I asked this on the soplex mailing list, but no answer yet:
http://listserv.zib.de/pipermail/soplex/2022-August/000001.html
I tried scip, and it took 30sec. Maybe because it performs pre-solve.
Is there an easy way to achieve my objective:
Specify an initial solution (something that I have, which is better than a random init), and use the solver for a limited time to find a better feasible solution
Reply from the mailing list:
http://listserv.zib.de/pipermail/soplex/2022-August/000002.html