Assignment-Routing Optimization with Cutting-Plane Subtour Elimination: Solver and Benchmark Dataset

TL;DR

This work proposes a method to solve a joint routing-assignment optimization problem using an exact MIP formulation with Gurobi, including cutting-plane subtour elimination, including cutting-plane subtour elimination.

Abstract

We study a joint routing-assignment optimization problem in which a set of items must be paired one-to-one with a set of placeholders while simultaneously determining a Hamiltonian cycle that visits every node exactly once. Both the assignment and routing decisions are optimized jointly to minimize the total travel cost. In this work, we propose a method to solve this problem using an exact MIP formulation with Gurobi, including cutting-plane subtour elimination. With analysis of the computational complexity and through extensive experiments, we analyze the computational limitations of this approach as the problem size grows and reveal the challenges associated with the need for more efficient algorithms for larger instances. The dataset, formulations, and experimental results provided here can serve as benchmarks for future studies in this research area. GitHub repository: https://github.com/QL-YUAN/Joint-Assignment-Routing-Optimization

Figures (4)

• Figure 1: First four sample results showing the computed optimal cycle for $n=32$ (xq).
• Figure 2: First four sample results showing the computed optimal cycle for $n=32$ (ic).
• Figure 3: First four sample results showing the computed optimal cycle for $n=100$.
• Figure 4: First four sample results showing the computed optimal cycle for $n=200$.