Keywords: structural optimization, stochastic search methods, combinational optimization, harmony search algorithm, steel frames, design to BS5950.

The design steel frames requires the selection of steel sections for its members from a discrete set of practically available steel profiles. This selection should be carried out in such way that the structure has the minimum weight or cost while the behaviour and performance of the structure is within the limitations described by the code of practice. Such structural decision making problems fall into the subject of discrete optimization in which finding the optimum solution is a difficult task. Early optimum design algorithms based on a wide range of powerful mathematical programming methods have failed to satisfy the needs of practicing engineers. Integer programming, branch and bound algorithm and dynamic programming methods are some of these techniques that are used in the discrete optimum design of steel structures. However, practical applications of these algorithms have shown that they are not very efficient for the optimum design of large size steel structures.

In recent years, structural optimization has witnessed the emergence of novel and innovative design techniques. These stochastic search techniques make use of ideas taken from the 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, the cooling process of molten metals through annealing and finding the shortest path between the nest and food source of ant colonies in a numerical algorithm. These methods are non-traditional 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. 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. Jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find the optimum solution.

In this study the harmony search based optimum design algorithm is presented that determines the optimum sectional designations for the members of a steel frame. The behavioural and performance limitations are imposed according to BS5950. The objective function is taken as the minimum weight. The list of Universal Beam and Universal Column sections is considered from which the algorithm selects the steel sections for the frame members. The member grouping is allowed so that the same section can be adopted for each group. The combined strength constraints are considered for beam-columns that requires consideration of the lateral torsional buckling constraints. It is shown that the harmony search based optimum design algorithm is a robust and efficient approach in obtaining the optimum solution. A number of design examples is considered to demonstrate the application of the algorithm.

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