Tuning Strategies in Constrained Simulated Annealing for Nonlinear Global Optimization

This paper studies various strategies in constrained simulated annealing (CSA), a global optimization algorithm that achieves asymptotic convergence to constrained global minima (CGM) with probability one for solving discrete constrained nonlinear programming problems (NLPs). The algorithm is based on the necessary and suucient condition for discrete constrained local minima (CLM) in the theory of discrete Lagrange multipliers and its extensions to continuous and mixed-integer constrained NLPs. The strategies studied include adaptive neighborhoods , distributions to control sampling, acceptance probabilities, and cooling schedules. We report much better solutions than the best-known solutions in the literature on two sets of continuous benchmarks and their discretized versions. A general discrete constrained nonlinear programming problem (NLP) is formulated as follows: minimize x f(x) (1) subject to g(x) 0 h(x) = 0 where x = (x 1 ; : : : ; x n) is a vector of discrete variables, f(x) is a lower-bounded objective function, g(x) = g 1 (x); ; g k (x)] T is a set of k inequality constraints,