  Aggregation functions largely determine the convergence and diversity
performance of multi-objective evolutionary algorithms in decomposition
methods. Nevertheless, the traditional Tchebycheff function does not consider
the matching relationship between the weight vectors and candidate solutions.
In this paper, the concept of matching degree is proposed which employs
vectorial angles between weight vectors and candidate solutions. Based on the
matching degree, a new modified Tchebycheff aggregation function is proposed,
which integrates matching degree into the Tchebycheff aggregation function.
Moreover, the proposed decomposition method has the same functionality with the
Tchebycheff aggregation function. Based on the proposed decomposition approach,
a new multiobjective optimization algorithm named decomposition-based
multi-objective state transition algorithm is proposed. Relevant experimental
results show that the proposed algorithm is highly competitive in comparison
with other state-of-the-art multiobjetive optimization algorithms.
