Chapter 9 Applying the Implicit Redundant Representation Genetic Algorithm in an Unstructured Problem Domain A.M. Raich and J. Ghaboussi Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign Urbana, IL 61801

9.1 Introduction An evolutionary-based method called the implicit redundant representation genetic algorithm (IRR GA) is applied to evolve synthesis design solutions for an unstructured, multi-objective frame problem domain. The synthesis of frame structures presents a design problem that is difficult, if not impossible, for current design and optimization methods to formulate, let alone search. Searching for synthesis design solutions requires the optimization of structures with diverse structural topology and geometry. The topology and geometry define the number and the location of beams and columns in the frame structure. As the topology and geometry change during the search process, the number of design variables also changes. To support the search for synthesis design solutions, an unstructured problem formulation that removes constraints that specify the number of design variables is used. Current optimization methods, including the simple genetic algorithm (SGA) are not able to model unstructured problem domains since these methods are not flexible enough to change the number of design variables optimized. The unstructured domain can be modeled successfully using the location-independent and redundant IRR GA representation. The IRR GA uses redundancy to encode a variable number of locationindependent design variables in the representation of the problem domain. During evolution, the number and location of the encoded variables dynamically change within each individual and across the population. The IRR GA provides several benefits: redundant segments protect existing encoded design variables from the disruption of crossover and mutation; new design variables may be designated within previously redundant segments; and the dimensions of the search space dynamically change as the number of design variables represented changes (Raich & Ghaboussi, 1997). The IRR GA synthesis design method is capable of generating novel frame designs that compare favorably with solutions obtained using a trial-and-error design process (Raich & Ghaboussi, 1999).