In this paper, the problem of scheduling smart homes (SHs) residential loads is considered aiming to minimize electricity bills and enhance the user comfort. The problem is addressed as a multi-objective constraint mixed-integer optimization problem (CP-MIP) to model the constrained load operation. As the CP-MIP optimization problem is non-convex, a novel hybrid search technique, that combines the Relaxation and Rounding (RnR) approach and metaheuristic algorithms to enhance the accuracy and relevance of decision variables, is proposed. This search technique is implemented through two stages: the relaxation stage in which a metaheuristic technique is applied to get the optimal rational solution of the problem. Whereas, the second stage is the rounding process which is applied via stochastic rounding approach to provide a good-enough feasible solution. The scheduling process has been done under time-of-use (ToU) dynamic electricity pricing scheme and two powering modes (i.e., powering from the main grid only or powering from a grid-tied photovoltaic (PV) residential power system), in addition, four metaheuristics [i.e., Binary Particle Swarm Optimization (BPSO), Self-Organizing Hierarchical PSO (SOH-PSO), JAYA algorithm, and Comprehensive Learning JAYA algorithm (CL-JAYA)] have been utilized. The results reported in this study verify the effectiveness of the proposed technique. In the 1st powering mode, the electricity bill reduction reaches 19.4% and 20.0% when applying the modified metaheuristics, i.e. SOH-PSO and CL-JAYA, respectively, while reaches 56.1%, and 54.7% respectively in the 2nd powering scenario. In addition, CL-JAYA superiority is also observed with regard to the user comfort.
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