﻿ 基于遗传算法的森林抚育间伐小班智能选择
 林业科学  2017, Vol. 53 Issue (9): 63-72 PDF
DOI: 10.11707/j.1001-7488.20170908
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#### 文章信息

Wang Jianming, Wu Baoguo, Liang Qiyang

Forest Thinning Subcompartment Intelligent Selection Based on Genetic Algorithm

Scientia Silvae Sinicae, 2017, 53(9): 63-72.
DOI: 10.11707/j.1001-7488.20170908

### 作者相关文章

Forest Thinning Subcompartment Intelligent Selection Based on Genetic Algorithm
Wang Jianming, Wu Baoguo , Liang Qiyang
School of Information Science and Technology, Beijing Forestry University Beijing 100083
Abstract: 【Objective】This study investigated the intelligent selection method of subcompartments based on spatial analysis and genetic algorithm(SGA)in order to provide decision support for formulating forest management plan, conducting under the thinning target control.【Method】Huamugou forest farm, in Chifeng City, Inner Mongolia, was selected as research area to simulate intelligent selection. According to the basic condition of thinning target and operator, the initial small class collection was chosen from continuous distribution of tiny space by spatial query or point buffer analysis. Initial radius and step of point buffer analysis were calculated dynamically by annulus control algorithm(ACA). Urgency indicator, difficulty indicator and site indicator constituted the objective condition formula(OCF), whose value measured the coincidence level of task object. The mathematical model was built by maximum value of OCF and task area. The solution could be obtained by improved genetic algorithm(IGSEGA), which selected the best subcompartments from the initial small class collection, and obtained the most optimal small class collection.【Result】The parameters of OCF were set with task requirement. In research area, the task area was 300 hm2, upper limit as 5% and other conditions. The parameters of GA were as following:gene crossover probability as 0.6, gene variation rate as 0.3, gene variable-length coefficient as 3, iterations as 100. The initial radius as 1 407 m was acquired by ACA, and the radius of expansion was only one time to construct the initial small class collection. Analytical efficiency of general point buffer was lower than ACA because of the uncertainty of initial radius and steps. The initial subcompartment collection could be generated through 14 to 15 iterations because the initial adaptive value was close to the optimal solution by IGSEGA, and the efficiency of solving was higher than the ordinary SGA. The center point of forestry station, 40 subcompartments were obtained and conformed to the objective value. This experiment results showed that the IGSEGA is intelligent and effective.【Conclusion】This paper proposed a concept of forest thinning subcompartment intelligent selection, and constructed the OCF with urgency indicator, difficulty indicator and site indicator. The mathematical model of subcompartment selection was constructed and solved by IGSEGA. Analytical efficiency of buffer analysis was greatly improved by ACA. The research designed a new genetic algorithm encoding with greedy strategy and its genetic operator. It provided an effective method and technology for the concept of forest thinning subcompartment intelligent selection, and decision support for the follow-up forest management activities.
Key words: forest thinning    subcompartments selection    greedy strategy    genetic algorithm    subcompartments intelligent selection algorithm

1 研究区概况与研究方法 1.1 研究区概况

1.2 数据准备

1.3 小班选择问题的数学模型构建 1.3.1 选择规则

1.3.2 属性因子

 ${\rm{DL}} = \left\{ {{\rm{d}}{{\rm{l}}_1},{\rm{d}}{{\rm{l}}_2},{\rm{d}}{{\rm{l}}_3}} \right\}。$ (1)

 $G = \left\{ {{g_1},{g_2},{g_3},{g_4},{g_5}} \right\}。$ (2)

 $R = \left\{ {t\left| {f\left( t \right) \in {\rm{d}}{{\rm{l}}_1} \cap g \cap y \cap u \cap x} \right.} \right\}。$ (3)

1.3.3 数学模型表达

 $\left\{ \begin{array}{l} {S_{{\rm{sel}}}} = \sum\limits_{\begin{array}{*{20}{c}} {i = 1}\\ {t \in R} \end{array}}^n {S\left( {{t_i}} \right)\left| {F\left( t \right)} \right.} \\ {S_{\rm{c}}} \le {S_{{\rm{sel}}}} \le \left( {1 + h\% } \right){S_{\rm{c}}} \end{array} \right.。$ (4)

