Global and well-distributed Pareto frontier by modified normalized normal constraint methods for bicriterion problems
Important efforts have been made in the last years to develop methods for the construction of Pareto frontiers that guarantee uniform distribution and that exclude the non-Pareto and local Pareto points. Nevertheless, these methods are susceptible of improvement or modifications to reach the same level of results more efficiently. This paper presents some of these possibilities, based on two types of techniques: those based on nonlinear optimization and those based on genetic algorithms. The first provides appropriate solutions at reasonable computational cost though they are highly dependent on the initial points and on the presence or absence of local minima. The second technique does not present such dependence although computational cost is higher. Since the construction of the Pareto frontier is usually off-line, that computational cost is not a restrictive factor. Goodness of the improvements proposed in the paper are shown with two bicriterion examples.
pareto frontier nonlinear optimization genetic algorithms multiobjective optimization engineering design