The Combined Heat and Power Economic Dispatch (CHPED) is a real-world optimization problem with several complex constraints that has been a topic of studies around energy systems and optimization processes. This paper attempts to conceptualize a potent algorithm by combining the Modified Grasshopper Optimization Algorithm (MGOA) and the Improved Harris Hawks Optimizer (IHHO) for attaining a better balance between the beginning stages of global search and the latter stages of global convergence. The proposed attempt is abbreviated as MGOA-IHHO. Firstly, the chaotic and Opposition-Based Learning (OBL) methods are invoked to generate the initial population. Second, the mathematical model of the conventional Grasshopper Optimization Algorithm (GOA) is modified using Sine–Cosine Acceleration Coefficients (SCAC) to simulate the global exploration at the initial iterations and graduating to the global convergence at the final stages of optimization. Hence, it is named MGOA. Finally, the adaptive search mechanism integrates the two improved search phases of HHO with a search phase of MGOA to improve the performance of the proposed optimization method. This mechanism investigates the best solution for the aging level of the individual during the optimal evaluation process for choosing an appropriate search phase in MGOA-IHHO. The intended effect of the proposed MGOA-IHHO method is verified with other nature-inspired methods on standard single-objective test functions including 23 benchmark problems, 30 test suits of IEEE Congress on Evolutionary Computation 2017 (CEC2017), and four CHPED problems. The statistical results ascertain that the proposed hybridized MGOA-IHHO is capable of providing promising results when compared with its variants and optimization algorithms introduced in the literature.