On the Performance of Different Genetic Programming Approaches for the SORTING Problem

In genetic programming, the size of a solution is typically not specified in advance, and solutions of larger size may have a larger benefit. The flexibility often comes at the cost of the so-called bloat problem: individuals grow without providing additional benefit to the quality of solutions, and the additional elements can block the optimization process. Consequently, problems that are relatively easy to optimize cannot be handled by variable-length evolutionary algorithms. In this article, we analyze different single- and multiobjective algorithms on the sorting problem, a problem that typically lacks independent and additive fitness structures. We complement the theoretical results with comprehensive experiments to indicate the tightness of existing bounds, and to indicate bounds where theoretical results are missing.