The smoothed number of Pareto-optimal solutions in bicriteria integer optimization
研究了双准则整数优化问题在平滑分析模型下帕累托最优解的期望数量，证明了几乎紧的多项式界，并改进了背包问题和双准则最短路径问题中启发式算法的运行时间结果。
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 the number of enumerated solutions, which is exponential in the worst case. We study bicriteria integer optimization problems in the model of smoothed analysis, in which inputs are subject to a small amount of random noise, and we prove an almost tight polynomial bound on the expected number of Pareto-optimal solutions. Our results give rise to tight polynomial bounds for the expected running time of the Nemhauser-Ullmann algorithm for the knapsack problem and they improve known results on the running times of heuristics for the bounded knapsack problem and the bicriteria shortest path problem.