A semi-supervised learning technique assisted multi-objective evolutionary algorithm for computationally expensive problems

Abstract

Existing multi-objective evolutionary algorithms (MOEAs) have demonstrated excellent efficiency when tackling multi-objective tasks. However, its use in computationally expensive multi-objective issues is hindered by the large number of reliable evaluations needed to find Pareto-optimal solutions. This paper employs the semi-supervised learning technique in model training to aid in evolutionary algorithms for addressing expensive multi-objective issues, resulting in the semi-supervised learning technique assisted multi-objective evolutionary algorithm (SLTA-MOEA). In SLTA-MOEA, the value of every objective function is determined as a weighted mean of values approximated by all surrogate models for that objective function, with the weights optimized through a convex combination problem. Furthermore, the number of unlabelled solutions participating in model training is adaptively determined based on the objective evaluations conducted. A group of tests on DTLZ test problems with 3, 5, and 10 objective functions, combined with a practical application, are conducted to assess the effectiveness of our proposed method. Comparative experimental results versus six state-of-the-art evolutionary algorithms for expensive problems show high efficiency of SLTA-MOEA, particularly for problems with irregular Pareto fronts.