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A methodology for topology and performance redesign of complex structures by LargE Admissible Perturbations (LEAP) has been developed since 1983 in the Department of Naval Architecture and Marine Engineering, the University of Michigan. LEAP theory has successfully solved various redesign problems for performance and simultaneous topological and performance changes. The redesign problem is defined as a two-state problem that consists of two structural states, States S1 and S2. State S1 has undesirable characteristics or performance which does not satisfy designer specifications. The unknown State S2 has the desired structural response and/or performance. The relation between State S1 and State S2 is highly nonlinear with respect to its response or topology. So far, LEAP algorithms have solved various redesign problems for large structural changes (on the order of 100%–500%) of State S1 with only one finite element analysis.