An apparatus and method is disclosed for solving optimization problems without the need to build mathematical models or rules. The inventive method combines the structure of a single-loop feedback control system and optimization search engine mechanisms. Running in real-time, a Model-Free Adaptive (MFA) optimizer can automatically search for the optimal operating point for a dynamic system when a parabolic relationship exists between the input and output. The MFA optimizer comprises a user-selected Min/Max setter to define the searching objective, a process acting-mode search engine to determine if the process is running in direct-acting or reverse-acting mode, a maximum search engine and a minimum search engine to find the maximum or minimum. This apparatus and method is useful in fuel-and-air ratio optimization for combustion processes, yield optimization for chemical or biological reactors, and operating efficiency optimization for coal or ore ball mills.