Optimum Design of Concrete Cantilever Retaining Walls using the Harmony Search Algorithm

Optimum cost design of reinforced concrete cantilever retaining walls with harmony search algorithm is presented in this paper. The reinforced concrete cantilever retaining wall is the most common type among the retaining wall structures. In the formulation of the optimum design problem the height and thickness of stem, length of toe projection and the thickness of stem at base level, the length and thickness of base, the depth and thickness of key and the distance from toe to the key are treated as design variables. The values of these design variables are required to be selected from a design pool due to practical reasons which contains list of discrete numbers starting from the minimum value and increasing with a certain increment up to the maximum value for each variable. The design constraints are implemented according to the provisions of ACI 318-05. The optimum design satisfies the factor of safety for failure modes, strength, serviceability and other required limitations to attain practically acceptable shapes. The main target of the problem is to explore the conditions supporting the backfill safely, and to ensure that both the structure and the soil surrounding do not fail and that the deformations take place are within acceptable limits. The objective function is taken as the overall cost of the retaining wall. The optimum design problem formulated according to ACI 318-05 turns out to be a discrete programming problem. The solution of the design problem is obtained by using the harmony search algorithm (HS) which is one of the recent additions to metaheuristic techniques. The HS algorithm does not require any initial values for the design variables and uses a random search instead of a gradient search, so derivative information is unnecessary. In addition, harmony search algorithm uses few parameters which are initially specified and consists of simple steps which make it easy to implement. Number of design examples are presented to demonstrate the efficiency and robustness of the algorithm presented.