Multiple-Try Simulated Annealing for Constrained Optimization

In the large class of robust optimization methods, stochastic programming and stochastic optimization gained popularity thanks to the theoretical guarantees of the algorithms. This paper focuses on simulated annealing, a stochastic-based algorithm for numerical optimization problems with a good global exploration ability. However, the global optimum values cannot always be guaranteed without a slowly decreasing cooling schedule. This ultimately negatively impacts the convergence speed of the algorithm. This deficiency is overcome in this study by a new stochastic optimization algorithm built on generalized Metropolis and simulated annealing (SA) algorithms. The ergodicity of the proposed constrained multiple-try Metropolis SA is proved. Several constrained optimization benchmarks and challenging real-world high-dimensional problems from finance were considered for assessing the performance of the proposed algorithm.