The traveling salesman problem in surgery: economy of motion for the FLS Peg Transfer task

In the Peg Transfer task in the Fundamentals of Laparoscopic Surgery (FLS) curriculum, six peg objects are sequentially transferred in a bimanual fashion using laparoscopic instruments across a pegboard and back. There are over 268 trillion ways of completing this task. In the setting of many possibilities, the traveling salesman problem is one where the objective is to solve for the shortest distance traveled through a fixed number of points. The goal of this study is to apply the traveling salesman problem to find the shortest two-dimensional path length for this task.

A database platform was used with permutation application output to generate all of the single-direction solutions of the FLS Peg Transfer task. A brute-force search was performed using nested Boolean operators and database equations to calculate the overall two-dimensional distances for the efficient and inefficient solutions. The solutions were found by evaluating peg object transfer distances and distances between transfers for the nondominant and dominant hands.

For the 518,400 unique single-direction permutations, the mean total two-dimensional peg object travel distance was 33.3 ± 1.4 cm. The range in distances was from 30.3 to 36.5 cm. There were 1,440 (0.28 %) of 518,400 efficient solutions with the minimized peg object travel distance of 30.3 cm. There were 8 (0.0015 %) of 518,400 solutions in the final solution set that minimized the distance of peg object transfer and minimized the distance traveled between peg transfers. Peg objects moved 12.7 cm (17.4 %) less in the efficient solutions compared to the inefficient solutions.

The traveling salesman problem can be applied to find efficient solutions for surgical tasks. The eight solutions to the FLS Peg Transfer task are important for any examinee taking the FLS curriculum and for certification by the American Board of Surgery.