In this paper, a multiobjective and simultaneous two-problem allocation of a hybrid distributed generation (HDG) system comprises of solar panels, wind turbines, and battery storage is proposed in a 33-bus unbalanced distribution network which can decrease total losses and improve power quality (PQ). The PQ indices are defined as voltage swell, total harmonic distortion, voltage sag, and voltage unbalance. In this study, the two problems of hybrid system design and its allocation in the distribution network are solved simultaneously. In the allocation problem, the HDG is placed ideally in the network to reduce energy losses and enhance PQ indices. The HDG is measured to minimize the cost of energy generation, including the initial investment, maintenance, and operation costs. The decision variable including the size of HDG components and its location is optimally determined via escaping bird search (EBS) algorithm which is inspired by the maneuvers of the swift bird to avoid predation. The results cleared that the proposed methodology using the wind and solar resources integrated with battery storage reduced the losses, voltage swell, total harmonic distortion, voltage sag, and voltage unbalance by 34.31%, 49.60%, 0.25%, 40.19%, and 2.18%, respectively, than the base network via the EBS and the results demonstrated the better network performance using all renewable resources against wind or solar application only. The outcomes demonstrated the superiority of the EBS in achieving the highest improvement of the different objectives compared with particle swarm optimization (PSO) and manta ray foraging optimization (MRFO). Moreover, the superior capability of the EBS-based methodology is proved in comparison with previous studies.