Benefits of Implicit Redundant Representation Genetic Algorithms in Solving Conceptual Design, Damage Identification, and Sensor Layout Inverse Problems

1. Abstract Solving large-scale inverse problems in structural design, damage identification, and sensor layout using multi-objective genetic algorithm optimization methods requires the use of advanced representations. The implicit redundant representation (IRR) provides a flexible encoding that has shown significant benefits in solving 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, like introns in biological genes. The encoded variable locations and values are able to dynamically change and selforganize during search through selection, crossover, and mutation. In searching for the optimal form of the structure 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. The benefit provided is the broad range of designs that can be evaluated during a single search process. The Pareto-optimal sets of designs that are generated using the IRR also serve to define the tradeoffs that occur in meeting the objectives as the topology and geometry of the structure changes. In damage detection, optimization is often used to try to determine the location and extent of damaged elements using collected measurement data. The IRR is able to work with only a small subset of all possible damaged elements during the search process, which allows the optimization method to scale better with problem size. In addition, searching for near-optimal sensor layouts to use to collect measurement information requires the ability to represent solutions having different numbers of sensors in the same genetic algorithm population. The flexibility provided by the IRR is again beneficial in evolving Pareto-optimal sets of layouts that define the tradeoff between maximizing information collected versus minimizing the number of sensors. The genetic algorithm representations discussed hold significant promise in enhancing ability to solve large-scale inverse problems by providing the benefit of working with a variable number of design variables. This flexibility can be leveraged to reduce the implicit size of the problem optimized or to compare designs that have markedly different forms or layouts. 2.