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

• Published in: Structural and multidisciplinary optimization Vol. 20; no. 1; pp. 29 - 36
• Main Author: Hilding, D.
• Format: Journal Article
• Language: English
• Published: Berlin Springer 01.08.2000; Springer Nature B.V
• Subjects: Algorithms; Asymptotes; Economic models; Exact sciences and technology; finite elements; Frictionless contact; Fundamental areas of phenomenology (including applications); gradient-based algorithms; Mechanical contact (friction...); method of moving asymptotes (MMA); NATURAL SCIENCES; NATURVETENSKAP; Nonlinear programming; Optimization; Optimization algorithms; Physics; Quadratic programming; Smoothing; smoothing procedure; Solid mechanics; Structural and continuum mechanics; Tribology and mechanical contacts; trusses; unilateral constraints; Sensitivity analysis; Truss structure; Smoothing; Sequential method; Heuristic method; Unilateral; Mechanical contact; Numerical method; Quadratic programming; Structural analysis; Constrained optimization
• ISSN: 1615-147X; 1615-1488; 1615-1488
• DOI: 10.1007/s001580050133

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.