*4.2. Optimization Problem*

The problem of jointly maximizing the satisfaction while minimizing the power consumption *f*2(*u*) can be formulated as a multi-objective (MOO) problem:

$$\min \|f\_1(u, t), -f\_2(u, t)\|\_{\prime} \tag{8}$$

$$\text{s.t. } L[t] \le \; E\_{\text{coou}} \tag{9}$$

where,

$$f\_1(t, \mu) = L[t],\tag{10}$$

$$f\_2(t, \mu) = ES'[t].\tag{11}$$

$$t \in \{k, k+1, \ldots, k+23\} \tag{12}$$
