Rational user - A sufficient condition for global convergence in interactive evolutionary computation

In interactive evolutionary computation (IEC), the relationship between user evaluation and user preference is an important factor of the convergence. Firstly, based on the dominated relationship between user evaluation and user preference, four kinds of users in IEC are put forward: absolute rational user, limited rational user, limited nonrational user and absolute nonrational user. Secondly, four theorems about the global convergence of IEC are proved. They illustrate the idea that the rational user is a sufficient condition for the global convergence of IEC. The theorems also point out that two kinds of elitist preservation strategies are necessary for the global convergence of IEC: fitness elitist preservation and satisfaction elitist preservation. Finally, the experimental results validate the above conclusion and show that it is a sufficient condition that as long as the user keeps rational, the algorithm convergence is ensured when other conditions are ready for the convergence.