Optimum Design of Steel Skeleton Structures - Music-Inspired Harmony Search Algorithm: Theory and Applications - page 85

Optimum Design of Steel Skeleton Structures
Mehmet Polat Saka
Engineering Sciences Department, Middle East Technical University, Ankara, Turkey
[e-mail]
Abstract. Designing steel skeleton structures optimally is a tedious task for designers. They
need to select the appropriate steel sections for the members of a steel frame from a discrete list
that is available in the practice. Assigning arbitrarily any one of these sections to any member
of the steel frame generates one possible design combination. The total number of such combi-
nations is quite large and finding out which one these combinations produces the optimum
design by trial is almost practically impossible. The harmony search algorithm is a recently de-
veloped technique for determining the solution of such combinatorial optimization problems. In
this chapter, harmony search algorithm based optimum design methods are introduced for mo-
ment resisting steel frames, grillage systems, geodesic domes and cellular beams. The design
problems of these steel structures are carried out according to British and American Design
Codes respectively. The design examples considered in both structural systems have shown that
harmony search algorithm is an effective and robust technique to find the optimum solutions of
combinatorial structural optimization problems.
Keywords: Structural Optimization, Optimum Design of Steel Structures, Metaheuristic Search
Techniques, Harmony Search Method, Combinatorial Structural Optimization.
1 Introduction
Optimum structural design algorithms provide a useful tool to a steel designer by
which she/he can determine the optimum topology, the optimum geometry and the
optimum steel profiles for the members of a steel structure such that the steel structure
can be constructed by using adequate steel material but not more. Structural design
optimization achieves these goals such that design constraints specified by steel de-
sign codes are satisfied under the applied loads and the weight or the cost of the steel
frame under consideration is the minimum. When formulated, two types of structural
optimization problems can be distinguished. In some design problems the design vari-
ables can have continuous values. However in some others it is required that the val-
ues of design variables have to be selected from a set of discrete values. The optimum
design problem of steel skeleton structures falls into the second category. A structural
steel designer has to select steel sections from a discrete set which contains certain
designations of steel profiles that are produced by steel mills. Hence the formulation
of a steel frame design optimization problem turns out to be a discrete programming
problem [1]. Obtaining solutions to discrete programming problems is more difficult
than finding solutions to programming problems with continuous variables [2]. This
may be one of the reasons why early mathematical programming techniques devel-
oped have dealt with continuous variables [3-5]. Later some of these algorithms have
been extended to address discrete optimization problems as well. A comprehensive