In fact, the forward air supply optimization design is a multi-parameter optimization process, where the optimization variables are the air outlet design parameters and the optimization targets are the full design requirements. Existing optimization methods are generally classified into two main categories: gradient-based optimization methods and non-gradient-based optimization methods. Gradient-based methods do not handle nonlinear problems well and are easily trapped in local optima [8; 9]. While the Navier-Stokes equations are highly nonlinear, global optimization often requires the use of non-gradient-based meta-heuristic optimization approaches (a series of general-purpose heuristic optimization approaches) such as a genetic algorithm [10], a differential evolution algorithm [11], simulated annealing [12], particle swarm optimization (PSO) [13], sequential quadratic programming [14], etc. Based on these algorithms, various types of algorithms have been developed to optimize single-objective and multi-objective problems, and a mixture of them is also an effective strategy in practical optimization applications, such as the combination of simulated annealing and particle swarm optimization [15]. In this paper, the authors compiled some of the newest studies, as shown in Table 1. It can be found that studies based on meta-heuristic optimization approaches and meta-heuristic optimization approaches combined with artificial neural networks are mainstream in air supply design, air conditioning system operation, and building structure design. This is due to the rapid development of computing power and the excellent global search capability of the algorithm itself. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Authors** & **Other Tools** & **Situations** \\ \hline CFD-based adjoint & [PERSON] et al. (2018) [16] & The centroid-based hierarchical cluster analysis & Steady-state and single-objective \\  & [PERSON] et al. (2023) [17] & Particle-swarm-optimizer–grey-wolf-optimization & Transient and multi-objective \\ Artificial neural & [PERSON] et al. (2022) [18] & Whale optimization algorithm & Steady-state and multi-objective \\  & [PERSON] et al. (2022) [19] & Grey wolf optimization & Steady-state and multi-objective \\  & [PERSON] et al. (2022) [20] & Technique for order preference with similarity to an ideal solution (TOPSIS) & Steady-state and multi-objective \\  & [PERSON], [PERSON] et al. (2022) [21] & PSO & Steady-state and single-objective \\  & [PERSON] et al. (2023) [22] & Non-dominated sorting genetic algorithm-II (NSGA-II) & Multi-objective \\ Proper orthogonal decomposition (POD) & [PERSON] et al. (2021) [23] & Radial basis functions & Steady-state and multi-objective \\  & [PERSON], [PERSON] et al. (2021) [24] & [PERSON] et al. (2021) [24] & Steady-state and multi-objective \\ Multi-step joint optimization & [PERSON] et al. (2023) [25] & Three flow field characteristic indicators & Transient and multi-objective \\  & [PERSON] et al. (2023) [26] & NSGA-II & Steady-state and multi-objective \\ Meta-heuristic optimization approaches & [PERSON] et al. (2022) [27] & Improving the strength Pareto evolutionary algorithm-2 (SPEA-2) & Steady-state and multi-objective \\  & [PERSON] et al. (2023) [28] & NSGA-II & Multi-objective \\  & [PERSON] et al. (2022) [29] & NSGA-II and K-means & Multi-objective \\  & [PERSON] et al. (2023) [30] & NSGA-III and TOPSIS & Multi-objective \\  & [PERSON] et al. (2023) [31] & PSO & Steady-state and single-objective \\  & [PERSON] et al. (2023) [32] & Genetic algorithm & Steady-state and single-objective \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Some of the newest studies on air conditioning.