## 1 Introduction  
Building energy consumption contributes approximately 20 to 40% to the total energy consumption in developed countries and has exceeded other major sectors like industrial and transportation [1]. Smart grid is a major step forward to an energy efficient future of the humankind which allows integration of advanced sensing and communication technologies and various control methodologies in order to achieve optimum energy flow [2]. One of the important features of smart grid is the development and incorporation of demand-response strategies [3]. Demand-response [4; 5] refers to the change in power consumption of an electric utility end-use customer to better match the load-demand with the power supply for reliable function of the power grid. The customer may adjust the load-demand by postponing some tasks that require larger amount of electric power or may decide to pay higher prices for the electricity in order to complete the tasks. The utility companies may provide incentives to the customer for demand-response actions. Obviously, it is difficult for the consumer to manually participate in demand-response programs. This explicates the need of an automated system to communicate with smart grid and make optimal decisions on behalf of the customer to achieve the goal of demand-response strategy. This automated system usually called home energy management system (HEMS) is connected to smart-grid by means of bi-directional communications. Advanced sensors and smart-meters are employed to receive/send data and control signals between smart-home and the power utility [6]. Advanced control algorithms are incorporated into HEMS to schedule or operate the appliances in the desired way. The development of appropriate scheduling algorithms has been isolated as one of the crucial challenges for the next generation of real-time systems [7]. Extensive research has been dedicated to the problem of electric load scheduling with focus on different objectives, such as customer comfort [8], minimization of electricity cost [9], reduction of energy usage [10], shifting the electric load [11], etc. Moreover, various methods have been used to investigate this problem, which include, mixed-integer programming [12; 13; 14; 15], stochastic programming [16; 17], evolutionary algorithms [18; 19], heuristic-based algorithms [20; 21; 22; 23; 24], game-theory [25], and learning-based algorithms [26; 27]. [PERSON] et al. [28] presented a study on optimal scheduling of typical household appliances. The scheduling model has been formulated as a non-linear integer program by considering the electricity cost, participation incentive and scheduling-inconvenience in the objective function. The approach showed a 25% reduction in the electricity cost for the particular case. [PERSON] et al. [13] proposed a home energy management system for a smart home equipped with distributed energy resources (DERs) and thermal storage facility. The proposed scheduling technique considered the energy cost and the peak-load demand in the multi-objective function and analysed the results under different weather season scenarios. [PERSON] et al. [14] investigated deterministic problem of day ahead scheduling of appliances by modeling the decision problem in more realistic way and show benefit of the proposed approach by looking into two case studies based on different tariffs in Sweden and NYC. However, the cost calculation in the approach is not based on real-time prices but on tariff which is known 24 h in advance. A few studies on the appliance-scheduling with different pricing schemes, such as time-of-use (TOU) pricing [28], inclining block rate (IBR) pricing [10], and their combinations have also been reported in the literature. In Reference [29], a new pricing scheme active consumption level pricing scheme (ACLP), based upon the consumption level (CL) of consumers has been proposed. The scheme encourages consumers to keep their energy consumption within a price-invariant-band (PIB).