To better balance the spectral efficiency (SE) and energy efficiency (EE) in the massive multiple-input multiple output system with a large number of users (MaMIMO-LU), the SE-EE tradeoff is originally constructed as a constrained large-scale multi-objective problem (CLSMOP) for the power allocation of users. To solve this CLSMOP, a constrained large-scale multi-objective evolutionary algorithm (CLSMOEA), considering the dimensionality reduction as well as the balance of objectives and constraints, is explored. The Lagrange multiplier is first used to construct a two-scale optimization model, bridging original large-scale decision space of variables and small-scale decision space of coefficients of Lagrange multiplier. The decision transfer algorithm is then designed to switch between large-scale original decision space and small-scale parametric decision space, while achieving the maximum dimensionality reduction. Finally, the two-scale evolution strategy is proposed for the alternative optimizations in the two decision spaces emphasizing objectives and constraints, respectively. In summary, the optimization in large-scale space pushes the population to unconstrained Pareto front (PF), the optimization in small-scale space helps the population cross the infeasible areas to approach constrained PF, and the GD-based reproduction of offspring further guarantees the solution convergence. Ten representative and state-of-the-art constrained multi-objective evolutionary algorithms (MOEAs) and unconstrained MOEA have been compared to the proposed CLSMOEA to demonstrate its effectiveness through comparative experiments on some well-known benchmark problems (with 1000 variables), and MaMIMO-LU (with 1024 antennas and 256, 512, and 1024 users). Experimental results show that the proposed CLSMOEA can obtain the best SE-EE tradeoff.

为了更好地平衡具有大量用户的大规模多输入多输出系统 （MaMIMO-LU） 中的频谱效率 （SE） 和能效 （EE），SE-EE 权衡最初被构造为用于用户功率分配的受限大规模多目标问题 （CLSMO）。为了解决这个 CLSMOP 问题，探索了一种考虑降维以及目标和约束平衡的受约束大规模多目标进化算法 （CLSMOEA）。首先使用拉格朗日乘子构建双尺度优化模型，桥接了拉格朗日乘子的原始大规模变量决策空间和小尺度决策空间的系数。然后设计决策转移算法，在大规模原始决策空间和小规模参数决策空间之间切换，同时实现最大降维。最后，针对分别强调目标和约束的两个决策空间中的替代优化，提出了双尺度进化策略。综上所述，大尺度空间下的优化将种群推向无约束的帕累托前沿 （PF），小尺度空间下的优化帮助种群跨越不可行区域接近约束 PF，基于 GD 的后代繁殖进一步保证了解收敛。将 10 种具有代表性和最先进的约束多目标进化算法 （MOEA） 和无约束 MOEA 与提出的 CLSMOEA 进行了比较，以通过对一些众所周知的基准问题（具有 1000 个变量）和 MaMIMO-LU（具有 1024 个天线和 256、512 和 1024 个用户）的比较实验来证明其有效性。 实验结果表明，所提出的 CLSMOEA 可以获得最佳的 SE-EE 权衡。