An Efficient Simulated Annealing Algorithm For Design Optimization Of Truss Structures

摘要

This paper presents an optimization algorithm based on Simulated Annealing. The algorithm - denoted as CMLPSA (Corrected Multi-Level & Multi-Point Simulated Annealing) - implements an advanced search mechanism where each candidate design is selected from a population of trial points randomly generated. Therefore, CMLPSA is in principle similar to meta-heuristic algorithms dealing with a pool/population of designs rather than with a single trial point such as it is usually done in classical simulated annealing. The multi-point strategy is adopted for both feasible and infeasible intermediate designs. In the former case, perturbations given to optimization variables are forced to follow the current rate of change exhibited by the cost function. In the latter case, 4th order approximate line search is performed in the neighbourhood of each feasible trial point generated in the current annealing cycle. Furthermore, CMLPSA includes a multi-level annealing strategy where trial points are generated by perturbing all design variables simultaneously (global level) or one by one (local level). Global or local search is performed basing on the current trend seen in the optimization process. CMLPSA is tested in six structural optimization problems where the objective is to minimize the weight of bar trusses - with up to 200 elements - subject to constraints on nodal displacements, member stresses and critical buckling loads. Test cases include both sizing and lay-out optimization variables. The computationally most expensive problem has 200 design variables and 3500 optimization constraints. CMLPSA is compared with other state-of-the-art SA algorithms and advanced global optimization methods like Heuristic Particle Swarm Optimization (HPSO) and Harmony Search (HS) recently presented in literature. Numerical results clearly demonstrate efficiency and robustness of CMLPSA. In particular, CMLPSA found better designs than the other SA-based algorithms and converged much more quickly to the optimum than HPSO and HS. Furthermore, CMLPSA is insensitive to initial design.