With the smart grid development, the modern electricity market is reformatted, where residential consumers can actively participate in the demand response (DR) program to balance demand with generation. However, lack of user knowledge is a challenging issue in responding to DR incentive signals. Thus, an Energy Management Controller (EMC) emerged that automatically respond to DR signal and solve energy management problem. On this note, in this work, a hybrid algorithm of Enhanced Differential Evolution (EDE) and Genetic Algorithm (GA) is developed, namely EDGE. The EMC is programmed based with EDGE algorithm to automatically respond to DR signals to solve energy management problems via scheduling three types of household load: interruptible, non-interruptible, and hybrid. The EDGE algorithm has critical features of both algorithms (GA and EDE), enabling the EMC to generate an optimal schedule of household load to reduce energy expense, carbon emission, Peak to Average Ratio (PAR), and user discomfort. To validate the proposed EDGE algorithm, simulations are conducted compared to the existing algorithms like Binary Particle Swarm Optimization (BPSO), GA, Wind Driven Optimization (WDO), and EDE. Results illustrate that the proposed EDGE algorithm outperforms benchmark algorithms in energy expense minimization, carbon emission minimization, PAR alleviation, and user discomfort maximization.