Constrained Higher-Order Binary Optimization for Wireless Communications Systems Using Ising Machines

2025-09-24

AI Summary

This paper addresses large-scale higher-order binary optimization (HOBO) problems in wireless communications, characterized by high-order polynomial objective functions and strict inequality constraints. We propose an augmented Lagrangian iterative framework tailored for Ising machine solvers. Our method avoids auxiliary variables by locally approximating the higher-order objective via first-order Taylor expansion, directly yielding a quadratic unconstrained binary optimization (QUBO) formulation. Inequality constraints are incorporated through the augmented Lagrangian method, enabling efficient solution via quantum-inspired classical algorithms. Evaluated on phase optimization for simultaneous wireless information and power transfer (SWIPT) systems, the approach achieves faster convergence and superior performance compared to conventional heuristics, significantly improving resource allocation efficiency. The framework provides a scalable, low-overhead hardware-adaptive paradigm for constrained HOBO problems, bridging the gap between complex combinatorial optimization and emerging neuromorphic and quantum-annealing hardware.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

This paper develops an algorithmic solution using Ising machines to solve large-scale higher-order binary optimization (HOBO) problems with inequality constraints for resource optimization in wireless communications systems. Quadratic unconstrained binary optimization (QUBO) aims to solve a special category of these problems widely encountered in engineering and science. To solve QUBO instances, specialized Ising machines have been designed, while sophisticated quantum annealing algorithm and quantum-inspired classical heuristics have been developed. However, the application of QUBO in wireless communications has limited practical interest mainly due to the complexity of resource optimization problems which are often characterized by high-order polynomial terms and strict inequality constraints. To overcome these bottlenecks and take advantage of recent advancements in Ising machines, in this paper, we propose an iterative algorithmic solution to solve HOBO problems, which is based on the augmented Lagrangian method to handle constraints. Specifically, Taylor expansion is employed to approximate higher-order polynomials to quadratic ones in the augmented Lagrangian function, which enables the solution of a single QUBO problem at each iteration without auxiliary variables. As an illustrative case study, we consider the problem of phase optimization in a simultaneous wireless information and power transfer system, where a reconfigurable intelligent surface with 1-bit phase resolution is used to facilitate information/energy transfer. Simulation results verify that the proposed algorithm achieves satisfactory performance and outperforms heuristic benchmark schemes.

Problem

• Solving large-scale higher-order binary optimization problems with inequality constraints
• Overcoming limitations of QUBO for wireless resource optimization problems
• Developing algorithmic solution using Ising machines for constrained HOBO problems

Innovation

• Augmented Lagrangian method handles inequality constraints
• Taylor expansion approximates higher-order polynomials to quadratic
• Iterative algorithm solves single QUBO without auxiliary variables