Problems in the control and identification of structural dynamic systems can lead to multimodal optimization problems, which are difficult to solve using classical gradient based methods. In this work, optimization problems pertaining to the vibration control of smart structures and the exploration of isospectral systems are addressed. Isospectral vibrating systems have identical natural frequencies, and existence of the isospectral systems proves non-uniqueness in system identification. For the smart structure problem, the optimal location(s) of collocated actuator(s)/sensor(s) and the optimal feedback gain matrix are obtained by maximizing the energy dissipated by the feedback control system. For the isospectral system problem, both discrete and continuous systems are considered. An error function is designed to calculate the error between the spectra of two distinct structural dynamic systems. For the discrete system, the Jacobi matrix, derived from the given system, is modified and the problem is posed as an optimization problem where the objective is to minimize the non-negative error function. Isospectral spring-mass systems are obtained. For the continuous system, finite element modeling is used and an error function is designed to calculate the error between the spectra of the uniform beam and the non-uniform beam. Non-uniform cantilever beams which are isospectral to a given uniform cantilever beam are obtained by minimizing the non-negative error function. Numerical studies reveal several isospectral systems, and optimal gain matrices and sensor/actuator locations for the smart structure. New evolutionary algorithms, which do not need genetic operators such as crossover and mutation, are used for the optimization. These algorithms are: Artificial bee colony (ABC) algorithm, Glowworm swarm optimization (GSO) algorithm, Firefly algorithm (FA) and Electromagnetism inspired optimization (EIO) algorithm.