This study introduces a mixed-integer second-order conic programming (MISOCP) model for the effective management of load and energy in active distribution networks featuring prosumers. A multi-objective function is devised to concurrently minimize various costs, including prosumer electricity costs, network energy loss costs, load shedding costs, and costs associated with renewable energy resource outages. The methodology involves determining optimal active power adjustment points for photovoltaic (PV) resources and integrated energy storage systems (ESSs) within network buildings, in conjunction with a demand-side management program. To achieve the optimal solution for the proposed MISOCP model, a robust hybrid algorithm is presented, integrating the modified particle swarm optimization (MPSO) algorithm and the genetic algorithm (GA). This algorithm demonstrates a heightened capability for efficiently converging on challenging problems. The proposed model is evaluated using a distribution network comprising 33 buses, a practical distribution network, and a distribution network comprising 118 buses. Through comprehensive simulations in diverse cases, the results highlight the innovative contributions of the model. Specifically, it achieves a noteworthy reduction of 26.2% in energy losses and a 17.72% decrease in voltage deviation. Additionally, the model proves effective in augmenting prosumer electricity sales, showcasing its potential to improve the overall efficiency and sustainability of active distribution networks.