution points to design evolutionary strategy. By Plücker coordinates, solution points are projected to line elements composed of position vectors and momentum ones. The position vectors contain Euclidean coordinate information, while the momentum vectors provide extra distribution metrics which can help better evaluate the distribution of solutions, so as to design a more effective environment selection strategy
    • Euclidean distance is not suitable in high-dimensional space because of its poor discrimination, making the nearest neighbor search unstable, which leads to the selection of nondominated solutions even harder. This work designs a new distance function is designed as a more effective distance-based estimator. It makes the distance-based niche construction and the line complex-based environmental selection more effective
    • A novel MaOEA named NSGA-III/LCD is proposed by integrating the line complex-based environmental selection strategy into an NSGA-III framework to achieve better convergence while maintaining the diversity of solutions. Extensive experiments have been conducted to verify its highly competitive performance by comparing it with several well-known state of the art MOEAs

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