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Encouraging households to spread electricity use throughout the day, aggregated shifting can lower coincident peaks and ease stress on urban grids. This elevates home energy management systems (HEMS) as a key enabling technology, since sustained peak reduction often requires coordinated control of household distributed energy resources (DERs). However, existing HEMS approaches face two major limitations. First, they inadequately accommodate heterogeneous occupant preferences, limiting occupant-centric scheduling, where energy should be dispatched to balance multiple and conflicting objectives while maintaining comfort. Second, they rarely incorporate photovoltaic (PV) generation uncertainty into occupant-centric scheduling; when multiple competing objectives and tightly coupled constraints are optimized simultaneously, forecast errors can lead to infeasible schedules, unexpected peak demand, and comfort violations. To address these challenges, this paper proposes a stochastic, many-objective, occupant-centric HEMS framework that explicitly represents PV generation uncertainty while accommodating and balancing heterogeneous occupant constraints and priorities. A case study of a Swedish detached house considers four occupant-oriented criteria: cost savings, environmental impact, energy autonomy, and peak-load mitigation. The results demonstrate that the proposed framework generates more robust schedules than the deterministic framework, reducing the mean absolute error by 33.3 %. Moreover, under equally weighted objectives, it outperforms the rule-based strategy by reducing electricity costs by 9.5 %, CO2 emissions by 9.3 %, and peak demand by 52 %, while maintaining thermal comfort. The framework supports robust and occupant-centric residential energy management, thereby demonstrating its potential for scalable deployment to unlock demand-side flexibility at the community and city levels.