## 2 Literature Review
[39] applied an enhanced differential evolution algorithm (EDEA), GWO, and a hybrid framework of EDEA and GWO to develop an optimal scheduling strategy for residential appliances in the presence of an ESS and RERs. The implemented idea was to minimize the consumer electricity cost and reduction in the PAR under RTP and CPP tariff schemes. [PERSON] et al. [40] designed a scheduling problem for residential consumer home appliances by using a harmony search algorithm (HSA), EDEA, and a hybrid framework of HSA and EDEA. The minimization of the electricity consumption charges and decrease in the PAR were the main objectives. In this model, the RTP tariff scheme was used for the electricity consumption cost calculation. Simulation results demonstrated that the above-mentioned methodology achieved the defined objectives in an effective way. [PERSON] et al. [41] developed a model for residential consumers to diminish their electricity consumption charges under a ToU tariff scheme. They applied a mixed-integer non-linear programming (MINLP) scheme without considering the PAR in their proposed model. An integer linear programming (ILP) scheme was proposed for residential areas in [PERSON] et al. [42] to meet the supply-demand balance objective while reducing the consumption cost of electricity. Since the proposed scheme could schedule the home appliances in an optimal way, the supply-demand balance goal was achieved after the optimal scheduling of household appliances for several consumers. This study ignores the users' comfort in the modeling. A dynamic programming (DP)-based appliance scheduling model is proposed in [PERSON] et al. [43] for the optimal shifting of consumers' household appliances in a defined time interval by considering the appliance preferences set by the consumers. The main aim of this scheduling strategy was to decrease the consumer electricity consumption charges by rescheduling consumer home appliances from a high-tariff time interval to a low-tariff time interval according to their preferences. Keeping in mind the above literature, it can be summarized that the design of a HEMS has been optimized by various algorithms: MILP, EDA, linear programming (LP), PSO, DP, convex programming (CP), bacterial foraging algorithm (BFA), score-based intelligent home energy management algorithm, ILP, Dijkstra algorithm, and MINLP. Nevertheless, in some scenarios, these techniques are unable to deal with the volatile nature of different appliances. Furthermore, the convergence rate in some cases was found to be extremely slow because these algorithms were often stuck in local minimum solution. Some important practical constraints, such as the maximization of user comfort, dynamic pricing scheme, and the integration of an ESS and RERs, are somehow rarely considered while using such techniques. In addition, previously proposed models were based on the deterministic modeling of the load, ESS, and RERs. As RERs, such as solar and wind, are weather-dependent, the energy produced by these resources is variable and uncertain. This variability is generally modeled through stochastic or probabilistic approaches. Therefore, this paper presents an optimal design of a HEMS incorporated with the probabilistic modeling of the loads, ESS, and PV by considering RTP and CPP tariff schemes to provide a reduced consumption cost and a better consumption pattern, which indicates reduction in PAR using a GWO, GA, and the proposed hybrid (HGWGA) technique.