Optimal placements of flexible objects: An adaptive simulated annealing approach

Abstract

This paper deals with the computation of equilibrium states for the placement of flexible objects within a rigid boundary. The equilibrium states have to be calculated from uniformly distributed random initial placements. The final placements must ensure that any particular object is deformed only within the limit of elasticity of the material. A simulated annealing approach has been proposed and implemented in [2] to solve the problem. In this study, an adaptive simulated annealing algorithm is proposed with time complexity upper bounded by 0(n·ln2n). The general approach is to determine at a given temperature and a given grid size whether the optimization has achieved a stable state, which will be defined later. The temperature and the grid size are then decreased adaptively. In terms of both run-time and final force of the placement, better results are obtained when compared with those obtained in [2].