A heuristic smoothing procedure for avoiding local optima in optimization of structures subject to unilateral constraints

Abstract

Structural optimization problems are often solved by gradient-based optimization algorithms, e.g. sequential quadratic programming or the method of moving asymptotes. If the structure is subject to unilateral constraints, then the gradient may be nonexistent for some designs. It follows that difficulties may arise when such structures are to be optimized using gradient-based optimization algorithms. Unilateral constraints arise, for instance, if the structure may come in frictionless contact with an obstacle. This paper presents a heuristic smoothing procedure (HSP) that lessens the risk that gradient-based optimization algorithms get stuck in (nonglobal) local optima of structural optimization problems including unilateral constraints. In the HSP, a sequence of optimization problems must be solved. All these optimization problems have well-defined gradients and are therefore well-suited for gradient-based optimization algorithms. It is proven that the solutions of this sequence of optimization problems converge to the solution of the original structural optimization problem.¶The HSP is illustrated in a few numerical examples. The computational results show that the HSP can be an effective method for avoiding local optima.