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Benchmarking Classical and Quantum Optimization Approaches for Rider-Order Assignment

Tharrmashastha SAPV, Surya Prakash Palanivel, Jasjyot Singh Gulati, M Maruthu Pandi

TL;DR

This study addresses rider–order assignment as a constrained binary optimization problem, formulating it as a QUBO with hard and soft constraints to capture realistic logistics costs. It benchmarks classical (Greedy, SCIP), quantum-inspired (SQA, CIM), and gate-based (QAOA, QAOAnsatz) solvers across small and large instance regimes derived from Bangalore, with a post-repair step to enforce feasibility. Findings show classical solvers deliver the best runtime and objective performance, while QAOAnsatz improves constraint handling over QAOA; SQA and CIM provide near-feasible solutions for larger problems but at higher computational cost, and soft-constraint violations are more common in quantum-inspired solutions at scale. The work offers a practical benchmark and guidance for deploying hybrid classical–quantum optimization in realistic, constrained logistics problems, aiding future research in scalable quantum-assisted routing and allocation.

Abstract

The logistics industry is widely regarded as a promising application domain for emerging optimization paradigms, including quantum computing. The Rider-Order Assignment problem is a practically motivated optimization problem arising in online food delivery and related logistics applications. While the problem is closely related to the classical matching problem, the inclusion of realistic operational constraints renders it computationally challenging. In this work, we formulate the Rider-Order Assignment problem as a constrained binary optimization problem and perform a comparative analysis of classical, quantum-inspired, and gate-based quantum solvers for this problem across multiple instance sizes. Solver performance is assessed using solution quality, computational runtime, and constraint satisfaction, with a consistent post-processing procedure applied to ensure feasibility.

Benchmarking Classical and Quantum Optimization Approaches for Rider-Order Assignment

TL;DR

This study addresses rider–order assignment as a constrained binary optimization problem, formulating it as a QUBO with hard and soft constraints to capture realistic logistics costs. It benchmarks classical (Greedy, SCIP), quantum-inspired (SQA, CIM), and gate-based (QAOA, QAOAnsatz) solvers across small and large instance regimes derived from Bangalore, with a post-repair step to enforce feasibility. Findings show classical solvers deliver the best runtime and objective performance, while QAOAnsatz improves constraint handling over QAOA; SQA and CIM provide near-feasible solutions for larger problems but at higher computational cost, and soft-constraint violations are more common in quantum-inspired solutions at scale. The work offers a practical benchmark and guidance for deploying hybrid classical–quantum optimization in realistic, constrained logistics problems, aiding future research in scalable quantum-assisted routing and allocation.

Abstract

The logistics industry is widely regarded as a promising application domain for emerging optimization paradigms, including quantum computing. The Rider-Order Assignment problem is a practically motivated optimization problem arising in online food delivery and related logistics applications. While the problem is closely related to the classical matching problem, the inclusion of realistic operational constraints renders it computationally challenging. In this work, we formulate the Rider-Order Assignment problem as a constrained binary optimization problem and perform a comparative analysis of classical, quantum-inspired, and gate-based quantum solvers for this problem across multiple instance sizes. Solver performance is assessed using solution quality, computational runtime, and constraint satisfaction, with a consistent post-processing procedure applied to ensure feasibility.
Paper Structure (8 sections, 2 equations, 7 figures)

This paper contains 8 sections, 2 equations, 7 figures.

Table of Contents

  1. Formulation of the Rider-Order Assignment Problem
  2. Experimental Setup
  3. Solvers
  4. QUBO Formulation of the Rider-Order Assignment Problem
  5. Problem Instances
  6. Evaluation Metrics
  7. Results
  8. Conclusion

Figures (7)

  • Figure 1: The Average objective cost of the small instance solvers normalized by the objective cost of SCIP.
  • Figure 2: The Average objective cost of the large instance solvers normalized by the objective cost of SCIP.
  • Figure 3: The Average runtime of the large instance solvers normalized by the runtime of SCIP.
  • Figure 4: The GF Constraint violations for small instance solvers.
  • Figure 5: The SLA Constraint violations for small instance solvers.
  • ...and 2 more figures