An integrated genetic algorithm complemented with direct search for optimum design of RC frames

Abstract

This paper presents an improved optimum design method for reinforced concrete (RC) frames using an integrated genetic algorithm (GA) with a direct search method. A conventional genetic algorithm occasionally has limitations due to a low convergence rate in spite of high computing times. The proposed method in this research uses a predetermined section database (DB) when determining trial sections for the next iteration.

From an initial section determined by substituting calculated member forces into a regression formula, a direct search that determines a final discrete solution is followed within a limited range in the section database. Due to the fast convergence and the sequential determination of feasible trial sections close to the final optimum solution, an introduction of the search procedure at each iteration allows difficulties to be solved during the application of a conventional GA to large RC structures.

Finally, the effectiveness of the introduced design procedure is verified through correlative tests of the introduced design procedure.

Introduction

Mathematical programming methods such as the Lagrangian multipliers method [1], linear programming [2], [3] and sequential unconstrained minimization techniques [3] are typically used in the optimal design of structural members. Considerable progress has been made in this area [4].

However, numerous design variables in a reinforced concrete (RC) section, including the dimensions of the section, the steel bar area, the cover thickness, and the clear distance between the steel bar, etc. makes the solution procedure much too complex [5]. Additionally, the optimal design of RC members also requires a user to take into account the practical limitations in the dimensions of the concrete sections and the sizes of the steel bars [6].

As a solution for the difficulties in the design of large complex RC structures, a simple but effective algorithm was introduced. On the basis of section database [7], this produces a practical optimum design while complying with the mentioned restrictions. In parallel with the algorithm, a direct search method, which is composed of two steps of determining a continuous solution and finding the final discrete solution within the database, was also proposed. Its efficiency was verified by comparing the obtained results with those from previous work [5].

Nevertheless, to achieve a global optimum solution at the structural level regardless of the change in the initial trial sections, it is necessary to include a global minimization algorithm such as a design sensitivity analysis [8]. This algorithm is especially required when the member forces are determined on the basis of a nonlinear structural analysis considering plastic deformation and the accompanying force redistribution [9]. An introduction of a genetic algorithm (GA) [10], [11], [12] has been used as part of this effort. And as a resultant, successful applications to small structures have been reported [5].

However, a direct application of a conventional genetic algorithm usually causes a very high computational burden induced from too much iteration. So that a lot of complementary approaches to overcome this weakness are introduced by combining the genetic algorithm with a neural network [13], [14], a nonlinear programming method, or a Hook and Jeeves’ method [15]. Nevertheless, it is also true that the application of the genetic algorithm is occasionally accompanied by a decrease in the reliability of the results. This aspect is due to the inherent difficulties in each procedure.

Accordingly, to cope with the abovementioned difficulties in applying GA and to elevate both the convergence together with the fitness of solution, this paper introduces an improved optimum design method. Both the convergence and the fitness of solution are used as a measure for the efficiency of the algorithm. This proposed algorithm uses GA complemented with a direct search within predetermined design section database.

The use of a predetermined section database in which all of the geometric constraints of the section are already considered beforehand during the construction of the database simplifies the iteration procedure. This database makes it possible to select all feasible sections for the next iteration, because these trial sections are determined in the feasible region.

This implies that the proposed method provides a considerable improvement for the stability of the design procedure and the convergence speed. The efficiency of the proposed method is verified through correlation studies between the design results and those obtained by other approaches.