Physics-Informed Optimization via Ising Spin System Evolution

Nature evaluates fitness through dynamic interactions between organisms and their environments, as exemplified by Darwinian evolution. Conversely, physical systems—such as those described by the Ising spin model—quantify a form of "fitness" via measurable macroscopic properties, notably energy. Drawing on this analogy and the principles of Evolutionary Computation (EC), we introduce EvoIsing, a physics-informed optimization method grounded in the Ising model’s energy minimization dynamics. By mapping combinatorial problem costs to binary variables and embedding them into the Ising system’s energy landscape via differential spin dynamics, EvoIsing exploits the natural tendency of analog spins to evolve toward low-energy states. Experiments across multiple binary optimization tasks demonstrate robust performance gains and reliability compared to traditional methods, underscoring the utility of energy-based dynamics for solving complex problems including Ising problem, maximum cut problem and traveling salesman problem. Notably, this implicit energy-based evaluation mechanism obviates explicit fitness and selection procedures typical in EC, thereby potentially mitigating issues like premature convergence and heavy computational overhead. Ultimately, this work advocates a broader synthesis of physics-informed models and evolutionary strategies, opening new avenues for efficient, nature-inspired optimization methods that transcend conventional fitness-driven paradigms.