Coupling Feasibility Pump and Large Neighborhood Search to solve the Steiner team orienteering problem

Hybridizing adaptive large neighborhood search with kernel search: a new solution approach for the nurse routing problem with incompatible services and minimum demand

“…Finally, note that when an arc between two nodes $$i$$ and $$j$$ has been selected (either $$x_{ij}=1$$ or $$x_{ji}=1$$), then $$w_i=w_j$$. This can be imposed by the following Arc‐Vertex Inference Cuts inequalities introduced by Assunção and Mateus (2021): $$\begin{equation} \begin{aligned} & w_i - w_j \le 1 - (x_{ij}+x_{ji}) & (i,j) \in A, i \not= 0, j \not= n+1,\\ & w_j - w_i \le 1 - (x_{ij}+x_{ji}) & (i,j) \in A, i \not= 0, j \not= n+1. \end{aligned} \end{equation}$$…”