Fig. 4: Hardware test results for solving the Burma14 problem using the Probabilistic Greedy Algorithm.

a Map of the Burma14 problem, where the solid line represents the known optimal solution and the dashed line indicates the best solution obtained using the classic greedy algorithm. b Total distance statistics of TSP solutions across the range of k_BT = 1–400. The red dashed line marks the known optimal solution, while the green, orange and red solid lines connect the maximum, minimum, and average total distances, respectively, obtained at each k_BT value. c Distribution of solution distances at six selected k_B T values, showing improved performance and reaching the optimal solution when k_B T is in the range of 40–60. d Relationship between the best path distance and the number of iterations for four selected k_B T values. When k_B T = 60, the optimal solution can be achieved within 1000 iterations. e Scatter plot of the best solutions across k_B T = 1–400 (left) and density distribution plots of solutions within 0, 50, and 100 kilometers of the known best solution (right). Each density plot is based on 100 independent solution runs using the probabilistic greedy algorithm.