The current commercially viable light detection and ranging systems demand continuous, full-scene, and dynamic two-dimensional point scanning, while featuring large aperture size to ensure long distance operation. However, the biasing architecture of large-area arrays with numerous individually controlled tunable elements is substantially complicated. Herein, inverse design of a perimeter-controlled active metasurface for two-dimensional dynamic beam steering at mid-infrared regime is theoretically presented. The perimeter-control approach simplifies biasing architecture by allowing column-row addressing of the elements. The metasurface consists of a periodic array of plasmonic patch nanoantennas in a metal-insulator-metal configuration, wherein two active layers of indium arsenide are incorporated into its building block. The metasurface profile facilitates wide phase modulation of on the reflected light at the individual element level through applying independent voltages to its respective columns and rows. The multi-objective genetic algorithm (GA) for optimizing user-defined metrics toward shaping desired far-zone radiation pattern is implemented. It is demonstrated that multi-objective GA yields better results for directivity and spatial resolution of perimeter-controlled metasurface by identifying the design tradeoffs inherent to the system, compared to the single-objective optimizer. A high directivity and continuous beam scanning with full and wide field-of-view along the azimuth and elevation angles are respectively maintained.