Comparison of tree and graph encodings as function of problem complexity

In this paper, we analyze two general-purpose encoding types, trees and graphs systematically, focusing on trends over increasingly complex problems. Tree and graph encodings are similar in application but offer distinct advantages and disadvantages in genetic programming. We describe two implementations and discuss their evolvability. We then compare performance using symbolic regression on hundreds of random nonlinear target functions of both 1-dimensional and 8-dimensional cases. Results show the graph encoding has less bias for bloating solutions but is slower to converge and deleterious crossovers are more frequent. The graph encoding however is found to have computational benefits, suggesting it to be an advantageous trade-off between regression performance and computational effort.

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