Archive Management in Interactive Evolutionary Computation with Minimum Requirement for Human User's Fitness Evaluation Ability

Interactive evolutionary computation (IEC) has a large potential ability as a personalized optimization technique to search for preferred solutions. In IEC, evolution of a population is driven by human user’s preference through his/her subjective fitness evaluation. As a result, different solutions are obtained by different users for the same problem. One important challenge in the design of an efficient IEC algorithm is to decrease the human user’s burden in fitness evaluation. We have proposed an idea of a (1+1)ES model of IEC with the minimum requirement for human user’s fitness evaluation ability under the following assumptions: (i) human users can evaluate only a single solution at a time, (ii) human users can remember only the previously examined single solution, (iii) the evaluation result is whether the current solution is better than the previous one or not, and (iv) human users can perform a prespecified number of evaluations in total. This model always has a single archive solution, which is used as the final solution when its execution is terminated. In this paper, we generalize the (1+1)ES model of IEC to a general (μ+1)ES model where μ is not a constant but a variable control parameter. More specifically, the value of μ is controlled so that only a single solution is obtained after the final generation (i.e., μ=1 at the final generation whereas μ can be more than one in the other generations). We show how we can derive the upper bound on the value of μ at each generation from the requirement of μ=1 at the final generation and the above-mentioned four assumptions. We also examine the search behavior of the (μ+1)ES model for various values of μ.