Global optimization analysis of slope stability by simulated annealing with dynamic bounds and Dirac function

In slope stability analysis, the search for the minimum factor of safety is a difficult NP-hard global minimization problem as the objective function is non-smooth and non-convex and there are multiple local minima. The use of a simulated annealing method where the control variables are controlled within dynamic domains instead of the conventional static domains is proposed. A simple transformation technique for slopes with a soft band domain (equivalent to a Dirac function) is also proposed. With these improvements, the minimum factor of safety for complicated problems can be determined with high accuracy and reasonable computer time. The proposed algorithm is demonstrated to be efficient and effective for various difficult problems.