The convex hull cheapest insertion heuristic is known to produce good solutions to the Traveling Salesperson Problem in Euclidean spaces, but it has never been extended to the non-Euclidean problem. This paper proposes an adaptation that uses multidimensional scaling to first project the points from a non-Euclidean space into a Euclidean equivalent space, thereby enabling the generation of a convex hull that initializes the algorithm. To evaluate the proposed algorithm, non-Euclidean spaces are created by adding separators to the Euclidean 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 88% and 99% of the cases studied, respectively. When compared with metaheuristic algorithms, the proposed heuristic's tour costs are lower than the solutions found by the genetic algorithm and ant colony optimization algorithm 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，但该方法从未被推广至非欧几里得问题。本文提出一种改进方案：首先通过多维标度法将非欧几里得空间中的点投影至等价的欧几里得空间，从而能够生成用于初始化算法的凸包。为评估所提算法，通过在欧几里得TSPLIB基准数据集中添加分隔符，或采用L1范数作为度量，构建了非欧几里得空间进行测试。实验表明，改进后的启发式算法在所研究案例中分别以88%和99%的占比优于常用的最近邻启发式算法与最近插入启发式算法。与元启发式算法相比，所提启发式算法的路径成本在87%和95%的实例中分别低于遗传算法和蚁群优化算法求得的解。