Nowadays the optimization of residential loads under varying hourly

energy prices is a topic of interest. The embedding of home

automation systems intends to help customers to control and manage

smartly with their energy consumption. In this work we tackle an

energy pricing problem in which an energy provider maximizes its

profit that is the total revenue received from selling energy to

customers minus total expenses associated with energy peak costs in

a given scheduling horizon. At the same time customers minimize

their electricity bills and scheduling properly all their

appliances. Thus the customers follow the several objectives at the

same time which is more realistic situation. We model this problem

as a bi-level program with two objectives at a lower level. Bi-level

optimization is an appropriate mathematical programming tool if one

wants to coordinate a hierarchical organization where a decision at

the upper level is influenced by a decision at a lower

level (Ben--Ayed1993, Dempe 2002). In such case multi-objective

optimization should be involved. Here we tackle a bi-level problem

with two objectives and the discrete variables at a lower level.

Multi-level multi-objective optimization problems are inherently

difficult, in particular, because of multiple lower level optima,

non-convex feasible region and computational complexity. We propose

a new exact method to find a feasible bi-level solution among a

potentially large set of compromise lower level solutions.