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Hybrid interval multi-objective optimization problems are common in real-world applications. These problems involve both explicit and implicit objectives, and the values of these objectives are intervals. Few previous methods are suitable for them. An evolutionary algorithm with a large population and a user's interval preferences was presented to effectively solve the problems in this paper. In the proposed algorithm, a similarity-based strategy was employed to estimate the interval values of implicit objectives of evolutionary individuals that the user had not evaluated in order to alleviate user fatigue; the user's preferences to different objectives were expressed precisely as intervals by solving an auxiliary optimization problem; a sorting scheme based on the user's preferences was proposed to guide the population evolving toward the user's preferred regions. We applied the proposed method to an interior layout problem, which is a typical optimization problem with both interval parameters in the explicit objective and interval value of the implicit objective. The proposed algorithm was compared with four other optimization algorithms on the interior layout problem. Experimental results validated its effectiveness and superiority over the compared algorithms in terms of solution quality and the number of user's evaluations.

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