The convex hull cheapest insertion heuristic is known to produce good solutions to the Traveling Salesperson Problem in Euclidean spaces, but it has not been extended to the non-Euclidean case. The proposed adaptation uses multidimensional scaling to first project the points into a Euclidean space, thereby enabling the generation of the convex hull that initializes the algorithm. To evaluate the proposed algorithm, non-Euclidean spaces are created by adding impassable separators to the TSPLIB benchmark data-set, or by using the L1 norm as a metric. This adapted heuristic is demonstrated to outperform the commonly used Nearest Neighbor heuristic and Nearest Insertion heuristic in 89% and 99% of the cases studied, respectively. When the genetic algorithm and ant colony optimization algorithms are provided 1 minute of computation time, the proposed heuristic tour costs are lower than the mean metaheuristic solutions found in 87% and 95% of the instances, respectively.

翻译：凸包最廉价插入启发式算法已知能在欧几里得空间中为旅行商问题生成优质解，但尚未被推广至非欧几里得情形。所提出的改进方案首先使用多维标度法将点投影至欧几里得空间，从而能够生成用于初始化算法的凸包。为评估所提出的算法，通过向TSPLIB基准数据集中添加不可通行的分隔物，或使用L1范数作为度量，创建了非欧几里得空间。实验证明，该改进启发式算法在89%和99%的研究案例中分别优于常用的最近邻启发式算法和最近插入启发式算法。当为遗传算法和蚁群优化算法提供1分钟计算时间时，所提出的启发式路径成本在87%和95%的实例中分别低于所找到的元启发式解的平均值。