Rachmawati Ramya, Ozlen Melih, Reinke Karin J, Hearne John W
School of Mathematical and Geospatial Sciences RMIT University, Melbourne, Australia ; Mathematics Department, Faculty of Mathematics and Natural Sciences, University of Bengkulu, Bengkulu, Indonesia.
School of Mathematical and Geospatial Sciences RMIT University, Melbourne, Australia.
Springerplus. 2015 Oct 21;4:630. doi: 10.1186/s40064-015-1418-4. eCollection 2015.
The increasing frequency of destructive wildfires, with a consequent loss of life and property, has led to fire and land management agencies initiating extensive fuel management programs. This involves long-term planning of fuel reduction activities such as prescribed burning or mechanical clearing. In this paper, we propose a mixed integer programming (MIP) model that determines when and where fuel reduction activities should take place. The model takes into account multiple vegetation types in the landscape, their tolerance to frequency of fire events, and keeps track of the age of each vegetation class in each treatment unit. The objective is to minimise fuel load over the planning horizon. The complexity of scheduling fuel reduction activities has led to the introduction of sophisticated mathematical optimisation methods. While these approaches can provide optimum solutions, they can be computationally expensive, particularly for fuel management planning which extends across the landscape and spans long term planning horizons. This raises the question of how much better do exact modelling approaches compare to simpler heuristic approaches in their solutions. To answer this question, the proposed model is run using an exact MIP (using commercial MIP solver) and two heuristic approaches that decompose the problem into multiple single-period sub problems. The Knapsack Problem (KP), which is the first heuristic approach, solves the single period problems, using an exact MIP approach. The second heuristic approach solves the single period sub problem using a greedy heuristic approach. The three methods are compared in term of model tractability, computational time and the objective values. The model was tested using randomised data from 711 treatment units in the Barwon-Otway district of Victoria, Australia. Solutions for the exact MIP could be obtained for up to a 15-year planning only using a standard implementation of CPLEX. Both heuristic approaches can solve significantly larger problems, involving 100-year or even longer planning horizons. Furthermore there are no substantial differences in the solutions produced by the three approaches. It is concluded that for practical purposes a heuristic method is to be preferred to the exact MIP approach.
破坏性野火发生频率的增加，导致生命和财产损失，这促使消防和土地管理机构启动广泛的燃料管理计划。这涉及到对诸如规定火烧或机械清理等燃料减少活动的长期规划。在本文中，我们提出了一个混合整数规划（MIP）模型，该模型可确定燃料减少活动应在何时何地进行。该模型考虑了景观中的多种植被类型、它们对火灾事件频率的耐受性，并跟踪每个处理单元中每个植被类别的年龄。目标是在规划期内将燃料负荷降至最低。安排燃料减少活动的复杂性导致了复杂数学优化方法的引入。虽然这些方法可以提供最优解，但计算成本可能很高，特别是对于跨越景观和长期规划期的燃料管理规划。这就提出了一个问题，即精确建模方法在其解决方案中与更简单的启发式方法相比能好多少。为了回答这个问题，我们使用精确的MIP（使用商业MIP求解器）和两种启发式方法运行所提出的模型，这两种启发式方法将问题分解为多个单周期子问题。第一种启发式方法是背包问题（KP），它使用精确的MIP方法解决单周期问题。第二种启发式方法使用贪婪启发式方法解决单周期子问题。我们从模型易处理性、计算时间和目标值方面对这三种方法进行了比较。该模型使用来自澳大利亚维多利亚州巴旺 - 奥特韦地区711个处理单元的随机数据进行了测试。仅使用CPLEX的标准实现，对于长达15年的规划期才能获得精确MIP的解。两种启发式方法都可以解决大得多的问题，涉及100年甚至更长的规划期。此外，三种方法产生的解决方案没有实质性差异。结论是，出于实际目的，启发式方法比精确的MIP方法更可取。
