Due to rapid population growth, technology, and economic development, electricity demand is rising, causing a gap between energy production and demand. With the emergence of the smart grid, residents can schedule their energy usage in response to the Demand Response (DR) program offered by a utility company to cope with the gap between demand and supply. This work first proposes a novel optimization-based energy management framework that adapts consumer power usage patterns using real-time pricing signals and generation from utility and photovoltaic-battery systems to minimize electricity cost, to reduce carbon emission, and to mitigate peak power consumption subjected to alleviating rebound peak generation. Secondly, a Hybrid Genetic Ant Colony Optimization (HGACO) algorithm is proposed to solve the complete scheduling model for three scenarios: without photovoltaic-battery systems, with photovoltaic systems, and with photovoltaic-battery systems. Thirdly, rebound peak generation is restricted by using Multiple Knapsack Problem (MKP) in the proposed algorithm. The presented model reduces the cost of using electricity, alleviates the peak load and peak-valley, mitigates carbon emission, and avoids rebound peaks without posing high discomfort to the consumers. To evaluate the applicability of the proposed framework comparatively with existing frameworks, simulations are conducted. The results show that the proposed HGACO algorithm reduced electricity cost, carbon emission, and peak load by 49.51%, 48.01%, and 25.72% in scenario I; by 55.85%, 54.22%, and 21.69% in scenario II, and by 59.06%, 57.42%, and 17.40% in scenario III, respectively, compared to without scheduling. Thus, the proposed HGACO algorithm-based energy management framework outperforms existing frameworks based on Ant Colony Optimization (ACO) algorithm, Particle Swarm Optimization (PSO) algorithm, Genetic Algorithm (GA), Hybrid Genetic Particle swarm Optimization (HGPO) algorithm.