Solving Optimization Problems with Intervals and Hybrid Indices Using Evolutionary Algorithms

Optimization problems with intervals and hybrid indices are common in real-world applications. Previous theories and methods suitable for them, however, are few. We present a large population evolutionary algorithm with a user's interval preferences to effectively solve the problems above in this study. In this algorithm, a large population is adopted to improve the performance of the algorithm in exploration. A similarity-based strategy is employed to estimate the implicit indices of the individuals that the user has not evaluated to alleviate the user's fatigue. When Pareto domination is utilized to compare different individuals, the user's preferences to the individuals with the same rank are calculated to further distinguish their performance. In addition, the user's preferences to different indices, expressed with intervals, are quantified by solving another optimization problem. We apply the proposed algorithm to the interior layout problem, a typical optimization one with both interval parameters in the explicit index and interval value of the implicit index, and compare it with other three optimization algorithms. The experimental results validate its superiority.