This paper proposes a modified version of a contemporary metaheuristic named Harris Hawks Optimizer (HHO) that mimics the foraging strategies used by Harris hawks. It is first argued that exploration ability of HHO is weaker than its exploitation. In addition, the initial position of hawks has the greatest impact on the convergence of the solutions in a similar manner to other metaheuristic algorithms. Then, we applied the Fractional-Order Gauss and 2xmod1 Chaotic Maps to generate the initial population as well as applying the operators of the Moth-Flame Optimization (MFO) to improve the exploration of HHO. In addition, the concept of evolutionary Population Dynamics (EPD) is applied to prevent premature convergence and stagnation in local optima. The method proposed in this work is called FCHMD and evaluated using a set of thirty-six mathematical functions and five engineering problems. The results of the FCHMD are compared with a number of well-known metaheuristics. It can be observed that the FCHMD algorithm outperforms its competitors on the majority of case studies.