Hardware Acceleration of Simulated Annealing for Constraint Satisfaction Problems

Combinatorial optimization of a discrete system with an arbitrary set of constraints is a computationally intensive task typically solved by search algorithms that iteratively explore the solution space. Simulated annealing (SA), a metaheuristic algorithm inspired by physical annealing processes, solves this class of problems by performing a stochastic search wherein thermally modulated acceptance criteria enable probabilistic transitions across high-energy states. This allows the system to escape local minima and progressively converge toward a global optimum, even within complex and non-convex solution landscapes. In this work, we present the hardware acceleration of SA for spatial optimization under constrained environments, specifically targeting drone placement for maximum coverage while avoiding no-fly zones. Stochasticity is introduced through a true random number generator based on two-dimensional (2D) materials, which initializes the system states and drives probabilistic transitions. The system energy is evaluated using a Boolean logic circuit, wherein the acceptance of candidate solutions is governed by a programmable 2D circuit with tunable threshold behavior. This hardware implementation achieves an 1800-fold acceleration compared to exhaustive brute-force trials. Furthermore, simulations of the annealing accelerator reveal that the degree of search acceleration scales favorably with both system size and agent count, demonstrating enhanced efficiency in larger and more complex configurations. This work also underscores the potential of 2D-material-enabled stochastic and programmable hardware for real-time constrained optimization.