Approximation algorithms for combinatorial multicriteria optimization problems

Abstract The computational complexity of combinatorial multiple objective programming problems is investigated. NP‐completeness and # P ‐completeness results are presented. Using two definitions of approximability, general results are presented, which outline limits for approximation algorithms. The performance of the well‐known tree and Christofides' heuristics for the traveling salesman problem is investigated in the multicriteria case with respect to the two definitions of approximability.