可行性泵随机化步骤的改进
Improving the Randomization Step in Feasibility Pump
摘要：
可行性泵（FP）是求解混合整数线性规划（MILP）的一种成功的原始启发式算法。该算法由三个主要组成部分：舍入分数的解决方案，一个混合整数，投影不可行的解决方案的LP松弛，和一个随机化步骤时使用的算法失速。虽然已经提出了对原始可行性泵的许多概括和改进，但它们主要集中在舍入和投影步骤上。我们开始对可行性泵中的随机化步骤进行更深入的研究。为此，我们提出了一个新的随机化步骤的基础上的WalkSAT算法求解SAT实例。首先，我们提供了理论分析，显示了该随机化步骤的潜力;据我们所知，这是第一次对可行性泵或其变体的运行时间进行理论分析。此外，我们还进行计算实验，将所提出的修改到一个国家的最先进的可行性泵代码，加强了新的随机化步骤的实用价值。
英文摘要：
Feasibility pump (FP) is a successful primal heuristic for mixed-integer linear programs (MILP). The algorithm consists of three main components: rounding fractional solution to a mixed-integer one, projection of infeasible solutions to the LP relaxation, and a randomization step used when the algorithm stalls. While many generalizations and improvements to the original Feasibility Pump have been proposed, they mainly focus on the rounding and projection steps. We start a more in-depth study of the randomization step in Feasibility Pump. For that, we propose a new randomization step based on the WalkSAT algorithm for solving SAT instances. First, we provide theoretical analyses that show the potential of this randomization step; to the best of our knowledge, this is the first time any theoretical analysis of running-time of Feasibility Pump or its variants has been conducted. Moreover, we also conduct computational experiments incorporating the proposed modification into a state-of-the-art Feasibility Pump code that reinforce the practical value of the new randomization step.
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