Open Access

Henning Cui, Andreas Margraf, Jörg Hähner

• Cartesian Genetic Programming (CGP) suffers from a specific limitation: Positional bias, a phenomenon in which mostly genes at the start of the genome contribute to a program output, while genes at the end rarely do. This can lead to an overall worse performance of CGP. One solution to overcome positional bias is to introduce reordering methods, which shuffle the current genotype without changing its corresponding phenotype. There are currently two different reorder operators that extend the classic CGP formula and improve its fitness value. In this work, we discuss possible shortcomings of these two existing operators. Afterwards, we introduce three novel operators which reorder the genotype of a graph defined by CGP. We show empirically on four Boolean and four symbolic regression benchmarks that the number of iterations until a solution is found and/or the fitness value improves by using CGP with a reorder method. However, there is no consistently best performing reorderCartesian Genetic Programming (CGP) suffers from a specific limitation: Positional bias, a phenomenon in which mostly genes at the start of the genome contribute to a program output, while genes at the end rarely do. This can lead to an overall worse performance of CGP. One solution to overcome positional bias is to introduce reordering methods, which shuffle the current genotype without changing its corresponding phenotype. There are currently two different reorder operators that extend the classic CGP formula and improve its fitness value. In this work, we discuss possible shortcomings of these two existing operators. Afterwards, we introduce three novel operators which reorder the genotype of a graph defined by CGP. We show empirically on four Boolean and four symbolic regression benchmarks that the number of iterations until a solution is found and/or the fitness value improves by using CGP with a reorder method. However, there is no consistently best performing reorder operator. Furthermore, their behaviour is analysed by investigating their convergence plots and we show that all behave the same in terms of convergence type.…