COCONUT Environment

An open source platform for interval global optimization


For download information of our solvers please visit the Downloads page.


coco_gop_ex is a new interval global optimization method for solving bound constrained problems. Its predecessor is a small standalone software by M. C. Markót that was re-implemented in the COCONUT Environment and enhanced by various new methods. New methods include advanced interval function evaluations using DAGs (first and second order derivatives with backward automatic differentiation, slopes, slopes of derivatives, bicentered forms, evaluations on the Karush-John conditions, etc.) and new algorithmic elements (inclusion/exclusion boxes, local search, constraint propagation).

The key publication about coco_gop_ex is

M. C. Markót and H. Schichl. Bound constrained interval global optimization in the COCONUT Environment. J. Global Optimization 60(4), 751–776, 2014.

In the publication above, we tested our solver against the prestigious BARON software on an extensive set of bound constrained problems. We found that in addition to accepting a wider class of bound constrained problems and providing more output information (by locating all global minimizers), coco_gop_ex is competitive with BARON in terms of the solution success rates and it often outperforms BARON in running time.

Runtimes coco_gop_ex vs. BARON
Running times of coco_gop_ex vs. BARON - Copyright M. C. Markót sand H. Schichl

The figure above shows the logarithmic ratio of the running time between coco_gop_ex and BARON on the 130 problems accepted by both solvers. The figure shows a clear advantage of our method. In particular, on 15 instances coco_gop_ex was faster than BARON by about one magnitude or more, while it was slower by the same amount for only six problems. In two cases we observed the advantage of coco_gop_ex with two orders of magnitudes or more. In average, coco_gop_ex was around 21% faster over the set of problems solved by both software systems.


The other built-in solver of COCONUT, cocos, was written during the first COCONUT project. This algorithm uses a simple strategy involving constraint propagation and heuristic search only- At present cocos is mainly intended for demonstration and basic comparison purposes.