预算约束燃料处理调度问题的一种改进解法
An improved solution approach for the Budget constrained Fuel Treatment Scheduling problem
摘要：
本文考虑了预算约束的燃料处理调度（BFTS）问题，在野火缓解的背景下，目标是通过适当的燃料处理活动抑制火灾蔓延的潜力。给定由连续的单位周期表示的时间范围，景观被划分为单元格并表示为网格图，其中每个单元格具有随时间增加的燃料年龄，并且如果在此期间不进行处理则变得陈旧：每当两个相邻的单元格陈旧时，这会引起潜在的高火灾风险。在适当的燃料处理下，电池燃料年龄可以重置为零，但每个时期的处理预算有限。该问题要求找到待处理的细胞的合适选择，以便在整个时间范围内最小化旧的连续细胞的存在。我们证明了问题BFTS是强NP-完全的路径，从而在网格图，并表明，没有多项式时间的近似算法存在，除非P = NP。我们提供了一个增强的整数线性规划制定的问题，相对于相关的文献，显示出有效地解决了ILP求解器上合理的大尺寸的情况。最后，我们考虑了一个更难的周期性的问题，目的是找到一个周期的治疗计划与周期的长度T，并提出了一个数学方法能够有效地解决这些情况下，ILP求解器应用到ILP制定遇到困难。
英文摘要：
This paper considers the budget constrained fuel treatment scheduling (BFTS) problem where, in the context of wildfire mitigation, the goal is to inhibit the potential of fire spread in a landscape by proper fuel treatment activities. Given a time horizon represented by consecutive unit periods, the landscape is divided into cells and represented as a grid graph where each cell has a fuel age that increases over time and becomes old if no treatment is applied in the meantime: this induces a potential high fire risk whenever two contiguous cells are old. Cells fuel ages can be reset to zero under appropriate fuel treatments but there is a limited budget for treatment in each period. The problem calls for finding a suitable selection of cells to be treated so as to minimize the presence of old contiguous cells over the whole time horizon. We prove that problem BFTS is strongly NP-complete on paths and thus on grid graphs and show that no polynomial time approximation algorithm exists unless P = NP. We provide an enhanced integer linear programming formulation of the problem with respect to the relevant literature that shows up to be efficiently solved by an ILP solver on reasonably large size instances. Finally, we consider a harder periodic variant of the problem with the aim of finding a cyclic treatment plan with cycles of length T and propose a matheuristic approach capable of efficiently tackling those instances where an ILP solver applied to the ILP formulation runs into difficulties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
