A numerical comparison of commonly - used algorithms for structural optimisation

The thesis makes, a qualitative and a quantitative comparison of algorithms used to solve now-linear structural optimisationproblems. Algorithms are categorised into linearization, feasible direction and transformation methods. From each category, algorithms are selected (by considering applicability restrictions, anticipated computational effectiveness and efficiency, supplementary program requirements and program development effort) for a numerical comparison of computational effort. The algorithms chosen are:- the Method of Approximate Programming, a Method of Feasible Directions and the Sequential Unconstrained Minimization Technique. Newton's, Fletcher- Powell's, Stewart's and Powell's methods are chosen for use with SUMT. The algorithms are used In the study to minimize the weight of eight test structures:- four pin-jointed plane trusses and four plane stress plates, all subject to two load cases, member stress limits and design variable limits. The finite element stiffness method was used for structural analyses, function and derivative evaluations. Details and FORTRAN IV program listings are given for the algorithms. Estimates are developed of the relative computational effort required by each algorithm in terms of the Central Processor Unit (CPU) time required when an IBM 360/67 computer is used. Measurements are reported for each algorithm of the CPU time used on an IBM 370/145 computer

Heuristic Solution Methods for Multi-resource Generalized Assignment Problems

Industrial Engineerin

On Tightness of Constraints

The tightness of a constraint refers to how restricted the constraint is. The existing work shows that there exists a relationship between tightness and global consistency of a constraint network. In this paper, we conduct a comprehensive study on this relationship. Under the concept of k-consistency (k is a number), we strengthen the existing results by establishing that only some of the tightest, not all, binary constraints are used to predict a number k such that strong k-consistency ensures global consistency of an arbitrary constraint network which may include non-binary constraints. More importantly, we have identified a lower bound of the number of the tightest constraints we have to consider in predicting the number k. To make better use of the tightness of constraints, we propose a new type of consistency: dually adaptive consistency. Under this concept, only the tightest directionally relevant constraint on each variable (and thus in total n - 1 such constraints where n is the number of variables) will be used to predict the level of "consistency" ensuring global consistency of a network