This paper considers the optimal placement of collocated piezoelectric actuator–sensor pairs on flexible beams using a model-based linear quadratic regulator (LQR) controller. A finite element method based on Euler–Bernoulli beam theory is used. The contributions of piezoelectric sensor and actuator patches to the mass and stiffness of the beam are considered. The LQR performance is taken as the objective for finding the optimal location of sensor–actuator pairs. The problem is formulated as a multi-input multi-output (MIMO) model control. The discrete optimal sensor and actuator location problem is formulated in the framework of a zero–one optimization problem which is solved using genetic algorithms (GAs). Classical control strategies like direct proportional feedback, constant gain negative velocity feedback and the LQR optimal control scheme are applied to study the control effectiveness. The study of the optimal location of actuators and sensors is carried out for different boundary conditions of beams like cantilever, simply supported and clamped boundary conditions.