Gurobi Optimizer 4.5 Released

Houston, Texas - June 2011

Gurobi Optimizer 4.5 widens its performance lead over competing solvers.

The recently released Gurobi Optimizer 4.5 continues to outperform other optimization solvers on important industry benchmarks. Gurobi consistently solves optimization models faster than either CPLEX or XPRESS, whether using 1, 4, or 12 processing cores. In some benchmarks, Gurobi mean performance is more than 8 times that of the competition. In addition, when time limits are imposed on solution time, Gurobi often finds solutions where other solvers cannot. Faster solution times and greater reliability are important features in an optimization solver, leading to more useful results and increased user productivity.

Professor Hans Mittelmann of Arizona State University publishes a set of standard benchmark results for a wide range of optimization solvers and optimization problem types. On eight different benchmarks, data is provided that allows one to compare the performance of the three leading commercial optimization solvers on linear and mixed-integer programming problems. When the full spectrum of benchmarks is considered, a clear picture emerges: Gurobi Optimizer 4.5 consistently outperforms CPLEX 12.2.0.2 and XPRESS 7.2. Details on these benchmarks can be found on Professor Mittelmann's website, Benchmarks for Optimization Software.

Gurobi dominates on mixed-integer-programming (MIP) benchmarks

  • MIPLIB 2010: On this important new benchmark that measures the time to obtain proven optimal solutions for a set of 87 MIP models, Gurobi outperforms both CPLEX and XPRESS, whether using 1 or 12 CPU cores.
  • Feasibility: In benchmark tests that measure how long it takes to find the first feasible solution to a MIP problem, Gurobi dominates the competition, finding solutions more than 3 times as fast as CPLEX on average and more than 8 times as fast as XPRESS.
  • Infeasibility: Proving a MIP model has no feasible solution can be an important step in model development. Gurobi solves this problem 20% faster than CPLEX and 80% faster than XPRESS.
  • Pathological: While Gurobi does not win this benchmark, Professor Mittelmann states: "This benchmark is not giving a representative impression of the relative performance of the codes". The benchmark tests are presented simply to show that even the best MIP codes can exhibit pathologically bad behavior. Because the set of tested models changes frequently, the "winners" for this benchmark are subject to change.
  • MIQP: In benchmark tests that measure performance on mixed-integer programming models with quadratic objective functions, Gurobi dominates the competition, solving these models more than twice as fast on average.

A '-' indicates that no data is available.

* From Prof. Mittelmann: "This benchmark is not giving a representative impression of the relative performance of the codes".

Benchmark Competitor Solve Times
Compared to Gurobi
CPLEX XPRESS
P=1 P=4 P=12 P=1 P=4 P=12
MIPLIB 2010 1.40x - 1.20x 1.01x - 1.15x
Feasibility 3.57x - - 8.16x - -
Infeasibility - 1.20x - - 1.80x -
Pathological* - - 0.90x - - 1.04x
MIQP - 2.43x - - 2.22x -

The table below provides a different view of how Gurobi performs on the mixed-integer-programming tests. It shows the number of cases in each benchmark where a solver fails to solve the model within the specified time limit (the time limit varies depending on the test suite). The lower the value, the more solutions were found within the time limit. For example, Gurobi solved all models in the MIPLIB 2010 test set when using 12 cores, while XPRESS failed on 7 (of 87) instances. Overall Gurobi Optimizer 4.5 fails to find a solution within the given time limits much less frequently than either CPLEX or XPRESS.

A '-' indicates that no data is available.

* Several of the CPLEX and XPRESS failures were due to crashes or out-of-memory conditions.

Benchmark # Tests Number of Failed Tests
Gurobi CPLEX XPRESS
P=1 P=4 P=12 P=1 P=4 P=12 P=1 P=4 P=12
MIPLIB 2010 87 12 - 0 13 - 3* 14 - 7
Feasibility 34 2 - - 5 - - 7 - -
Infeasibility 12 - 0 - - 0 - - 1 -
Pathological 17 - - 5 - - 3* - - 8*
MIQP 24 - 0 - - 2 - - 2 -

Gurobi dominates on linear-programming benchmarks

  • Dual Simplex and Barrier with Crossover: The dual simplex and barrier algorithms are frequently used to solve linear-programming problems. Benchmark test results clearly demonstrate that Gurobi is the fastest solver, whether using 1 or 4 processing cores.
  • Barrier without Crossover: This test set captures an unusual situation: a linear-programming problem is solved with the barrier, but the traditional crossover step is skipped. Models where this is necessary are rare in practice, and as a result the test suite is small and limited. Delving into the benchmark details reveals that Gurobi does better on the larger, more difficult tests, demonstrating Gurobi‚Äôs excellence in real world applications.

A '-' indicates that no data is available.

Benchmark Competitor Solve Times
Compared to Gurobi
CPLEX XPRESS
P=1 P=4 P=1 P=4
LP Dual Simplex 1.36x - 1.16x -
LP Barrier with Crossover - 1.50x - 1.16x
LP Barrier without Crossover - 2.04x - 0.76x

Gurobi Optimization provides optimization solvers that are used in a wide range of industries. For more information on Gurobi Optimizer 4.5, its performance, and how it can help you solve your optimization problems, contact info@gurobi.com.