  Reconfigurable Intelligent Surface (RIS) is a revolutionizing approach to
provide cost-effective yet energy-efficient communications. The transmit
beamforming of the base station (BS) and discrete phase shifts of the RIS are
jointly optimized to provide high quality of service. However, existing works
ignore the high dependence between the large number of phase shifts and
estimate them separately, consequently, easily getting trapped into local
optima. To investigate the number and distribution of local optima, we conduct
a fitness landscape analysis on the sum rate maximization problems. Two
landscape features, the fitness distribution correlation and autocorrelation,
are employed to investigate the ruggedness of landscape. The investigation
results indicate that the landscape exhibits a rugged, multi-modal structure,
i.e., has many local peaks, particularly in the cases with large-scale RISs. To
handle the multi-modal landscape structure, we propose a novel niching genetic
algorithm to solve the sum rate maximization problem. Particularly, a niching
technique, nearest-better clustering, is incorporated to partition the
population into several neighborhood species, thereby locating multiple local
optima and enhance the global search ability. We also present a minimum species
size to further improve the convergence speed. Simulation results demonstrate
that our method achieves significant capacity gains compared to existing
algorithms, particularly in the cases with large-scale RISs.
