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A technoeconomic optimization problem for a domestic grid-connected PV-battery hybrid energy system is investigated. It incorporates the appliance time scheduling with appliance-specific power dispatch. The optimization is aimed at minimizing energy cost, maximizing renewable energy penetration, and increasing user satisfaction over a finite horizon. Nonlinear objective functions and constraints, as well as discrete and continuous decision variables, are involved. To solve the proposed mixed-integer nonlinear programming problem at a large scale, a competitive swarm optimizer-based numerical solver is designed and employed. The effectiveness of the proposed approach is verified by simulation results.