Abstract:The convex hull cheapest insertion heuristic is known to generate good solutions to the Euclidean Traveling Salesperson Problem. This paper presents an adaptation of this heuristic to the non-Euclidean version of the problem and further extends it to the problem with precedence constraints, also known as the Sequential Ordering Problem. To test the proposed algorithm, the well-known TSPLIB benchmark data-set is modified in a replicable manner to create non-Euclidean instances and precedence constraints. The proposed algorithm is shown to outperform the commonly used Nearest Neighbor algorithm in 97% of the cases that do not have precedence constraints. When precedence constraints exist such that the child nodes are centrally located, the algorithm again outperforms the Nearest Neighbor algorithm in 98% of the studied instances. Considering all spatial layouts of precedence constraints, the algorithm outperforms the Nearest Neighbor heuristic 68% of the time.