The smoothed number of Pareto-optimal solutions in bicriteria integer optimization

Abstract A well-established heuristic approach for solving bicriteria optimization problems is to enumerate the set of Pareto-optimal solutions. The heuristics following this principle are often successful in practice. Their running time, however, depends on number enumerated solutions, which exponential worst case. We study integer model smoothed analysis, inputs subject a small amount random noise, and we prove an almost tight polynomial bound expected Our results give rise bounds time Nemhauser-Ullmann algorithm knapsack problem they improve known times bounded shortest path problem.