Researchers solve Steiner Traveling Salesman Problem with Time Windows and Pickup Delivery using LeapCQMHybrid

The complexities of modern logistics demand increasingly sophisticated route planning, and researchers are now applying the power of quantum computing to address these challenges. Alessia Ciaccoa, Francesca Guerriero, and colleagues from the University of Calabria and TECNALIA are pioneering new approaches to the Steiner Traveling Salesman Problem, a notoriously difficult optimisation task that incorporates time windows, pickup and delivery requirements, and vehicle capacity. Their work introduces a novel combination of mathematical modelling and quantum-classical hybrid algorithms, designed to find efficient routes for complex distribution networks. By developing specialised formulations and a preprocessing technique to reduce computational load, the team demonstrates the potential for quantum computing to solve realistic, large-scale routing problems, offering a significant step towards next-generation logistics optimisation.

Researchers also considered extensions to the STSP, including simultaneous pick-up and delivery with time windows, to create a more realistic and challenging problem. The core approach involves formulating the STSP as a Quadratic Unconstrained Binary Optimization (QUBO) problem, a format suitable for solving with quantum annealers.

The team explored hybrid quantum-classical algorithms, combining the strengths of both types of computing, often using the quantum annealer to find good initial solutions or explore the solution space efficiently, then refining the results with classical local search algorithms. Extensive benchmarking compared quantum algorithms against classical methods to assess performance and identify potential advantages. The research demonstrates effective ways to formulate the STSP and its variations as QUBO problems, and reveals that hybrid quantum-classical algorithms often outperform pure classical or quantum approaches. To overcome computational difficulties, scientists formulated two specialized mathematical models: an arc-based model and a node-oriented model. Both models were implemented on the D-Wave’s LeapCQMHybrid platform, which harnesses the combined power of quantum and classical techniques for solving constrained optimization tasks.

Furthermore, the team pioneered a preprocessing reduction method that systematically eliminates redundant connections within the network, substantially enhancing computational performance and scalability. This reduction technique streamlines the problem, allowing for faster and more efficient solution finding. The methodology enables the solving of realistic problem instances, demonstrating the potential of hybrid quantum approaches for next-generation routing optimization. To tackle the inherent computational difficulty of this problem, scientists formulated two specialized mathematical models, an arc-based model and a node-oriented model, and implemented them on the D-Wave’s LeapCQMHybrid platform, a system that combines the strengths of both quantum and classical computing techniques. Furthermore, the researchers introduced a preprocessing reduction method that effectively eliminates redundant connections, significantly enhancing computational performance and scalability. Experiments demonstrate that these hybrid quantum approaches are capable of solving problem instances of realistic size, representing a substantial advancement over existing methods. To address the computational difficulty of this problem, researchers developed two mathematical formulations, an arc-based model and a node-oriented model, and a preprocessing reduction method to improve scalability. Experimental results demonstrate the potential of hybrid quantum-classical approaches to solve realistic instances of the STSP-TWPD, with the preprocessing method successfully reducing model size and improving solution feasibility. Future research directions include exploring different quantum platforms and embedding strategies, integrating additional realistic constraints into the model, and developing standardized benchmark datasets to facilitate further evaluation and comparison of optimization techniques.