### Evolutionary Algorithms for Multiobjective Optimization with Applications in Portfolio Optimization.

Abstract

Multiobjective optimization (MO) is the problem of maximizing/minimizing a set of nonlinear
objective functions (modeling several performance criteria) subject to a set of nonlinear
constraints (modeling availability of resources). The MO problem has several applications in
science, engineering, finance, etc. It is normally not possible to find an optimal solution in MO,
since the various objective functions in the problem are usually in conflict with each other.
Therefore, the objective in MO is to find the Pareto front of efficient solutions that provide a
tradeoff between the various objectives.
Classical techniques assign weights to the various objectives in the MO problem, and solve
the resulting single objective problem using standard algorithms for nonlinear optimization.
Moreover, these techniques only compute a single solution to the problem forcing the decision
maker to miss out on other desirable solutions in the MO problem.
We investigate the use of evolutionary algorithms to solve MO problems in this thesis.
Unlike classical methods, evolutionary strategies directly solve the MO problem to find the
Pareto front. These algorithms use probabilistic rules to search for solutions and are very
efficient in solving medium sized MO problems. We use evolutionary algorithms to compute
the efficient frontier in the classical Markowitz mean-variance optimization problem in finance,
and illustrate our results on an example.