A Comparative Benchmark of Ising Machines, MIP Solvers, and Evolutionary Algorithms for Permutation Optimisation

Permutation problems, such as the Travelling Salesman Problem (TSP) and the Quadratic Assignment Problem (QAP), form a well-established class of combinatorial optimisation problems with broad applications in routing, assignment, and scheduling. Metaheuristics, particularly Evolutionary Algorithms (EAs), have been widely demonstrated to yield high-quality solutions for these problems. In parallel, classical commercial solvers based on Mixed-Integer Programming (MIP), including CPLEX and Gurobi, have also been extensively applied. In recent years, there has been growing interest in quantum, quantum-inspired, and quantum-hybrid approaches for solving combinatorial optimisation problems. This paper presents a comparative analysis of six optimisation solvers: Genetic Algorithm (GA), Estimation of Distribution Algorithm (EDA), CPLEX, Gurobi, Digital Annealer (DA), and a quantum-hybrid Nonlinear solver (NL), applied to permutation problems. We evaluate solver performance in terms of runtime, solution quality relative to optimality, and scalability across instances of TSP and QAP. Our results highlight the promising performance of the quantum-hybrid Nonlinear solver across all evaluation metrics.