Evolutionary algorithms for optimization problems with uncertainties and hybrid indices

Many optimization problems in real-world applications contain both explicit (quantitative) and implicit (qualitative) indices that usually contain uncertain information. How to effectively incorporate uncertain information in evolutionary algorithms is one of the most important topics in information science. In this paper, we study optimization problems with both interval parameters in explicit indices and interval uncertainties in implicit indices. To incorporate uncertainty in evolutionary algorithms, we construct a mathematical uncertain model of the optimization problem considering the uncertainties of interval objectives; and then we transform the model into a precise one by employing the method of interval analysis; finally, we develop an effective and novel evolutionary optimization algorithm to solve the converted problem by combining traditional genetic algorithms and interactive genetic algorithms. The proposed algorithm consists of clustering of a large population according to the distribution of the individuals and estimation of the implicit indices of an individual based on the similarity among individuals. In our experiments, we apply the proposed algorithm to an interior layout problem, a typical optimization problem with both interval parameters in the explicit index and interval uncertainty in the implicit index. Our experimental results confirm the feasibility and efficiency of the proposed algorithm.