This work proposes a metaphor-less and algorithm-specific parameter-less algorithm, named as self-adaptive population Rao algorithm, for solving the single-, multi-, and many-objective optimization problems. The proposed algorithm adapts the population size based on the improvement in the fitness value during the search process. The population is randomly divided into four sub-population groups. For each sub-population, a unique perturbation equation is randomly allocated. Each perturbation equation guides the solutions toward different regions of the search space. The performance of the proposed algorithm is examined using standard optimization benchmark problems having different characteristics in the single- and multi-objective optimization scenarios. The results of the application of the proposed algorithm are compared with those obtained by the latest advanced optimization algorithms. It is observed that the results obtained by the proposed method are superior. Furthermore, the proposed algorithm is used to identify optimum design parameters through multi-objective optimization of a fertilizer-assisted microalgae cultivation process and many-objective optimization of a compression ignition biodiesel engine system. From the results of the computational tests, it is observed that the performance of the self-adaptive population Rao algorithm is superior or competitive to the other advanced optimization algorithms. The performances of the considered bio-energy systems are improved by the application of the proposed optimization algorithm. The proposed optimization algorithm is more robust and may be easily extended to solve single-, multi-, and many-objective optimization problems of different science and engineering disciplines.