A Comparative Study of Simulated Annealing with different Cooling Schedules for Geometric Optimization of a Heat Transfer Problem According to Constructal Design

Resumo

The Simulated Annealing is a widely used metaheuristic to combinatorial and optimization problems studied since 1983, when it was first proposed. This algorithm has a particular parameter, the cooling schedule (specifically the decrease of temperature) which is still defined for each problem empirically. This study has the aim to find the best cooling schedule(s) for geometric optimization of a heat transfer problem. More specifically it is performed the geometrical evaluation of an isothermal Y-shaped cavity intruded into conducting solid wall with internal heat generation. In this research, Constructal Design is employed to determine the constraints and objectives for geometric evaluation of this problem. The cooling schedule(s) recommended here will contribute for future applications of Simulated Annealing heuristic in association with Constructal Design to seek for the optimal shapes of complex geometries in heat transfer problems, as well as, evaluate the influence of geometric parameters over thermal performance of the problem. Six different methods of decrease of temperature are evaluated in twenty samples of thirty simulations for each cooling schedule. From these simulations, it was extracted the percentage of convergence to the global optimal point. Results showed that the Fast cooling schedule led to the worst performance in the seek for the global optimal shapes, while the three hybrid cooling schedules proposed here are the most recommended to find the optimal geometrical configurations in heat transfer problems in association with Constructal Design (BoltzExp, ConstExp1 and ConstExp2)