  We consider the edge-weighted online stochastic matching problem, in which an
edge-weighted bipartite graph G=(I\cup J, E) with offline vertices J and online
vertex types I is given. The online vertices have types sampled from I with
probability proportional to the arrival rates of online vertex types. The
online algorithm must make immediate and irrevocable matching decisions with
the objective of maximizing the total weight of the matching. For the problem
with general arrival rates, Feldman et al. (FOCS 2009) proposed the Suggested
Matching algorithm and showed that it achieves a competitive ratio of 1-1/e
\approx 0.632. The ratio has recently been improved to 0.645 by Yan (2022), who
proposed the Multistage Suggested Matching (MSM) algorithm. In this paper, we
propose the Evolving Suggested Matching (ESM) algorithm, and show that it
achieves a competitive ratio of 0.650.
