A multi-start heuristic approach for the split-delivery vehicle routing problem with minimum delivery amounts

•A novel and powerful local search operator inspired by node-ejection chains for SDVRP-MDA.•A new constructive algorithm uses node-insertion and route-addition steps adaptively.•Two different yet complementary constructive procedures to enhance the diversification.•Out of 32 instances tested with four minimal delivery fractions, we find 81 BKS and improve 43.•The proposed algorithm relies on only one parameter and requires minimal tuning efforts. We propose a new multi-start solution approach for the split-delivery vehicle routing problem with minimum delivery amounts (SDVRP-MDA). Initial solutions are generated by both node-insertion and route-addition procedures with a single parameter to control the restart. These solutions are then improved by a variable neighborhood descent metaheuristic with a novel search operator inspired by node-ejection chains. We test the proposed approach with 32 benchmark instances for four different minimum delivery fractions. Using the proposed algorithm, out of 128 cases tested, we find 81 best known solutions and 34 new best solutions; overall, we find 43 new best solutions.