1) 迫切程度  郁闭度(或疏密度)和森林灾害等级一定程度上反映了抚育间伐的迫切程度。在小班选择时，可指定郁闭度值或范围，若不指定，则按优先级默认选择郁闭度≥0.7以上的小班。数学表达如下：

 $\max Y\left| {\left[ {{Y_1},1} \right] = f\left( t \right),t \in R} \right.。$ (5)

 $\max {\rm{M}}{{\rm{u}}_t} = {Y_t} + \ln {Z_t},t \in R。$ (6)

2) 难易程度  可及度和距离反映了作业的难易程度。对可及度进行量化，即可及为1、将可及为2、不可及为3。在小班选择时，可指定可及度范围，若不指定，则按优先级进行选择。数学表达如下：

 $\max A\left| {\left[ {{A_1},{A_{\rm{u}}}} \right] = f\left( t \right),t \in R,A \in \left\{ {1,2} \right\}} \right.。$ (7)

 $\min D = f\left[ {d\left( {P,O} \right),t} \right],t \in R。$ (8)

 $A{D_t} = \frac{1}{{{A_t} \times {D_t}}}。$ (9)

3) 立地因子  选择抚育间伐小班还需考虑立地因子，因子和分级指标的选择以经营地区的相关研究为准或由经营者指定。采用无林地立地质量评价方法和数量化理论思想对立地因子各分级指标值进行评分，采用专家打分并通过模糊层次分析法计算因子间的相互重要程度。本文以内蒙古赤峰市桦木沟林场为试验地，分级指标值和因子权重的默认值采用内蒙古东南部立地质量评价研究成果(温阳等，2011韩焱云等，2014)。若用立地质量作为选择标准，选择立地条件好的小班时使用默认值，选择立地条件差的小班时则交换分级指标和因子权重的最大值和最小值。经营者还可根据实际需要，按任务需求的分级指标优先级从低到高分别重新赋值为[1, 2, …, n]，因子权重ω按任务需求的因子优先级重新赋值并进行归一化处理。

 ${c_t} = \sum\limits_{i = 1}^m {\sum\limits_{j = 1}^k {{X_t}\left( {i,j} \right){\omega _i}{b_{ij}}} } 。$ (10)

4) 目标条件函数  以迫切程度指标、难易程度指标和立地因子指标构建抚育间伐小班选择的目标条件函数。采用1-9标度法(陈迁等，1996)，通过专家打分建立模糊判断矩阵并使用模糊层次分析法计算各指标的权重值，得到3个指标权重值为：ε1=0.648 3、ε2=0.229 7、ε3=0.122 0。经营者可根据任务需要重新赋值指标权重并进行归一化处理。

 ${w_t} = {\rm{M}}{{\rm{u}}_t}{\varepsilon _1} + A{D_t}{\varepsilon _2} + {c_t}{\varepsilon _3}。$ (11)

 $\max\sum\limits_{i = 1}^n {{w_i} \times {x_i}} ,1 \le i \le n;$ (12)
 ${\rm{s}}{\rm{.}}\;{\rm{t}}{\rm{.}}\;{S_{{\rm{sel}}}} \ge {S_{\rm{c}}};$ (13)
 ${S_{{\rm{sel}}}} \le \left( {1 + h\% } \right){S_{\rm{c}}}。$ (14)

1.4 遗传算法选择小班 1.4.1 满足抚育间伐要求的初始小班集合生成

1) 计算所有小班平均面积：

 $\bar S = \sum\limits_{i = 1}^n {{S_i}/n} 。$ (15)

2) 计算整个林场地图区域内单位地图面积小班数：

 $\bar N = \frac{n}{{{\rm{Are}}{{\rm{a}}_{{\rm{map}}}}}}。$ (16)

3) 根据任务指定的面积，计算初始地图区域面积和半径。假设任务指定的面积为Sc，则根据小班平均面积S计算出大概需要m个小班，根据单位面积小班数N，可估算出m个小班大概需要的地图面积Area′，将Area′看作圆形区域，则可以计算出初始缓冲区半径r′

 $m = \frac{{{S_{\rm{c}}}}}{{\bar S}};$ (17)
 ${\rm{Area'}} = \frac{m}{{\bar N}};$ (18)
 $r' = \sqrt {{\rm{Area'}}/{\rm{\pi }}} 。$ (19)

