Keywords: structural optimization, grillage systems, combinational optimization, harmony search algorithm, steel structures.

In recent years, structural optimization witnessed the emergence of novel and innovative design techniques. These stochastic search techniques 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 nontraditional 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 the genetic algorithm mimics the survival of the fittest to establish a numerical search algorithm. It initiates the search for the fittest among the potential candidates that are randomly selected to form an initial population. The binary or any other type of coding is used to express the location number of the available sections within the list of practical sections for each design variable. By collecting these binary codes together for all the design variables a potential candidate is obtained for the solution of the optimum design problem. The genetic algorithm produces a new population from the initial population using a number of operators and it continues this process of generating populations with the expectation of reaching if not the fittest but a better individual who represents the optimum solution.

In the immune system algorithm, a population of antibodies is evolved to cover a set of antigens. Binary strings are proposed to model both antibodies and antigens. Similar to genetic algorithm, a random population is generated. After computing objective function values and a cumulative measure of constraint violations, feasible and infeasible individuals are separated. A number of feasible individuals are selected and called the antigen population. The infeasible individuals are subject to an immune system simulation, generating antibodies to the antigen population. The idea is to adapt infeasible solutions to current feasible solutions.

Ant colony optimization method is based on the simulation of swarm intelligence. It has been discovered that ants while being completely blind, can successfully commute between their nest and food sources by following the shortest path. When an ant travels, it leaves a chemical called pheromone along its path. A single ant initially moves randomly. But the ant comes after attempts to follow the path which has more pheromone deposited on it. While traveling along this path, it also lays additional pheromone on the path. This increases the amount of the pheromone which in turn increases the probability that any other ant from the colony will follow this path. Eventually after sometime, the colony moves on the shortest path between the nest and the food source. The ant colony optimization algorithm simulates this behavior of ants with addition of several artificial parameters.

The simulated annealing initiates the cooling process of molten metals through annealing. 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 starts being restricted. They slowly get ordered and finally form crystals having minimum potential energy. If the temperature is reduced at a very fast rate, the crystalline state may not be achieved at all; instead the system may end up in a polycrystalline state which may have a higher energy state than the crystalline state. Therefore, 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.

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. The pitch of each musical instrument determines the aesthetic quality, just as the objective function value is determined by the set of values assigned to each decision variable. In this study the harmony search algorithm is used to determine the optimum sectional designations of grillage systems which are widely utilized in bridge decks, ship hulls and in floors. The behavioral and performance limitations are imposed according to the LRFD-AISC standard. The objective function is taken as the minimum weight. The list of WF steel section is considered for the grillage members to be selected from. The harmony search algorithm first initializes the harmony memory by randomly generated solution vectors. A new harmony vector is obtained from the harmony memory consideration, pitch adjustment and randomization. If the new harmony vector is better than the worst harmony memory judged in terms of the objective function value, the new harmony is included in the memory instead of the existing worst harmony vector. These steps are separated until a termination criterion is satisfied. The algorithm is quite simple but efficient in obtaining optimum solutions. A number of design examples is considered to demonstrate the application of the algorithm.

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