Constrained simulated annealing with applications in nonlinear continuous constrained global optimization

This paper improves constrained simulated annealing (CSA), a discrete global minimization algorithm with asymptotic convergence to discrete constrained global minima with probability one. The algorithm is based on the necessary and sufficient conditions for discrete constrained local minima in the theory of discrete Lagrange multipliers. We extend CSA to solve nonlinear continuous constrained optimization problems whose variables take continuous values. We evaluate many heuristics, such as dynamic neighborhoods, gradual resolution of nonlinear equality constraints and reannealing, in order to greatly improve the efficiency of solving continuous problems. We report much better solutions than the best-known solutions in the literature on two sets of continuous optimization benchmarks.