الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The computational drawbacks of existing numerical methods have forced researchers to rely on heuristic algorithms. Heuristic methods are powerful in obtaining the solution of optimization problems. Although these methods give good solutions that probably may not the optimal one, they do not require the derivatives of the objective function and constraints. Also, the heuristics use probabilistic transition rules instead of deterministic rules. The Particle Swarm Optimization (PSO) method is a numerical optimization technique that simulates the social behavior of birds, fishes and bugs. In nature fish school, birds flock and bugs swarm not only for reproduction but also for other reasons such as finding food and escaping predators. Similar to birds seek to find food, the optimum design process seeks to find the optimum solution and each particle in the swarm represents a candidate solution of the optimum design problem.In the simplest version of PSO, each member of the particle swarm is moved through a problem space by two elastic forces. One force attracts it with random magnitude to the best location so far encountered by the particle; it is called Lbest (local best). The other force attracts the particle with random magnitude to the best location encountered by any member of the swarm which is typically denoted by Gbest (global best). The position and velocity of each particle are updated at each time step until the swarm as a whole converges to an optimum. As a member of stochastic search algorithms, PSO has drawbacks, from this drawbacks of PSO is its premature character, i.e. it could converge to local minimum.Although PSO converges to an optimum much faster than other evolutionary algorithms, it usually cannot improve the quality of the solutions as the number of iterations is increased. Several efforts have been made to enhance PSO.One of the important modifications on PSO is the using of Gauss Distribution instead of the velocity and position update equations of PSO, which introduced by Kennedy and denoted as Bare Bones PSO. Bare bones particle swarm optimization(BPSO) greatly simplifies the particles swarm by stripping away the velocity rule, but performance seems not good as canonical one in some tested problems .In the present study, the author introduces a new strategy to find the optimum design of steel frame using Gauss Distribution and PSO by combining them in the search. First, fast search is started using the normal PSO, which give a fast trapped to local optimum after a small number of iterations, then the Gaussian PSO start the fine tuning search. This strategy give good results and fast convergence compared to using normal PSO only and more simple from the other hybridization methods.In the present study, a modified fly-back mechanism is used to handle the problem specific constraints. Standard design problems selected from literature are used to evaluate the performance of the proposed technique. The comparison showed that design obtained using the present algorithm is more efficient and economical than that provided by other design approaches. The proposed technique significantly reduces the number of iterations required to reach the optimum design (200 to 400 iterations)and also allows using smaller number of particles (5 to 15 particles). The studied examples show that 100 iterations are enough for PSO fast search before starting Gaussian–PSO. Moreover, the studied examples show that the modified fly-back mechanism is powerful in particle swarm optimization technique.