2. Solution of multiobjective optim

2. Solution of multiobjective optimization problem
Any multi-objective optimization (minimization) problem (MOO), regardless of area of application, is
formulated as following:
where n is a number of objectives, gk and hj are inequality and equality constraints quantities of K and J
respectively, x - set of decision variables, S - decision domain for x. However, optimization might include both
minimization and maximization of objectives, for the sake of simplicity we will consider minimization problem. All
the ideas and approaches can be easily extended for maximization problems.
Fig. 1 Pareto front for two-objective optimization problem in objective domain
Unlike in case of single objective optimization, the non-trivial solution for problem (1) is not a single point, but a
number of points called Pareto-optimal solutions
Pareto-optimal point: a point x