More on Computational Effort Statistics for Genetic Programming Jens Niehaus and Wolfgang Banzhaf System Analysis Computer Science Department University of Dortmund D-44221 Dortmund, Germany {jens.niehaus,wolfgang.banzhaf}@cs.uni-dortmund.de Abstract. In this contribution we take a look at the computational ef- fort statistics as described by Koza. We transfer the notion from gener- ational genetic programming to tournament-selection (steady-state) GP and show why, in both cases, the measured value of the effort often differs from its theoretical counterpart. It is discussed how systematic estimation errors are introduced by a low number of experiments. Two reasons examined are the number of unsuccessful experiments and the variation in the number of fitness evaluations necessary to find a solution among the successful experiments. 1 Introduction Although more and more work is done examining the theory of genetic pro- gramming (GP) most of the publications use an empirical approach to rate new findings and modifications of traditional GP. For comparison purposes different kinds of statistics are needed. One of those used traditionally is the computa- tional effort statistics as presented in [4]. Lately, however, there were several publications which took a closer look at this measure [3,2,5] and came up with several problems regarding the accuracy of the empirically measured values. In this contribution we show how computational effort statistics can be used in conjunction with steady-state algorithms instead of generational GP (section 3). With such an approach it is possible to reduce the difference between a theoret- ical effort value and the measured one. We show further that other inaccuracies are still remaining. They relate to the number of unsuccessful experiments (sec- tion 5) and large differences in the number of fitness evaluations needed over several experiments (section 6). 2 Measurement and Calculation of the Computational Effort In [4] Koza describes a method to compare the results of different evolutionary methods, e.g. different modifications of GP. The so called computational effort C. Ryan et al. (Eds.): EuroGP 2003, LNCS 2610, pp. 164–172, 2003. c  Springer-Verlag Berlin Heidelberg 2003