论文标题
基于协作分解的进化算法，该算法整合了基于正常和罚款的边界交叉点，以进行多个目标优化
A collaborative decomposition-based evolutionary algorithm integrating normal and penalty-based boundary intersection for many-objective optimization
论文作者
论文摘要
近年来，基于分解的进化算法在多个目标优化方面已变得相当流行。但是，现有的分解方法仍然对多个目标优化问题（MAOPS）的各个边界的各种形状仍然非常敏感。一方面，锥体分解方法，例如基于罚款的边界交叉点（PBI），无法为具有非常凸面的横向前沿的MaOPS获得统一的边界。另一方面，包括正常边界相交（NBI）在内的平行分解方法的并行参考线可能会导致多样性差，因为在带有凹面边界的MaOPS的边界附近采样不足。在本文中，首先提出了一种协作分解方法，以整合并行分解和锥体分解的优势，以克服各自的缺点。该方法继承了NBI风格的TchebyCheff函数作为收敛度量，以增强PBI方法的分布的收敛性和均匀性。此外，该方法还可以自适应地调整NBI参考线向PBI参考线旋转的程度，以增强NBI方法的分布多样性。此外，提出了基于协作分解的进化算法（CODEA）以进行多个目标优化。基于协作分解的环境选择机制主要是在CODEA中设计的，旨在对边界层中与同一PBI参考线相关的所有个人进行排名，并选择最佳等级。将CODEA与85个基准测试实例上的几种流行算法进行了比较。实验结果表明，CODEA得益于合作分解，从而得益于高度竞争力，从而保持了融合，均匀性和分布多样性之间的良好平衡。
Decomposition-based evolutionary algorithms have become fairly popular for many-objective optimization in recent years. However, the existing decomposition methods still are quite sensitive to the various shapes of frontiers of many-objective optimization problems (MaOPs). On the one hand, the cone decomposition methods such as the penalty-based boundary intersection (PBI) are incapable of acquiring uniform frontiers for MaOPs with very convex frontiers. On the other hand, the parallel reference lines of the parallel decomposition methods including the normal boundary intersection (NBI) might result in poor diversity because of under-sampling near the boundaries for MaOPs with concave frontiers. In this paper, a collaborative decomposition method is first proposed to integrate the advantages of parallel decomposition and cone decomposition to overcome their respective disadvantages. This method inherits the NBI-style Tchebycheff function as a convergence measure to heighten the convergence and uniformity of distribution of the PBI method. Moreover, this method also adaptively tunes the extent of rotating an NBI reference line towards a PBI reference line for every subproblem to enhance the diversity of distribution of the NBI method. Furthermore, a collaborative decomposition-based evolutionary algorithm (CoDEA) is presented for many-objective optimization. A collaborative decomposition-based environmental selection mechanism is primarily designed in CoDEA to rank all the individuals associated with the same PBI reference line in the boundary layer and pick out the best ranks. CoDEA is compared with several popular algorithms on 85 benchmark test instances. The experimental results show that CoDEA achieves high competitiveness benefiting from the collaborative decomposition maintaining a good balance among the convergence, uniformity, and diversity of distribution.
