Topics in Multiobjective Optimization

Description

ABSTRACT: Multiobjective Optimization (MO) has many applications in such Fields as the internet, finance, biomedicine, management science, game theory and engineering. However, solving MO problems is not an easy task. Searching for all Pareto optimal solutions is an expensive and time-consuming process because there are usually exponentially large (or infinite) Pareto optimal solutions. Even for the simplest problem determining whether a point belongs to the Pareto curve is NP-hard. We present optimality conditions and duality for some multiobjective programming problems with generalized convexity. In particular, the general nondifferentiable multiobjective programming problem, a multiobjective fractional programming problem and a multiobjective variational programming problem, will be considered. One of the main techniques for solving multiobjective programming problems is the weighted sum approach. Based on this approach, we show that a parametric optimization technique can be useful to solve multiobjective programming problems. We also examined the biobjective Steiner tree problem. Based on an existing approximation algorithm for solving the Steiner tree problem, we found an approximation of efficient frontier of the biobjective Steiner tree problem and we found the approximation error. (Source: Google Books API)