Comparison and Automated Selection of Local Optimization Solvers for Interval Global Optimization Methods

We compare six state-of-the-art local optimization solvers with focus on their efficiency when invoked within an interval-based global optimization algorithm. For comparison purposes we design three special performance indicators: a solution check indicator (measuring whether the local minimizers found are good candidates for near-optimal verified feasible points), a function value indicator (measuring the contribution to the progress of the global search), and the running time indicator (estimating the computational cost of the local search within the global search). The solvers are compared on the COCONUT Environment test set consisting of 1307 problems. Our main target is to predict the behavior of the solvers in terms of the three performance indicators on a new problem. For this we introduce a k-nearest neighbor method applied over a feature space consisting of several categorical and numerical features of the optimization problems. The quality and robustness of the prediction is demonstrated by various quality measurements with detailed comparative tests. In particular, we found that on the test set we are able to pick a ‘best’ solver in 66–89% of the cases and avoid picking all ‘useless’ solvers in 95–99% of the cases (when a useful alternative exists). The resulting automated solver selection method is implemented as an inference engine of the COCONUT Environment.