This work presents a multi-objective optimization framework for systematic design-space exploration of a 28 GHz single-stage cascode LNA (Low noise amplifier) in 22 nm FDSOI technology using NSGA-II and MOPSO algorithms. The objectives of the paper include simultaneous minimization of noise figure (NF) and power consumption while maximizing gain under matching and stability constraints. Using device parameters and circuit models that were developed for a 22 nm FDSOI process technology, an optimization framework was created in Python, with the passive components $L_G$, $L_S$, $L_D$, $L_{OUT}$, and $C_{OUT}$ chosen to be the variables optimized. The NSGA-II optimized design achieves 1.7 dB NF, 17 dB gain, and 4.7 mW DC power, while MOPSO achieves 1.8 dB NF, 17.1 dB gain, and 5.0 mW power. NSGA-II provides improved Pareto diversity and slightly better output matching, whereas MOPSO reduces computational time by 24% with comparable RF performance. The results demonstrate effective multi-objective design-space exploration and controlled algorithm benchmarking at the schematic-level for mm-wave LNA design.