The computational complexity analysis of genetic programming (GP) has been started recently by analyzing simple (1+1) GP algorithms for the problems ORDER and MAJORITY. In this paper, we study how taking the complexity as an additional criteria influences the runtime behavior. We consider generalizations of ORDER and MAJORITY and present a computational complexity analysis of (1+1) GP using multi-criteria fitness functions that take into account the original objective and the complexity of a syntax tree as a secondary measure. Furthermore, we study the expected time until population-based multi-objective genetic programming algorithms have computed the Pareto front when taking the complexity of a syntax tree as an equally important objective.
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