  Recently surrogate functions based on the tail inequalities were developed to
evaluate the chance constraints in the context of evolutionary computation and
several Pareto optimization algorithms using these surrogates were successfully
applied in optimizing chance-constrained monotone submodular problems. However,
the difference in performance between algorithms using the surrogates and those
employing the direct sampling-based evaluation remains unclear. Within the
paper, a sampling-based method is proposed to directly evaluate the chance
constraint. Furthermore, to address the problems with more challenging
settings, an enhanced GSEMO algorithm integrated with an adaptive sliding
window, called ASW-GSEMO, is introduced. In the experiments, the ASW-GSEMO
employing the sampling-based approach is tested on the chance-constrained
version of the maximum coverage problem with different settings. Its results
are compared with those from other algorithms using different surrogate
functions. The experimental findings indicate that the ASW-GSEMO with the
sampling-based evaluation approach outperforms other algorithms, highlighting
that the performances of algorithms using different evaluation methods are
comparable. Additionally, the behaviors of ASW-GSEMO are visualized to explain
the distinctions between it and the algorithms utilizing the surrogate
functions.
