A coordinated optimization framework that integrated the price–incentive collaborative demand response (PIC-DR) mechanism and the improved dream optimization algorithm (IDOA) was proposed to address scheduling challenges caused by renewable energy volatility and the demand response in microgrids. First, a dual-track demand response mechanism was designed, that is, time-of-use pricing-guided load shifting, while dynamic incentive compensation enhanced user participation, thereby establishing a scheduling architecture that balanced economic efficiency with response reliability. Next, IDOA was introduced, incorporating a logistic map chaos perturbation mechanism to strengthen its global search capability and an adaptive dream-intensity strategy to balance exploration and exploitation, which significantly improved solution efficiency for high-dimensional constrained problems. Finally, the framework was validated using sensor-measured data from a residential microgrid in North China under gradient-based participation scenarios (0, 50, and 100%). The results demonstrated that, on the CEC test functions F8–F13, IDOA improved convergence accuracy by one to three orders of magnitude compared with traditional algorithms. Under full demand response participation, operational costs decreased by 27.5% and the peak-to-valley load difference decreased by 41.2%. The PIC-DR mechanism achieved a peak load shift of 18.7% through dynamic incentives, effectively mitigating renewable energy volatility. The study thus provided an economically efficient scheduling paradigm for microgrids with high renewable energy penetration.