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Solving large-scale structural design and damage identification problems using genetic algorithm optimization methods requires the use of advanced representations. The flexible implicit redundant representation (IRR) provides significant benefits for inverse problems in which the solution involves determining the optimal number of design variables, in addition to their values. The IRR encodes both variables and redundant segments in each individual. The encoded variable locations and values dynamically change and self-organize through crossover and mutation during optimization. In searching for optimal structural forms in conceptual design, the IRR provides the flexibility to represent designs having different numbers and locations of members and nodes, which supports the simultaneous optimization of topology, geometry, and member sizes. Therefore a broad range of designs can be evaluated during a single trial. The set of Pareto-optimal designs evolved by the IRR define the tradeoffs that occur in optimizing the objectives as the structural topology and geometry changes. In damage detection, optimization is often used to predict the location and extent of damages based on the structural response collected from measurement data. The IRR can work with a small subset of all possible damaged elements during the search process, which allows the method to scale well with problem size. The IRR genetic algorithm representation discussed holds significant promise in solving large-scale inverse problems by providing the benefit of working with a variable number of design variables. This flexibility is leveraged to reduce the implicit size of the problem domain searched and to compare designs having markedly different forms or topologies.