Abstract
Predicting the performance of Genetic Programming (GP) helps us identify whether it is an appropriate approach to solve the problem at hand. However, previous studies show that measuring the difficulty of a problem for GP and predicting GP performance are challenging issues. This paper presents a theoretical analysis of GP performance prediction problem and suggests an upper bound for GP performance. It means that the error of the best solution that is found by GP for a given problem is less than the proposed upper bound. To evaluate the proposed upper bound experimentally, a wide range of synthetic and real symbolic regression problems with different dimensions are solved by GP and consequently, a lot of actual GP performances are collected. Comparing the actual GP performances with their corresponding upper bounds shows that the proposed upper bounds are not violated for both synthetic and real symbolic regression problems. Then, the proposed upper bound is used to guide GP search. The results show that the proposed approach can find better results in comparison to Multi Gene Genetic Programming (MGGP).
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