A Compressed QUBO Format for Traveling Salesperson Problems

Ising machines have recently gained a significant attention as a promising approach to combinatorial optimization problems, which are notoriously challenging for conventional computers to solve efficiently. In contrast to conventional computers, Ising machines operate based on the principles of the Ising model derived from statistical mechanics. Ising machines tackle combinatorial optimization problems by transforming them into Quadratic Unconstrained Binary Optimization (QUBO) formulations. The Traveling Salesperson Problem (TSP) is a prominent example of such optimization challenges and is widely recognized for its computational difficulty on conventional computers. Although Ising machines offer the potential for efficiently solving TSPs, the process of a QUBO formulation, namely the generation of a QUBO matrix that represents a TSP, demands substantial memory resources and considerable computation overheads. This study proposes a compressed QUBO format for TSP. This format reduces the dimensionality of the QUBO matrix for TSP by leveraging repetitive values, structural patterns, and sparsity within the matrix. The proposed format enhances the efficiency of data preprocessing, significantly reducing both the computational time required for QUBO matrix generation and the associated memory usage. These improvements contribute to the practical applicability of digital hardware-based Ising machines for addressing large-scale combinatorial optimization problems, thereby expanding their utility in solving complex real-world challenges.