Unconstrained scalable test problems for single-objective bilevel optimization

In this paper, we propose a set of six test problems for single-objective bilevel optimization. The test-collection represents various difficulties which are commonly encountered in practical bilevel optimization problems. To support experiments with problems of different size, all of the test problems are scalable in terms of the number of variables. The problem set is also accompanied by a construction procedure, which helps to generate new test problems with controlled difficulties in convergence and interaction patterns between the two optimization levels. To provide a baseline result for easy comparisons, we have solved a 10 variable instance for each of the test problems using a simple bilevel evolutionary algorithm. The results presented may be used as a benchmark while evaluating the performance of any bilevel optimization algorithm.