In this paper, inverse design methodology, along with genetic algorithm (GA) optimization is employed for synthesis of optical metasurfaces. Despite many advantages of the ultimate forms of ultra-thin layers, the performance of metasurfaces is not yet satisfactory due to the limited range of either amplitude or phase gradients achievable with ‘units of canonical shapes’. In addition, the existing design methodologies by nature do not explicitly support incorporation of multi-functionality, multi-band and broadband applications within one unit cell. Utilizing inverse design methodologies, here we design ‘binary-digitized unit cells’ to overcome the above limitations by pushing the achievable phase and amplitude gradients to fundamental limits. We propose an optimization scheme based on our in-house developed Finite-Difference Time-Domain (FDTD) algorithm, genetic algorithm and GPU computing to optimize the ‘binary-digitized unit cells’ to achieve all possible combinations and independently controllable phase and amplitude gradients at a broad range of frequency spectrum. We present a library of such optimized unit cell patterns that can be utilized and transformed into ultra-thin metasurfaces with a variety of novel applications. In this fashion, conventional applications of metasurfaces, including beam-steering, lensing, and holography can be extended systematically by overcoming the inevitable limitations dictated by regular canonical unit cells. For example, by arranging the optimized unit cells in a unique fashion we present highly-efficient digitized plasmonic metasurface for directive radiation and beam-steering in space. Or by independently controlling the phase gradients at a finite set of frequencies one can obtain challenging functionalities such as achromatic bending and focusing of light irrespective of the frequency range. This will be of extreme benefit to the fields of photonics and metasurfaces, and the future of functional metasurfaces.