Voltage collapse tends to occur due to the voltage instability created during large faults. As a last resort, undervoltage load shedding (UVLS) is performed after all the available power operation and control mechanisms have been exhausted. Load shedding techniques have advanced from the conventional and adaptive methods that are less optimal compared to computational intelligence-based techniques. Recent works have identified hybrid algorithms to give more optimal solutions for UVLS problems with multi-objective functions. In this paper, a novel hybrid ABC-PSO algorithm, adapted from a software estimation project, is used to perform UVLS on a modified IEEE 14-bus system. Eight overload conditions are imposed on the system ranging from 105% to 140% loading, where FVSI ranking is used in identifying weak buses. The load shedding is then performed following decentralized relay settings of 3.5 seconds, 5 seconds and 8 seconds, which gives an overall 99.32% recovery of voltage profiles. The proposed hybrid ABC-PSO algorithm is able to shed optimal amounts of load, giving an 89.56% postcontingency load, compared to GA's 77.04%, ABC-ANN at 84.03% and PSO-ANN at 80.96%. This study has been simulated on MATLAB software, using the Power System Analysis Toolbox (PSAT) graphical user and commandline interfaces.