A VNS-based heuristic using both a facility as well as a customer type neighbourhood structure is proposed to solve the p-centre problem in the continuous space. Simple but effective enhancements to the original Elzinga–Hearn algorithm as well as a powerful ‘locate–allocate’ local search used within VNS are proposed. In addition, efficient implementations in both neighbourhood structures are presented. A learning scheme is also embedded into the search to produce a new variant of VNS that uses memory. The effect of incorporating strong intensification within the local search via a VND type structure is also explored with interesting results. Empirical results, based on several existing data set (TSP-Lib) with various values of p, show that the proposed VNS implementations outperform both a multi-start heuristic and the discrete-based optimal approach that use the same local search. 
The continuous p-centre problem: An investigation into variable neighbourhood search with memory