Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm—Corrigenda for this article is available here

TLDR

The authors introduce a new global optimization algorithm for continuous-variable functions, based on the simulated‑annealing framework. The algorithm performs an iterative random search with adaptive coordinate moves, permitting probabilistic uphill steps to escape local minima, and was benchmarked against Nelder–Mead and Adaptive Random Search on Rosenbrock and multimodal test functions in 2, 4, and 10 dimensions. It consistently locates the global optimum or a near‑optimal point, outperforming the compared methods, though it requires many function evaluations whose cost is predictable and only weakly dependent on the starting point.

Abstract

A new global optimization algorithm for functions of continuous variables is presented, derived from the “Simulated Annealing” algorithm recently introduced in combinatorial optimization. The algorithm is essentially an iterative random search procedure with adaptive moves along the coordinate directions. It permits uphill moves under the control of a probabilistic criterion, thus tending to avoid the first local minima encountered. The algorithm has been tested against the Nelder and Mead simplex method and against a version of Adaptive Random Search. The test functions were Rosenbrock valleys and multiminima functions in 2,4, and 10 dimensions. The new method proved to be more reliable than the others, being always able to find the optimum, or at least a point very close to it. It is quite costly in term of function evaluations, but its cost can be predicted in advance, depending only slightly on the starting point.