Keywords: structural optimization, discrete optimization, metaheuristic search techniques, ant colony optimization method, minimum weight design, steel space frames, trusses.

Many improvements took place in design optimization techniques during recent years. These improvements have helped engineers tremendously in finding the solutions of computationally intractable design problems. The existing optimization techniques can be broadly collected under two classes. The algorithms that require gradient calculations of the objective function and the constraints are called deterministic optimization techniques. These algorithms make use of mathematical principals and conditions to determine the maximum or minimum of a function that may be unconstrained or constrained. Whereas the second group of algorithms, which are called stochastic search methods, do not use gradient based information to make a move in search of the optimum solution in the design region. They make this move using certain rules which are called heuristics that simply indicate which move among the several alternatives is the best to adopt. This is why these techniques are called metaheuristic algorithms. Many design problems that engineers face in everyday practice consist of a large number of discrete design variables and mathematically complex design constraints that most of the gradient based optimization algorithms perform very poorly. This is why recent structural engineering optimization techniques developed are based on metaheuristic algorithms.

One of the recent metaheuristic techniques is the cuckoo search algorithm which simulates the breeding behaviour of certain cuckoo species into a numerical optimization technique [1]. The cuckoo search algorithm is a population based metaheuristic technique.

In this study the optimum design problem of moment resisting steel frames is formulated according to LRFD-AISC [2]. Design constraints include the displacement limitations, inter-storey drift restrictions of multi-story frames, strength requirements for beams and beam-columns. Furthermore, additional constraints are considered to satisfy practical requirements. These include three types of inequalities. The first type ensures that the flange width of the beam section at each beam-column connection of each storey is less than or equal to the flange width of column section. The second and third type of constraints are required to be included to make sure that the depth and the mass per metre of the column section at each storey at each beam-column connection are less than or equal to the width and mass of the column section at the lower storey. The design problem is found to be a discrete nonlinear programming problem. The cuckoo search optimization technique is employed to determine the optimum solution The design algorithm developed selects optimum sections for beams and columns of moment resisting frame such that above constraints are satisfied and the frame has the minimum weight. Furthermore the same design problem is also solved using the big bang-big crunch algorithm as well as the particle swarm optimizer. The optimum results obtained using three different metaheuristic techniques are compared. It is noticed that the cuckoo search algorithm performs better in obtaining the optimum solution compared with the other stochastic search techniques.

1

X.-S. Yang, S. Deb, "Engineering Optimization by Cuckoo Search", Int. J. Mathematical Modeling and Numerical Optimization, 1(4), 330-343, 2010.

2

LRFD-AISC, Manual of Steel Construction, "Load and Resistance Factor Design", Metric Conversion of the Second Edition, AISC, Vol. I & II, 1999.

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