Making a Complete Mess and Getting Away with it: Traveling Salesperson Problems with Circle Placement Variants

TL;DR

This letter proposes several novel solvers to address the Traveling Salesperson Problem with Circle Placement, its variant tailored for Dubins vehicles, and a crucial subproblem known as the Traveling Salesperson Problem on self-deleting graphs (TSP-SD).

Abstract

This paper explores a variation of the Traveling Salesperson Problem, where the agent places a circular obstacle next to each node once it visits it. Referred to as the Traveling Salesperson Problem with Circle Placement (TSP-CP), the aim is to maximize the obstacle radius for which a valid closed tour exists and then minimize the tour cost. The TSP-CP finds relevance in various real-world applications, such as harvesting, quarrying, and open-pit mining. We propose several novel solvers to address the TSP-CP, its variant tailored for Dubins vehicles, and a crucial subproblem known as the Traveling Salesperson Problem on self-deleting graphs (TSP-SD). Our extensive experimental results show that the proposed solvers outperform the current state-of-the-art on related problems in solution quality.

Figures (3)

• Figure 1: Blast hole drilling Salienko20.
• Figure 2: Example solutions ($v_i$ - $i^{th}$ node in cycle $c$, $e_{i,j}$ - edge from $v_i$ to $v_j$, $c_i$ - $i^{th}$ circle center, $\kappa_i$ - $i^{th}$ circle, $\theta_i$ - $i^{th}$ angular heading, $r$ - common radius). The paths start from $v_1$ and continue in the direction indicated by the arrow.
• Figure 3: Local search operators for the TSP-SD.

Theorems & Definitions (1)

• Definition 1