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Multi-Objective Routing Optimization Using Coherent Ising Machine in Wireless Multihop Networks

Yu-Xuan Lin, Chu-Yao Xu, Chuan Wang

TL;DR

This work tackles multi-objective routing in wireless multi-hop networks, an NP-hard problem, by formulating it as a Quadratic Unconstrained Binary Optimization (QUBO) and mapping it to an Ising Hamiltonian via a binary-to-spin transformation. A Coherent Ising Machine (CIM) built on a network of degenerate optical parametric oscillators is used to minimize the Ising energy, with dynamic pumping guiding convergence to near-optimal solutions. The authors demonstrate that CIM can find feasible and near-Pareto-optimal routes across networks with hundreds of nodes and thousands of edges, and provide a complexity analysis showing CIM’s growing efficiency with problem size compared to classical and some quantum approaches. The results suggest CIM as a scalable, topology-agnostic alternative to QAOA and VQE for large-scale routing optimization, with potential impact on practical wireless network design and optimization. All mathematical formulations are presented in a QUBO/Ising framework, enabling direct hardware-oriented optimization for complex routing objectives.

Abstract

Multi-objective combinatorial optimization in wireless communication networks is a challenging task, particularly for large-scale and diverse topologies. Recent advances in quantum computing offer promising solutions for such problems. Coherent Ising Machines (CIM), a quantum-inspired algorithm, leverages the quantum properties of coherent light, enabling faster convergence to the ground state. This paper applies CIM to multi-objective routing optimization in wireless multi-hop networks. We formulate the routing problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem and map it onto an Ising model, allowing CIM to solve it. CIM demonstrates strong scalability across diverse network topologies without requiring topology-specific adjustments, overcoming the limitations of traditional quantum algorithms like Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE). Our results show that CIM provides feasible and near-optimal solutions for networks containing hundreds of nodes and thousands of edges. Additionally, a complexity analysis highlights CIM's increasing efficiency as network size grows

Multi-Objective Routing Optimization Using Coherent Ising Machine in Wireless Multihop Networks

TL;DR

This work tackles multi-objective routing in wireless multi-hop networks, an NP-hard problem, by formulating it as a Quadratic Unconstrained Binary Optimization (QUBO) and mapping it to an Ising Hamiltonian via a binary-to-spin transformation. A Coherent Ising Machine (CIM) built on a network of degenerate optical parametric oscillators is used to minimize the Ising energy, with dynamic pumping guiding convergence to near-optimal solutions. The authors demonstrate that CIM can find feasible and near-Pareto-optimal routes across networks with hundreds of nodes and thousands of edges, and provide a complexity analysis showing CIM’s growing efficiency with problem size compared to classical and some quantum approaches. The results suggest CIM as a scalable, topology-agnostic alternative to QAOA and VQE for large-scale routing optimization, with potential impact on practical wireless network design and optimization. All mathematical formulations are presented in a QUBO/Ising framework, enabling direct hardware-oriented optimization for complex routing objectives.

Abstract

Multi-objective combinatorial optimization in wireless communication networks is a challenging task, particularly for large-scale and diverse topologies. Recent advances in quantum computing offer promising solutions for such problems. Coherent Ising Machines (CIM), a quantum-inspired algorithm, leverages the quantum properties of coherent light, enabling faster convergence to the ground state. This paper applies CIM to multi-objective routing optimization in wireless multi-hop networks. We formulate the routing problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem and map it onto an Ising model, allowing CIM to solve it. CIM demonstrates strong scalability across diverse network topologies without requiring topology-specific adjustments, overcoming the limitations of traditional quantum algorithms like Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE). Our results show that CIM provides feasible and near-optimal solutions for networks containing hundreds of nodes and thousands of edges. Additionally, a complexity analysis highlights CIM's increasing efficiency as network size grows

Paper Structure

This paper contains 17 sections, 21 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Network model
  4. Path Loss
  5. Bit Error Rate
  6. Hops
  7. Quadratic Unconstrained Binary Optimization Model
  8. Ising Model
  9. Coherent Ising Machine
  10. Dynamic Equations of CIM
  11. Experiment and Analysis
  12. Simulation Experiment
  13. Single-Objective Optimization
  14. Two-Objective Optimization
  15. Three-Objective Optimization
  16. ...and 2 more sections

Figures (5)

  • Figure 1: Example of a weighted directed graph.
  • Figure 2: Probability of feasible solutions and optimal solutions for a single objective
  • Figure 3: Probability of feasible solutions and optimal solutions for two objectives.
  • Figure 4: The solution space of 20 nodes
  • Figure 5: Probability of feasible solutions and optimal solutions for three objectives.