The European Green Deal calls for rapid decarbonization of the building and transport sectors, which together represent the largest share of Europe s greenhouse gas emissions. Heat pumps (HPs) and electric vehicles (EVs) are key to this transition, but when operated independently, they risk exacerbating evening demand peaks and straining the grid. Coordinated scheduling is therefore critical to unlock their full flexibility potential. This study applies the Non-dominated Sorting Genetic Algorithm II (NSGA-II), a multi-objective optimization method, to coordinate the operation of air-source HPs, bidirectional EVs, and photovoltaic (PV) generation. The model simultaneously minimizes electricity costs under time-of-use pricing, reduces CO2 emissions using time-varying carbon intensity, and smooths net load variability to mitigate grid impacts. Simulations use real household data from a cold-climate region (Dresden), focusing on representative cold and average days where heating demand strongly drives electricity consumption and emissions. Results show that NSGA-II identifies diverse operational schedules that balance competing objectives, enabling households or operators to prioritize cost, emissions, or grid stability. Coordinated control delivers cost savings and emission reductions, particularly during high-demand winter evenings. Overall, the framework demonstrates that residential flexibility can support decarbonization and enhance grid stability without requiring major infrastructure upgrades.