4) 在初始缓冲区内选择符合基本条件的小班，累加小班面积，若总面积S′大于指定面积Sc上限值，则生成初始小班集合；否则转到下一步。

5) 若总面积S′小于指定面积Sc，则需要扩增上一次缓冲区半径。先计算指定面积Sc和上一次查询面积S′的差S-，然后根据步骤3方法计算面积差值S-所需的小班数m-

 ${m^ - } = \frac{{{S^ - }}}{{\bar S}} = \frac{{{S_{\rm{c}}} - S'}}{{\bar S}}。$ (20)

 ${\rm{Are}}{{\rm{a}}^ - } = \frac{{{m^ - }}}{{\bar N}};$ (21)
 ${\rm{Are}}{{\rm{a}}^ * } = {\rm{Are}}{{\rm{a}}^ - } + {\rm{Area'}};$ (22)
 ${r^ * } = \sqrt {{\rm{Area'}}/{\rm{\pi }}} 。$ (23)
 $\Delta r = {r^ * } - r'。$ (24)

6) 确定新缓冲区后，转到步骤4，生成初始小班集合，进行后续计算，如果选择出符合要求的最优化小班集合则结束，否则重复上述步骤。

1.4.2 基于遗传算法的智能选择算法

1) 智能选择算法流程  森林抚育间伐小班智能选择算法根据任务目标进行求解，先根据基本条件通过空间查询或点缓冲区分析并使用ACA算法选择出初始小班集合，通过式(11) 计算小班权重并利用贪婪策略对初始小班集合中的小班进行遗传算法编码，再对编码的染色体进行交叉、选择等遗传操作，直到得到最优解或达到迭代次数为止，算法流程如图 1所示。

 图 1 森林抚育间伐小班智能选择算法流程 Fig.1 Flowchart of subcompartments intelligent selection algorithm

2) 遗传算法染色体结构  传算法的基本思想是将问题的求解表示成“染色体”，即对问题进行编码操作(邱荣祖等，2010)。染色体的基本组成元素是“基因”，由不同的基因构成“染色体”(张国梁等，2016)。本文基因对应小班，用小班编号进行编码。以初始小班集合构成遗传算法的初始解空间，通过式(11) 计算小班权重(目标条件值)，以面积指标和上限值为限制条件，求解出权重值最大、最符合任务目标的小班集合。

 图 2 智能化小班选择的染色体结构 Fig.2 Architecture of chromosome for intelligent subcompartment selection

3) 适应值函数  遗传算法的关键是适应值，其反映了个体适应环境的能力，本文中适应值反映的是最接近任务目标的小班集合能力。适应值函数与目标函数之间存在着对应关系，在此直接使用目标函数转换为适应值函数。小班智能化选择技术的遗传算法适应值函数为：

 $W = \sum\limits_{i = 1}^n {{w_i} \times {x_i}} 。$ (25)

4) 交叉算子  本文构建的染色体由基础小班集合和候补小班集合2个子染色体组成，编码具有特殊性，故改进了标准遗传算法的交叉操作，在2个子染色体中进行，主要有单点交叉、多点交叉和变长交叉等。

(1) 单基因交叉  按一定的概率pc在基础小班集合后半部分基因中随机取一个基因(小班)，同时在候补小班集合中随机取一个基因，二者进行交换，形成新的个体(小班集合)。如个体1中，基础小班集合和候补小班集合基因位数分别为mn，随机在基础小班集合中取[m/2, m]间的一个基因T[i]与候补小班集合的随机基因T[j]进行交换，生成新的个体，如图 3所示。

 图 3 单基因交叉 Fig.3 Single gene crossover

(2) 基因段交叉  基因段交叉与单基因交叉类似，只是交换二者的一个基因段。如2个子染色体的基因位数分别为mn，随机在基础小班集合中[m/2, m]间取一段长度为c的基因{[T1, T2, …, Tc], 2≤cn}，在候补小班集合中截取等长的基因段进行交换，生成新的个体，如图 4所示。

(3) 变长交叉  变长交叉是对2个子染色体串以1对nn对1的方式进行基因位交叉，对于基础小班集合同样是取后半部分的基因进行操作。如2个子染色体基因位数分别为mn，在基础小班集合中[m/2, m]间随机取一段长度为c的基因，c∈{(0, n]∩(0, m/2)}，在候补小班集合中截取β×c长度的基因进行交叉，生成新的个体，β为(0, k]之间的随机数，k为基因变长系数，取值为正整数。

 图 4 基因段交叉 Fig.4 Gene segment crossover

2 结果与分析

3 结论与讨论

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