Approximating covering problems by randomized search heuristics using multi-objective models

The main aim of randomized search heuristics is to produce good approximations of optimal solutions within a small amount of time. In contrast to numerous experimental results, there are only a few theoretical ones on this subject. We consider the approximation ability of randomized search heuristics for the class of covering problems and compare single-objective and multi-objective models for such problems. For the VertexCover problem, we point out situations where the multi-objective model leads to a fast construction of optimal solutions while in the single-objective case even no good approximation can be achieved within expected polynomial time. Examining the more general SetCover problem we show that optimal solutions can be approximated within a factor of log n, where n is the problem dimension, using the multi-objective approach while the approximation quality obtainable by the single-objective approach in expected polynomial time may be arbitrarily bad. Categories and Subject ...

• Type: Conference
• Year: 2007
• Where: GECCO
• Authors: Tobias Friedrich, Nils Hebbinghaus, Frank Neumann, Jun He, Carsten Witt
• Keywords: Approximation, GECCO 2007, Optimal Solutions, Search Heuristics