Introduction to Nonlinear Multiobjective Optimization with Some Applications

Kaisa Miettinen
Department of Mathematical Information Technology
University of Jyväskylä, Finland
Department of Mathematics
Division of Optimization and Systems Theory
KTH, Stockholm


Many methods have been developed for multiobjective optimization. Typically, they aim at supporting a decision maker in finding the best compromise solution in problems where several conflicting criteria are to be optimized simultaneously. Because the compromise solutions, so-called Pareto optima, cannot be ordered without additional information, the solution process requires preference information from a decision maker in some form or another. In this talk, classes of various methods developed for nonlinear multiobjective optimization are outlined. Most attention is paid to interactive methods. In interactive methods, a solution pattern is formed and repeated several times, and in each iteration further information about the decision maker's preferences is inquired. In this way, the decision maker can learn about the nature of the problem and about the interdependencies among the criteria involved. (S)he can also adjust one's preferences while learning and concentrate on such solutions that seem most promising. Finally, some applications are considered and experiences of solving them with the methods described are discussed.