A Hyper-Transformer model for Controllable Pareto Front Learning with
  Split Feasibility Constraints
Tran Anh Tuan Nguyen Viet Dung Tran Ngoc Thang
Controllable Pareto front learning (CPFL) approximates the Pareto solution
set and then locates a Pareto optimal solution with respect to a given
reference vector. However, decision-maker objectives were limited to a
constraint region in practice, so instead of training on the entire decision
space, we only trained on the constraint region. Controllable Pareto front
learning with Split Feasibility Constraints (SFC) is a way to find the best
Pareto solutions to a split multi-objective optimization problem that meets
certain constraints. In the previous study, CPFL used a Hypernetwork model
comprising multi-layer perceptron (Hyper-MLP) blocks. With the substantial
advancement of transformer architecture in deep learning, transformers can
outperform other architectures in various tasks. Therefore, we have developed a
hyper-transformer (Hyper-Trans) model for CPFL with SFC. We use the theory of
universal approximation for the sequence-to-sequence function to show that the
Hyper-Trans model makes MED errors smaller in computational experiments than
the Hyper-MLP model.