Keywords: optimum design, minimum weight, steel frame, combinatorial optimization, swarm intelligence, particle swarm optimizer.

Emergence of meta-heuristic algorithms such as genetic algorithms, evolution strategies, tabu search and the simulated annealing method in optimization has provided another dimension to structural optimization. These algorithms are based on the simulation of paradigms found in the nature. They are inspired by analogies with physics, with biology and ethology. These techniques do need neither the gradient information nor the convexity of the objective function and constraints functions. Furthermore they do not even require an explicit relationship between the objective function and the constraints. Instead they are stochastic search methods that make them quite effective and versatile to counter the combinatorial explosion of possibilities. They can handle, with minor modifications, continuous, discrete or mixed optimization problems equally well.

One of the recent additions to meta-heuristic techniques is particle swarm optimization that is based on swarm intelligence. In nature fish school, birds flock and bugs swarm not only for reproduction but for other reasons such as finding food and escaping predators. There are implicit rules that each member of bird flock and fish school has to abide by so that they can move in a synchronized way without colliding. Each individual in a flock maintains an optimum distance from the neighbouring individuals so that the flock can move smoothly from one place to another. A particle swarm optimizer is a simulator of social behaviour that is used to realize the movement of a flock of birds. It is a population based optimization algorithm. Its population is called a swarm and each individual in the swarm is called a particle. Each particle flies through the problem space to search for an optimum. Hence a particle swarm optimizer initially considers the number of particles which are initialized randomly in the search space of an objective function. Each particle represents a potential solution of the optimization problem and it has two attributes. One is its current position in the search space and the other is its current velocity. The particles fly through the search space and their positions are updated based on each particle's personal best position as well as the best position found by the swarm. During iterations the objective function is evaluated for each particle and the fitness value is used to determine which position in the search space is better than others. This process is repeated until a predetermined maximum number of iterations are reached.

In this study the optimum design problem of unbraced steel frames is formulated according to the LRFD-AISC code (Load and Resistance Factor Design, American Institute of Steel Construction). Design constraints include the displacement limitations, inter-storey drift restrictions of multi-storey frames, strength requirements for beams and beam-columns. Furthermore, additional constraints are considered to satisfy practical requirements. The design problem turns out to be discrete nonlinear programming problem. The particle swarm optimization technique is employed to determine the optimum solution. It is noticed that the particle swarm optimizer requires fewer structural analysis steps in obtaining the optimum solution compared to the other stochastic search techniques.

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