TOOLS AND TECHNIQUES
Optimum Design of Steel Frames using Stochastic Search Techniques Based on Natural Phenomena: A Review
Engineering Sciences Department, Middle East Technical University, Ankara, Turkey
Optimum design of steel frames is a challenging task for the structural designer because of the fact that designers are not free to assume any value for the cross-sectional dimensions of the frame members but to select steel sections from a discrete set of practically available sections. The designer can arbitrarily assign any one of these available steel sections to any one of the member groups in the frame. After such assignment it becomes necessary to analyze the frame to find out whether the response of the frame under the external loading is within the limitations set by the design codes. It is apparent that quite large numbers of combinations are possible for the member groups of the frame depending upon the total number of practically available steel sections. For example, for a frame where the members are collected in eight groups and the total number of available sections is 272, there are 2.996065x1019 possible combinations that require to be considered. Some reduction may be achieved on this number by making use of the designer's practical experience but still an exhaustive search will require enormous computation time and effort to determine the optimum combination. This search may not be practically possible.
Early attempts to obtain the solution of such combinatorial problems utilized mathematical programming methods. Some structural optimization algorithms developed that are based on mathematical programming techniques such as integer programming, branch and bound method and dynamic programming were not very efficient due to the fact that mathematical programming methods make the assumption of continuous design variables while the design problem under consideration is discrete. However, in recent years novel and innovative search techniques have developed that make use of ideas taken from nature and do not suffer the discrepancies of mathematical programming based optimum design methods. The basic idea behind these techniques is to simulate the natural phenomena such as survival of the fittest, immune system, swarm intelligence and the cooling process of molten metals through annealing into a numerical algorithm. These methods are non-traditional stochastic search and optimization methods and they are very suitable and powerful in obtaining the solution of combinatorial optimization problems. They do not require the derivatives of the objective function and constraints and they use probabilistic transition rules not deterministic rules.
Among these; genetic algorithm mimics the survival of the fittest to establish a numerical search algorithm. In the immune system algorithm, a population of antibodies is evolved to cover a set of antigens. It has been discovered that ants, while being completely blind, can successfully commute between their nest and food sources by following the shortest path. Ant colony optimization algorithm simulates this behaviour of ants with the addition of several artificial parameters. At high temperature, the atoms in the molten metal can move freely with respect to each other, but as the temperature is reduced, the movement of the atoms becomes restricted. In order to achieve the absolute minimum energy state, the temperature needs to be reduced at a slow rate. Simulated annealing algorithm imitates this phenomenon. Particle swarm optimization is a population based stochastic optimization technique that is inspired by the social behaviour of bird flocking or fish schooling. One of the recent additions to these techniques is the harmony search algorithm. This approach is based on the musical performance process that takes place when a musician searches for a better state of harmony. In this paper a review of structural optimization techniques that are based on stochastic search algorithms is carried out.