Neural Multi-Objective Combinatorial Optimization with Diversity Enhancement (Appendix) A Reference point and hypervolume ratio The normalized hypervolume (HV) ratio is calculated as HV

NHDE-P, deploying NHDE to PMOCO [14], employs a hypernetwork to tackle the weight λ and diversity factor w for the corresponding subproblem. Specifically, according to the given λ and w, the hypernetwork generates the decoder parameters of the heterogeneous graph attention (HGA) model θ, which is an encoder-decoder-styled architecture, i.e., θ(λ, w) = [θ Following [14], the hypernetwork adopts a simple MLP model with two 256-dimensional hidden layers and ReLu activation. The MLP first maps an input with M + 2 dimensions to a hidden embedding h(λ, w), which is then used to generate the decoder parameters by linear projection. NHDE-M, deploying NHDE to MDRL [15], consists of three processes. In the inference process, the submodel is used to solve the corresponding subproblem.