Results are reported of testing a number of existing state of the art solvers for global constrained optimization and constraint satisfaction on a set of over 1000 test problems in up to 1000 variables.

Abstract. We discuss an implementation of a derivative-free generating set search method for linearly constrained minimization with no assumption of nondegeneracy placed on the constraints. The convergence guarantees for generating set search methods require that the set of search directions possesses certain geometrical properties that allow it to approximate the feasible region near the current iterate. In the hard case, the calculation of the search directions corresponds to finding the extreme rays of a cone with a degenerate vertex at the origin, a difficult problem. We discuss here how state-of-the-art computational geometry methods make it tractable to solve this problem in connection with generating set search. We also discuss a number of other practical issues of implementation, such as the careful treatment of equality constraints and the desirability of augmenting the set of search directions beyond the theoretically minimal set. We illustrate the behavior of the implementation on several problems from the CUTEr test suite. We have found it to be successful on problems with several hundred variables and linear constraints.

A benchmarking suite describing over 1000 optimization problems and constraint satisfaction problems covering problems from dierent traditions is described, annotated with best known solutions, and accompanied by recommended benchmarking protocols for comparing test results.

s from these two collections, and many additional constraint satisfaction problems (collected by EPFL, Lausanne). To use the benchmark eciently in our environment we must have AMPL-formulations of all test problems. The library GlobaLLib is written in GAMS-format. To get the AMPL-formulation, it is possible to use the gams2xx-converter from GAMS format to AMPL. But this tool fails sometimes (e.g., for unconstrained problems) . DAG's = directed acyclic graphs form the internal representation from which other representations are generated. DAG-formulations of almost all test problems for test libraries 1 (GlobalLib) and 2 (CUTE) were built from AMPL les. Further programs transform DAG- le for optimization model into GAMS format, LGO format, Globsol format. All problems in our benchmark are represented in a common format suitable for automatic execution on global optimization and constraint satisfaction software. To ensure that benchmarking results are comparable across dierent solve

A framework for simulating and estimating the state and functional topology of complex dynamic geometric networks