PENNON and other codes

The following results were collected from papers on PENNON and Hans Mittelmann's benchmark page. Some of them were not published yet.

 - The Higher The Better -

Performance profile (as introduced by Dolan and Moré; see also GAMS Performance World)  measures performance of solvers (two and more) on a set P of problems. Assuming that tp,s is a computing time required to solve problem p by solver s, one introduces a performance ratio as rp,s = tp,s / min{tp,s : for all solvers s}. The performance profile (np is the number of problems)
rhos(tau) = (1/np) size{p in P : rp,s <= tau}
is the probability that a performance ratio rp,s is within a factor tau of the best possible ratio. For instance, for tau = 2, rhos(tau) says how often can solver s get results in a time not worse that two-times the time of the best solver. Also, the higher rhos, the higher is the probability that solver s can solve all problems from P.

Michal Kocvara
June 30, 2003