A study of mathematical programming methods for structural optimization. Part I: Theory

Abstract

SUMMARYA comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.

Extended Multipoint Approximation Method

“…This problem was first described by Belegundu [8] and Arora [9]. The design objective is to minimize the weight of a tension/compression spring subject to constraints on shear stress, surge frequency and minimum deflections as shown in Figure 1.…”

“…The design variables include the wire diameter ; the mean coil diameter , and the number of active coils . (see detailed formulation in [8]) Figure 1. Schematic of the tension/compression spring with indication of design variables.…”

Fish swarm optimization algorithm applied to engineering system design

“…This problem was proposed by Arora (1989), Belegundu (1982) and He and Wang (2007). It is devoted to the minimization of the weight of a tension/compression spring as shown in Figure 3.…”

“…The approaches applied to this problem include eight different numerical optimization techniques (Belegundu, 1982), a numerical optimization technique called constraint correction at constant cost (Arora, 1989), a GA-based co-evolution model (Coello, 2000), and a co-evolutionary particle swarm optimization (He and Wang, 2007).…”

PSO algorithm based on GSO and application in the Constrained optimization

“…[7] 1 ( ) 0.012675 0.012730 0.012924 5.198500e-5 ref. [5] 0.012833 N/A N/A N/A ref. [4] 0.012730 N/A N/A N/A ref.…”