COPT 5.0 is released
COPT 5.0 highlights
- Improved COPT MIP solver performance by 50%- Added COPT SDP solver, which outperforms all existing SDP solvers
- Added a FeasRelax utility
COPT 5.0 performance overview
COPT 5.0 takes the leading position in several benchmark measurements, as shown in the summary below.
| Benchmark | Ranking | Notes |
|---|---|---|
| LP - Barrier | 1 | 33% faster than Gurobi |
| LP - Simplex | 1 | 43% faster than Gurobi |
| MIP - MIPLIB | 2 | 2.34x of Gurobi's solution time |
| SOCP | 3 | 10% behind Mosek, 3% behind Gurobi |
| Convex QP/QCP | 1 | 103% faster than Gurobi |
| SDP | 1 | 128% faster than Mosek |
COPT has been leading the LP performance benchmarks for most of the time since the first releases of its simplex and barrier solvers. We maintained the top LP position with COPT 5.0, and the COPT barrier solver reinforced its leading position against Gurobi with a 33% gap now.
There are three MIP benchmarks performed by Hans Mittelmann, namely MIPLIB 2017 Benchmark, Pathological MIP, and Infeasible MIP. The 240-problem MIPLIB 2017 Benchmark is the most important one which tells the overall performance of a MIP solver. According to the benchmark results, with no surprise, Gurobi still takes the leading position, with COPT ranking in the second place. However, compared with version 4.0, COPT 5.0 shows significant improvements in all three tests. Regarding the MIPLIB 2017 benchmark, the relative solution time compared to Gurobi is reduced from 3.50 to 2.34, demonstrating a speedup of 50% achieved for the COPT MIP solver in version 5.0. We also notice that a recent unofficial test using the same MIPLIB 2017 Benchmark set by Professor Qin Hu of Huazhong University of Science and Technology in China concluded that COPT 5.0 comes down to only 27% slower than Cplex, closing the gap between COPT and the established MIP solvers.
COPT 5.0 new solver: COPT SDP solver
In addition to improving the performance of the existing modules, our team also actively expands the ability of COPT.
As an important branch of convex optimization problems, SDP has powerful applications as it greatly extends the capability of traditional linear models while it can still be solved by numerical algorithms. Classic applications of SDP in academia and industry include portfolio optimization in finance, linear matrix inequality (LMI) in control theory, structural optimization in engineering design, convex relaxation of matrix completion and combinatorial optimization in machine learning, wireless sensing and location problems, and modeling of robust optimization problems, etc. In recent years, SDP has also been applied in more innovative areas such as Quantum Query.
According to the benchmark results, the newly added SDP solver comes with not only the best performance by also the highest successfully solved count (74 out of 75). With its initial release, COPT SDP has surpassed the previous top-ranked solver Mosek by 128%. It is worth pointing out that none of the solvers on the list was able to solve all 75 problems, mainly due to the fact that SDP problems are both large-scale and numerically difficult. We will keep improving our SDP solver to address these challenges.
COPT 5.0 new utility: FeasRelax
FeasRelax is a utility developed for resolving infeasible problems. For this type of problems, COPT 4.0 provided the IIS utility which can help users to quickly calculate the minimum set of conflicts that causes the model to be infeasible. Now, the Feasibility Relaxation (FeasRelax) provided by COPT 5.0 goes a step further and helps users to figure out how to make the smallest change to turn infeasible problems into feasible ones. After FeasRelax calculation, users can directly write the feasible model (.relax file) or obtain the minimum changes required for all variables and constraints.
For this "minimal change" calculation, COPT offers a variety of metrics and calculation modes. For detailed usage and measurement criteria, please refer to the user manual and examples within the COPT 5.0 package.
Apply now, upgrade now
COPT 5.0 is now released. It comes with great MIP performance improvements, a new fastest SDP solver and a new FeasRelax utility. If you are interested, you can apply for a free trial from the official website of Cardinal Operations at www.shanshu.ai/copt. For existing users, please feel free to apply for a version upgrade. We sincerely invite you to raise any problems encountered during your use, and we will do our best to create a better user experience.
COPT (Cardinal Optimizer) is a mathematical optimization solver for large-scale optimization problems. It includes high-performance solvers for LP, MIP, SOCP, SDP, convex QP and convex QCP. The optimizer supports all major operating systems (64-bit), including Windows, Linux, and MacOS. It provides interfaces to Julia, Python, PuLP, Pyomo, Fortran, C, C++, C#, Java, AMPL, GAMS and CVXPY.
