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.