Comparison of some penalty function based optimization procedures for the synthesis of a planar truss

Abstract

The present investigation examines the multibar truss optimization problem in the context of a general class of unconstrained optimization procedures in conjunction with various types of penalty function transformations. Specifically, the problem is transformed into a series of unconstrained minimization problems using the penalty function techniques of Heaviside and SUMT. These are solved using the methods of Rosenbrock (orthogonal directions), Powell (conjugate directions) and Nelder-Mead (Simplex). This resulted in many cases in substantial improvements being recorded over previously reported data. The paper includes a comparative study of the synthesis based on these procedures. In this context, the penalty function approach seems to offer greater possibilities to problems with non-linear merit functions.Other studies of penalty function based structural optimization problems have been made by, amongst others, Schmit and co-worker~,~ Marcal and GellatlyY8 Wollnerll and Pappas.12 In particular, MOe,lS has made extensive use of various penalty function techniques for the design of ship structures, where he has incorporated practical improvements relating to the derivation of feasible starting points, scaling, program parameter selection, convergence criteria, efficient line searches, etc. This paper is intended to be a follow-up and consolidation of this work by attempting a more systematic evaluation of the above penalty function based unconstrained minimization procedures as applied to the structural optimization area.

Mathematical and Metaheuristic Applications in Design Optimization of Steel Frame Structures: An Extensive Review

“…Numerical difficulties may also arise in the case of illconditioned minimization problems. In the field of optimum structural design these methods have been used by Kavlie and Moe [33,34], Griswold and Moe [35], and De Silva and Grant [36].…”

“…Consequently, the allowable axial compressive stress of inequality (25) is replaced by either (35) or (36), whichever applies.…”

“…It is apparent from (35), (36), (44), and (46) that and are also nonlinear expressions of area variables. Substitution of these into (51) increases the nonlinearity of the equation even further.…”