OPTIMUM DESIGN OF ROOF TRUSSES BY GENETIC ALGORITHMS

Abstract

Abstract : Structural design is a process by which the optimum solution is sought. In any design, certain criteria must be established to evaluate whether or not the optimum has been achieved. The design of a steel roof truss, in particular, involves making decisions about its topology, geometry, steel sections to be used for its members, and the spacing between trusses. All of these must be selected so that the final truss must be capable of resisting the loads that may act during its life and that the truss must be economical to produce. This decision-making problem, when formulated as a programming problem, turns out to be a nonlinear programming problem in which some of the design variables are discrete in nature while others are continuous. There are a vast number of algorithms developed in the past to obtain the solution to structural optimization problems where the design variables are selected from a continuous set. However, the optimum solutions obtained with these methods are not of interest to the practicing engineer. This is due to the fact that the design variables are usually discrete in nature. This necessitates considering this feature of the design parameters in the solution techniques to be developed. Certainly, there are a number of algorithms as well that can be used to solve structural optimization problems where the design variables are selected from a discrete set. However, these are cumbersome and require tedious computer programming The genetic algorithm is a comparatively recent addition to optimization methods that is quite suitable for use in structural design due to its ability to handle discrete design variables. These algorithms are search procedures based on the mechanics of natural selection and natural genetics. They apply the natural law of survival of the fittest to structural optimization. They initiate a search with an initial population consisting of a set of artificial creatures representing each possible design for the structure. The algorithm moves from one generation to another, during which some individuals are allowed to die while others are allowed to multiply. This is achieved by generating new individuals from the bits and pieces of the fittest of the old, occasionally adding new parts for good measures. This is performed through the three random genetic operators of reproduction, crossover, and mutation. Although genetic algorithms are randomized, they are not simple random walks. They efficiently exploit historical information to speculate on new search points, with expected improved performance. Their simplicity in approach and directness in discrete variables make them attractive compared to more mathematically complex methods. In this study, a genetic algorithm-based optimum design method is developed for roof trusses subjected to multiple loading cases. The algorithm obtains the roof truss with the minimum weight by selecting appropriate steel sections from available section tables while satisfying the design limitations given in BS5950. The design constraints in the design problem are implemented directly from the code. The algorithm has three versions. In the first, the optimum angle section designations are found for the truss members while the geometry and spacing between the trusses are kept fixed. In the second, the apex height is treated as a design variable in addition to member sizes. The third one considers the spacing between the trusses also as an additional design variable. In all these versions, the genetic algorithm has successfully obtained the optimum solution The design algorithm developed is applied to find the optimal solution of four different design problems in each seven different topologies is considered for the roof truss. In the first, the geometry and spacing are kept fixed and optimum equal leg angle designations are obtained for each roof truss topology. In the second the spacing is also made variable while the geometry is kept fixed. It is found that saving was possible in the overall weight of the roof if the spacing is made a variable design. In the third, the height of apex is treated as variable allowing the geometry to change while the spacing is kept fixed. In the fourth, the height of apex and the spacing are taken as variables in addition to member designations. It is shown that the latter yields to the lightest structure for the roof. It is shown that up to 15% savings was possible in the lightest topology when height and spacing are treated as variable as compared to fixed geometry and spacing. The genetic algorithm generally obtained the optimal solution efficiently for the design problems where the height and spacing are fixed. However when those were taken as design variables, it becomes necessary to rerun the program few times to detect the optimal solution. For the geometrical and topological design problems, the genetic algorithm has the tendency to settle down with the local optimum.