Assignment-Routing Optimization : Efficient Heuristic Solver with Shaking Algorithm

TL;DR

The paper tackles the joint assignment and routing problem arising in pickup-delivery settings by introducing a fast, modular heuristic that combines Hungarian-based assignment with a cycle-merging strategy to produce a feasible single tour. A shaking refinement, complemented by simulated annealing in a partial-shaking framework, iteratively updates the assignment and pickup sequence to approach near-optimal solutions with significantly reduced computation time compared to exact solvers. Empirical results show the method achieves near-optimal costs (within ~1%) across problem sizes up to $n=300$, with substantial speedups over Gurobi and OR-Tools, and scalability extending to larger instances. The approach is adaptable and extensible, enabling integration with additional optimization techniques and broader joint assignment–routing problems in robotics and logistics.

Abstract

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

Figures (5)

• Figure 1: Illustration of Workflow of The Proposed Hungarian algorithm
• Figure 2: Assignment of items towards placeholders with Hungarian algorithm
• Figure 3: Back assignment of items towards placeholders with Hungarian algorithm
• Figure 4: Initial Guess from Cycle Merging Algorithm
• Figure 5: Solution After Shaking and Simulated Annealing Process