In this work, a novel framework for optimal cooperative supervisory estimation of multi-agent linear time-invariant (LTI) systems is proposed which is applicable to a large class of multi-agent systems. This framework was recently developed by the authors based on the notion of sub-observers and a discrete-event system (DES) supervisory control. Each sub-observer estimates certain states that are conditioned on given inputs, outputs, and states information. Moreover, the cooperation among the sub-observers is managed by a DES supervisor. In this work, our proposed supervisory estimation framework is extended to the combinatorial optimization domain. When certain anomalies (faults) are present in the system, or the sensors and sub-observers become unreliable, the proposed optimal DES supervisor makes decisions regarding the selection and reconfiguration of sets of sub-observers to estimate all the system states, while simultaneously a performance index that incorporates the communication cost, computation cost, and reconfiguration cost, and the number of invalid state estimates is minimized. The application of our proposed methodology in a practical industrial process is demonstrated through numerical simulations.