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The convex hull cheapest insertion heuristic is known to generate goodsolutions to the Euclidean Traveling Salesperson Problem. This paper presentsan adaptation of this heuristic to the non-Euclidean version of the problem andfurther extends it to the problem with precedence constraints, also known asthe Sequential Ordering Problem. To test the proposed algorithm, the well-knownTSPLIB benchmark data-set is modified in a replicable manner to createnon-Euclidean instances and precedence constraints. The proposed algorithm isshown to outperform the commonly used Nearest Neighbor algorithm in 97% of thecases that do not have precedence constraints. When precedence constraintsexist such that the child nodes are centrally located, the algorithm againoutperforms the Nearest Neighbor algorithm in 98% of the studied instances.Considering all spatial layouts of precedence constraints, the algorithmoutperforms the Nearest Neighbor heuristic 68% of the time.

A Convex Hull Cheapest Insertion Heuristic for the Non-Euclidean and Precedence Constrained TSPs