The large-scale integration of renewable energy sources (RESs) and electric vehicles (EVs) has significantly increased the operational uncertainty, nonlinearity, and dimensionality of modern power systems, thereby challenging the effectiveness of conventional deterministic optimal power flow (OPF) techniques. To address these challenges, probabilistic optimal power flow (POPF) has emerged as a reliable framework capable of explicitly modeling the stochastic behavior of renewable generation and flexible EV loads while ensuring secure and economical system operation. In this paper, a novel hybrid multi-objective POPF framework is proposed by coupling an Artificial Bee Colony (ABC) algorithm enhanced with Adaptive Neighborhood Search (ANS) and Gaussian Perturbation (GP) strategies with the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The proposed framework simultaneously minimizes total fuel cost and pollutant emissions under AC power flow equality constraints and practical operational limits. Uncertainties associated with wind speed, solar irradiance, and EV charging/discharging behaviors are modeled using appropriate probability density functions, enabling a realistic representation of intermittency and demand-side flexibility. In addition, Flexible AC Transmission System (FACTS) devices, namely the Thyristor Controlled Series Compensator (TCSC) and Thyristor Controlled Phase Shifter (TCPS), are optimally incorporated to enhance voltage regulation, reduce transmission congestion, and improve overall system security. The hybrid ABC–ANS–GP mechanism strengthens global exploration through adaptive neighborhood control, while Gaussian perturbations effectively mitigate premature convergence in high-dimensional search spaces. The embedded NSGA-II ensures robust Pareto dominance ranking and diversity preservation, resulting in well-distributed and convergent trade-off solutions. The effectiveness of the proposed approach is evaluated on the IEEE 57-bus test system under three study scenarios: conventional POPF, POPF with RES and EV integration, and POPF with combined RES, EV, and FACTS deployment. Comparative analyses against the recently reported Quasi-Oppositional Artificial Hummingbird Algorithm (QOAHA) demonstrate that the proposed framework achieves an average reduction of 7–10% in total generation cost, a 9–13% emission reduction, and a 15–25% improvement in convergence speed. Furthermore, statistical assessments over multiple independent trials reveal a 35–45% reduction in solution dispersion, confirming superior robustness and consistency under uncertainty. These results validate the proposed framework as a scalable and effective solution for large-scale, uncertainty-aware, multi-objective power system optimization.