A new algorithm for the optimization of structures: simulated annealing

Abstract

The optimization of a real function is a problem that frequently occurs in structural theory. If the function is the potential energy and optimization means search for the minimum, the problem is structural analysis as usual. If the function represents a "cost", its optimization is transformed into a design method for the structure, actually, it can lead to the "better" design with respect to the "cost" considered. As mathematical problem, no way to solve it is known, but for a few particular cases in which function and variables fulfill specific conditions (continuity, differentiability, etc.). These conditions do not hold at all in practical cases and, consequently, it is possible only to look for approximations, for which several heuristics exist. Simulated annealing is an approximation algorithm towards the optimal solution. The basis is an analogy to the performance of simple themodinamical systems. In fact it is in use for some engineering problems. The present research shows how to use it on structural theory, pointing out its benefits (generality) and its drawbacks (slowness). With this goal in mind, the different problems of structural theory as well as some aspects of algorithm theory are examined briefly. The mathematical form of the algorithm is shown in more detail. In both cases, the "traveling salesman" problem is used as a paradigm of generic optimization. Finally, simulated annealing is used for approximating the optimal shape of isostatic trusses.