Open Access

Julian Trautwein, Michael Heider, Henning Cui, Jörg Hähner

• Ant-based metaheuristics have successfully been applied to a variety of different graph-based problems. However, for Cartesian Genetic Programming (CGP) only the impact of Max-Min Ant Systems has been tested. In this work, we try to fill this gap by applying four different popular ant-based metaheuristics as the optimizer (and therefore training algorithm) of CGP. The idea of combining CGP with ant-based metaheuristics is not novel but older works’ experimental design may not meet today’s standard. To compare these metaheuristics to the Evolution Strategies (ESs) commonly used in CGP, we benchmark against a standard CGP variant that uses a simplistic (1 + 4)-ES, mutation, and no crossover. Additionally, we include (μ + λ)-ES and (μ, λ)-ES in our experiments. We analyse the performance on datasets from the symbolic regression, regression, and classification domains. By tuning and evaluating various configurations, we can not affirm a significant improvement by usingAnt-based metaheuristics have successfully been applied to a variety of different graph-based problems. However, for Cartesian Genetic Programming (CGP) only the impact of Max-Min Ant Systems has been tested. In this work, we try to fill this gap by applying four different popular ant-based metaheuristics as the optimizer (and therefore training algorithm) of CGP. The idea of combining CGP with ant-based metaheuristics is not novel but older works’ experimental design may not meet today’s standard. To compare these metaheuristics to the Evolution Strategies (ESs) commonly used in CGP, we benchmark against a standard CGP variant that uses a simplistic (1 + 4)-ES, mutation, and no crossover. Additionally, we include (μ + λ)-ES and (μ, λ)-ES in our experiments. We analyse the performance on datasets from the symbolic regression, regression, and classification domains. By tuning and evaluating various configurations, we can not affirm a significant improvement by using ant-based methods with CGP as we encounter premature convergence—even with those ant-based metaheuristics that were originally proposed to overcome such problems. Despite our results being of negative nature, this work still gives important and interesting insights into the training of CGP models. The key contributions of our work are thus a more thorough benchmarking of these optimizers than has been done before. This should clear up doubts about the capabilities of ant-based metaheuristics in CGP. Furthermore, we include a roadmap on how they can be addressed to solve this complex optimization problem from the model building domain of machine learning.…