Yuan Qilong | Searcharxiv

arXiv2025

Assignment-Routing Optimization: Solvers for Problems Under Constraints

We study the Joint Routing-Assignment (JRA) problem in which items must be assigned one-to-one to placeholders while simultaneously determining a Hamiltonian cycle visiting all nodes exactly once. Extending previous exact MIP solvers with Gurobi and cutting-plane subtour elimination, we develop a solver tailored for practical packaging-planning scenarios with richer constraints.These include multiple placeholder options, time-frame restrictions, and multi-class item packaging. Experiments on 46 mobile manipulation datasets demonstrate that the proposed MIP approach achieves global optima with stable and low computation times, significantly outperforming the shaking-based exact solver by up to an orders of magnitude. Compared to greedy baselines, the MIP solutions achieve consistent optimal distances with an average deviation of 14% for simple heuristics, confirming both efficiency and solution quality. The results highlight the practical applicability of MIP-based JRA optimization for robotic packaging, motion planning, and complex logistics .

cs.AI↗

arXiv2025

Assignment-Routing Optimization : Efficient Heuristic Solver with Shaking Algorithm

This paper works on heuristic solver for joint assignment and routing optimization problem. Study on previous works shows that MIP based exact solvers can only provide efficient solutions for small to moderate size problems, due to exponentially growing computational complexity. This paper proposes to start with high quality initial guess through Hungarian algorithm based assignment and heuristic cycle merging algorithm. Subsequently, the solution is improved based on a proposed shaking algorithm to improve the assignment and routing sequence. In addition, the shaking approach also enables the Simulated Annealing algorithm to further improve the solution, which is very difficult if it is purely based on random sampling updates of item and placeholder sequences. Extensive experimental validation comparing with ground truth from the previously shared database shows that the introduced solver is much more efficient than the Gurobi solver especially for large size problems, with a 1000 node pair problem being solved within 1 min in Python implementation. The solution accuracy is within a percent in general as compared with ground truth in database. Although there are spaces for the proposed solver to be further improved with better accuracy, it works for practical applications with acceptable path quality and sufficient solver efficiency. Such shaking algorithms based solvers can also be applied to more general joint assignment and routing optimization problem with multiple type of items and corresponding placeholders. GitHub repository: https://github.com/QL-YUAN/Joint-Assignment-Routing-Optimization-Heuristic.git

math.CO↗