The deceptive degree of the objective function

Authors:
Yun-qiang Li
Affiliations:
Electronic Technique Institute, Zhengzhou Information Engineering University, Zhengzhou, China
Venue:
FOGA'05 Proceedings of the 8th international conference on Foundations of Genetic Algorithms
Year:
2005

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Abstract

In this paper we present a novel quantitative measure metric for the “degree of deception” of a problem. We present a new definition for the deceptive degree of a function. We investigate the relationship between the best solution and the monomial coefficients of a function, and we give theorems that show the usefulness of the new definition. The new definition can be applied in three ways: it gives a quantitative measure of deception, it simplifies the evaluation of the GA difficulty, and it gives a relationship between the deceptive degree and the polynomial degree. Furthermore we use the deceptive degree of a function to discuss Goldberg's Minimal Deceptive Problem and derive the same result as Goldberg did. Finally, we make experiments with a class of fitness functions to verify the relation between the canonical GA difficulty and the deceptive degree of a function for this class of functions.