A Mixed-Integer Conic Program for the Multi-Agent Moving-Target Traveling Salesman Problem

TL;DR

This paper introduces a novel Mixed-Integer Conic Program for the Multi-Agent Moving-Target Traveling Salesman Problem, significantly improving computational efficiency and solution quality over existing formulations.

Contribution

The paper presents a new MICP formulation for MA-MT-TSP, outperforming previous models in runtime and optimality gap reduction.

Findings

Achieves up to 100x faster runtimes

Over 90% reduction in optimality gap

Outperforms state-of-the-art methods

Abstract

The Moving-Target Traveling Salesman Problem (MT-TSP) seeks a shortest path for an agent that starts at a stationary depot, visits a set of moving targets exactly once, each within one of their respective time windows, and returns to the depot. In this paper, we introduce a new Mixed-Integer Conic Program (MICP) formulation for the Multi-Agent Moving-Target Traveling Salesman Problem (MA-MT-TSP), a generalization of the MT-TSP involving multiple agents. Our approach begins by restating the current state-of-the-art MICP formulation for MA-MT-TSP as a Nonconvex Mixed-Integer Nonlinear Program (MINLP), followed by a novel reformulation into a new MICP. We present computational results demonstrating that our formulation outperforms the state-of-the-art, achieving up to two orders of magnitude reduction in runtime, and over 90% improvement in optimality gap.