Towards global optimization with adaptive simulated annealing

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Abstract
The structure of the simulated annealing algorithm is presented and its rationale is discussed. A unifying heuristic is then introduced which serves as a guide in the design of all of the sub-components of the algorithm. Simply put this heuristic principle states that at every cycle in the algorithm the occupation density should be kept as close as possible to the equilibrium distribution. This heuristic has been used as a guide to develop novel step generation and temperature control methods intended to improve the efficiency of the simulated annealing algorithm. The resulting algorithm has been used in attempts to locate good solutions for one of the lens design problems associated with this conference viz. the " monochromatic quartet" and a sample of the results is presented. 1 Global optimization in the context oflens design Whatever the context optimization algorithms relate to problems that take the following form: Given some configuration space with coordinates r (x1 . . x) and a merit function written asffr) find the point r whereftr) takes it lowest value. That is find the global minimum. In many cases there is also a set of auxiliary constraints that must be met so the problem statement becomes: Find the global minimum of the merit function within the region defined by E. (r) 0 j 1 2 . . . p and 0 j 1 2 . . . q.

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