Improved global–local simulated annealing formulation for solving non-smooth engineering optimization problems

Abstract

This paper is concerned with a novel optimization algorithm that implements an enhanced formulation of simulated annealing (SA). The new algorithm is denoted as ISA (improved simulated annealing) in the rest of the paper. ISA includes a two-level random search: “global annealing” where all design variables are perturbed simultaneously and “local annealing” where design variables are perturbed one at a time. The improvement with respect to classical SA is in the fact that trial designs are generated always taking care to choose directions along which the cost function may improve. To this purpose, cost function sensitivities are computed in order to properly choose the size of each random perturbation. In addition, the optimization problem is linearized about the current design point if the optimizer ends up in an infeasible region or there is no significant reduction in cost even though the cost function gradient is not close to zero. The linearization is controlled by a trust region model. The optimization algorithm continuously shifts from global to local annealing based on the current best record at the beginning of each cooling cycle. Finally, the cooling schedule is automatically adjusted within ISA based on the convergence behavior. In this work, the ISA algorithm is successfully utilized to solve complicated optimization problems which exhibit non-smooth/non-convex behavior: (i) the large-scale (200 design variables and 3500 constraints) weight minimization of a 200 bar truss under five independent loading conditions; (ii) the configuration optimization of a cantilevered bar truss with 45 elements and 81 design variables; (iii) an example of reverse engineering where in-plane elastic properties of an eight-ply woven composite laminate are to be determined. The performance of ISA is compared to that of classical SA, gradient based optimization codes recently published in literature and commercial software. The results obtained in this study indicate that ISA is a very efficient optimization code. In fact, ISA was much faster than classical SA. The present code allowed about 300 kg weight saving in the 200 bar truss case and about 80 kg in the cantilevered bar truss case. In addition, the residual error on elastic constants in the material identification problem was less than 3%.