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DG integration improves distribution network performance and also enables microgrid (MG) formation for islanded operation. However, existing studies assume an isolated operation approach for islanded mode, which is unrealistic and increases overall system costs while adding complexity to the grid. This paper presents a dual-stage methodology for the efficient operation of distributed generation (DG) and shunt capacitor banks (SCBs) in radial distribution networks (RDNs) for both grid-integrated and islanded modes. The first stage proposes an improved Jaya algorithm (IJaya) to optimize DG and SCB allocation during grid-connected operation, aiming to reduce power loss and improve voltage profiles. IJaya employs a dynamic weight-based grid search to address premature convergence. The second stage formulates a multiobjective function for the islanded operation to minimize power loss and underutilization of DG-SCB capacity. Case studies on IEEE 33- and 69-bus RDNs show IJaya reduces power loss by 38.84 % and improves voltage by 3.26 % in grid-connected networks compared to existing methods. The proposed analytical approach for islanded operation tunes the source power factor, reducing DG-SCB underutilization by up to 15.83 % for power factors between 0.8 and 0.93. The results demonstrate that operating distributed resources near optimal capacities meets a larger portion of the island network's energy needs.