基于森林空间规划问题的模拟退火算法参数敏感性研究

Parameter Sensitivity of Simulated Annealing Algorithm in Forest Spatial Planning

[目的]以森林空间收获安排问题为基础,系统探讨模拟退火算法参数(初始解数量、初始温度、降温速率和每温度下重复次数)设置对森林空间规划问题目标解质量的影响。[方法]规划模型以10个5年规划分期内的最大化木材收获为基本目标,同时满足均衡收获和最大连续采伐面积约束。模拟数据由5个假设的栅格数据组成,共产生了3 300 81 600个0-1型决策变量。[结果]表明:各规划问题目标函数值的平均变异系数仅在0.18%14.95%间波动,说明模拟退火算法优化结果的高度稳定性;每温度下重复次数和初始温度分别与林分数量呈显著的多项式(R^2=0.85)和指数(R^2=0.66)关系,而降温速率则与林分数量倒数呈显著的多项式(R^2=0.98)关系,初始解数量虽不受林分数量影响,但至少应维持在500次以上。同时,研究还表明规划问题规模不仅显著影响各参数的取值,同时还显著影响算法获得满意解概率(PN)和求解效率(RE),其中满意解概率随林分数量的增加而呈显著线性增加趋势(R^2=0.98),但求解效率则呈显著线性下降趋势(R^2=0.55)。[结论]模拟退火算法优化结果具有高度稳定性,能够适应复杂森林规划问题的需求;模拟退火算法优化结果对参数设置和林分数量具有高度的敏感性,因此森林经营决策人员在采用模拟退火算法解决具体的森林规划问题时应慎重选择各参数的取值,以确保规划结果的稳定性和可靠性。

[ Objective ] To evaluate the effect of parameter setting on the target solution quality of forest spatial plan- ning via simulated annealing algorithm. [ Method ] The tested parameters included the number of initial solutions （N）, the number of iterations per new temperature （nrep）, initial temperature （T） and cooling rate （r）. The planning target was formulated to make timber production maximum over ten 5-year-planning periods, which should subject to the even-flow of harvest volume and area restriction model. The simulation datasets included five hypo- thetical datasets, which encompassed 3 300-81 600 binary decision variables. [ Result] The results showed that the coefficients of variation of objective function values for all the planning alternatives only varied from 0.18% to 14.95% , indicating the distinguished stability of simulated annealing algorithm. Parameters nrep and T can be esti- mated with the number of forests using polynomial （R2 = 0.85 ） and exponential （R2 = 0.66 ） functions respective- ly, however, the parameter r can be estimated with the reciprocal of the number of forests using polynomial function （ R2 = 0.98）. The values of parameter N was not related to the number of forests, but it should be somewhat above 500 times. Meanwhile, we also found that the number of units across a forest landscape not only affected the optimal values of each parameter, but also had significant effects on the probability of locating satisfactory solutions （PN） and resolution efficiency （RE） of simulated annealing algorithm, in which the PN increased linearly with the in- crease of number of units within a forest landscape （R2 = 0.98 ） , but the RE presented a typical linear downtrend for the analytical datasets （R2 = 0.55 ）. [ Conclusion] It is concluded that the quality of solutions of simulated an- nealing algorithm is sensitive to the parameters used and the size of planning options. In order to ensure the stability and quality of planning outputs, forest managers should detemfine the appropriate values of parameters of simulated annealing algorithm carefully when applied it to make forest planning in practice.