From the user's perspective, CPLEX and Gurobi work similarly. The available solver options are largely the same, though they are organized somewhat differently and have different names. The arrangements for free academic use of CPLEX and Gurobi (and Xpress) are also the same.
For linear mixed-integer problems, you can compare solvers simply by switching between "option solver cplex;" and "option solver gurobi;" (after setting options for each solver as appropriate). There are a few differences for other model types -- CPLEX recognizes "indicator" constraints, Gurobi accepts a broader range of integer quadratic inequalities -- but with successive new releases their features have tended to converge.
You can see some benchmarks comparing CPLEX, Gurobi, Xpress and other solvers at
http://plato.asu.edu/ftp/milpc.html
http://plato.asu.edu/ftp/perf_var.html
There is a lot of variability, between problems and between runs of the same solver with different random seeds, so it's advisable to do some careful testing on the models of interest to you.
Bob Fourer
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Subject: Re: [AMPL 8239] Can AMPL model Bilinear terms?
It seems that Grobi is showing more edges over CPLEX. With Tobias joing Grobi, I guess the gap between CPLEX and Grobi will continue to grow in the near future. Maybe we couldn't publish a paper on math program or journal on computing without comparing with Grobi by then. But this might be a bad news for authors. :)
As for using Grobi as an AMPL MILP solver, how different it is from CPLEX from user's perspective? Is Grobi for AMPL free for academic users?