## Third-Party Benchmarks

Octeract Engine has been benchmarked by Prof. Hans Mittelmann of Arizona State University. The tests were run on QPLIB, a library of all types of quadratic problems. QPLIB is an interesting library because of how problems are selected.

### Octeract Engine 1.07.29 vs other solvers

All solvers used 8 CPU cores. In contrast with other commercial solvers, the Engine used open-source solvers to solve all LP, MILP, and NLP subproblems so the results are closer to what you get out of the box.

## Parallel Computing Benchmarks for QPLib

Octeract Engine natively supports supercomputing. When 172 CPU cores were used to solve all non-convex problems of QPLib, this is what we observed.

### The difference in computing power is large enough to be significant

This comparison is not fully rigorous as the problems were solved by a newer version of the Engine and on different hardware. However, even when taking this into account, the comparison between the third-party, 8 core benchmarks and Octeract’s parallel scaling benchmarks is meaningful.

### Increasing CPU cores by 20 times result in twice the number of problems solved

With the CPU boost, Octeract Engine solved 24 problems instead of 14. Furthermore, 80% of these problems were solved at least 10 times faster (including perfect scaling of 20x for some problems).

### As the number of cores used increases, problems are solved proportionally faster

Octeract Engine is the only optimisation solver that uses the proprietary Kazazakis Distributed Algorithm (named after Octeract’s founder). When the Engine is running in parallel mode, it uses this algorithm to close the optimality gap and find the global solution faster.

## Octeract Benchmarks

Octeract Engine can do more than just solve QPs or MILPs. It can solve any mathematical structure, no matter how obscure, to guaranteed global optimality. This includes all trigonometric functions, (|f(x)|), (max(f(x),g(x))), (min(f(x),g(x))), (sqrt{f(x)}), and more.

### Using test problems from the literature as well as our own problems (most of which are designed to break solvers in various ways), we produced our own benchmarks.

Number of Problems
3016

Feasible Solutions
86%

Timeout (minutes)
30

## Performance Records

The performance of the Engine when solving problems from several industry-standard libraries and a wide range of non-linear structures, using just 1 CPU and a 30 minute timeout can be seen below.

MINLPLib

This library consists of problems from the mixed integer non-linear programming (MINLP) and non-linear programming (NLP) classes.

86
% Feasible Solutions

1464
Number of Problems

60
% Global Optimality

CoconutLib

This library contains a test set of continuous global optimisation problems.

92
% Feasible Solutions

1285
Number of Problems

71
% Global Optimality

QPLib

QPLib consists of a diverse class of quadratic programming problems. This includes both discrete and continuous problem instances of different characteristics.

62
% Feasible Solutions

360
Number of Problems

22
% Global Optimality

## Largest Problem Solved By Octeract Engine

In terms of problem size, the largest MINLP solved by Octeract Engine is:

110000

100000

40

### Seconds to Solve

The Engine can solve any non-linear problem in its initial form and it always returns a reliable solution.
If you are interested in trialing Octeract Engine, let us know.