The maximum power point tracking (MPPT) algorithms are used in PV power generation systems to handle the effect due to the partially shaded conditions. This paper confers the algorithms, modeling techniques, and control topologies of photovoltaic (PV) array systems are explored. The problems with conventional MPPT algorithms can be solved by applying various modern optimization algorithms that extract the maximum power from the solar panels. Various reliable techniques are discussed to identify the maximum power point globally. However, each method has advantages and limitations and, this paper presents reviews and findings from the existing optimized methods. The optimized algorithms presented in the various literatures are studied and analyzed. Also the average convergence time and the tracking efficiency for each algorithm are presented. The challenges in selecting a proper algorithm for partially shaded PV array are deliberated. Finally, the comparison between the stand-alone algorithms is presented for future research.