Approximation of Multiobjective Optimization Problems

Abstract

We discuss problems in multiobjective optimization, in which solutions to a combinatorial optimization problem are evaluated with respect to several cost criteria, and we are interested in the trade-off between these objectives, the so-called Pareto curve. The Pareto curve has typically an exponential number of points. However, it turns out that, under general conditions, there is a polynomially succinct curve that approximates the Pareto curve within any desired accuracy. The central computational question is whether such an approximate curve can be constructed efficiently (in polynomial time). We discuss conditions under which this is the case. We examine in more detail the class of linear multiobjective problems, and relate the multiobjective approximation to the single objective case. We will discuss also problems in multiobjective query optimization.