應用有空間運算子之模擬退火法於空間森林疏伐規劃問題

Abstract

森林的規劃除了考慮經濟層面，也必須考慮到生態環境的保護。碳在空氣中的含量會直接地影響氣候的變化，進而間接地影響了整個生態圈與人類。然而樹木會吸收空氣中的二氧化碳行光合作用，所以森林樹木的多寡會影響空氣中碳的含量。但是根據研究者所知，過去相關的森林規劃問題中，尚未有考慮碳吸存與碳排放的研究，因此本研究將碳的吸存和排放與森林規劃做結合。本研究把碳換算成金錢，當碳被樹木吸存時，可以獲得收益；當碳排放時，則會遭受到罰則，因此樹木的採伐雖然可以帶來收入，但過度採伐也會使碳排放而導致受罰。近年的森林採伐方式大多使用「疏伐」的方式，因為疏伐是選擇性的採伐，選擇適合的樹木做修剪，其他樹木則不做任何修剪，讓其繼續生長，使森林資源持續循環。 而本研究是給定森林樹木的樣貌後，在鄰連限制、均勻限制的情況下，對森林樹木做疏伐規劃，而寄望找到最大化的收入(即樹木疏伐量與碳排放的平衡點)。 模擬退火法(Simulated Annealing) 已被證明適用於森林規劃問題，因此本研究採用SA求解森林規劃問題並將其進行兩個部分的改良：第一部分是加入了空間運算子(spatial operator)，讓解在每個迴圈中多一次的區域搜尋(local search)，本研究的空間運算子是將中心點考慮與周圍的林地做相同的疏伐方式，其可讓解更具多樣性，可能因此更快找到最佳解；第二部分則是模擬退火法在尋找鄰近解的過程時，過濾了與目前相同的解，這樣的改良可以避免時間的浪費。接著本研究模擬了300座1600公頃人工森林，並將本篇研究的改良式模擬退火法與傳統模擬退火法進行比較，而可以發現改良式模擬退火法比傳統模擬退火有更好的結果，並用統計的檢定發現這兩個方法間有顯著的差異。除此之外，還分析了考慮碳吸存與未考慮碳吸存的差異，從結果可以發現考慮碳市場對於環境是較有利的。

Aside from economic aspect, spatial forest planning is also concerned with being in harmony with ecological and environmental protection with spatial concerns. At-mospheric CO2 level directly affects climate change, and further, indirectly affects the whole ecosystem and human. Forests are capable of sequestrating carbon via photo-synthesis, and hence, increasing forests can decrease the CO2 level in the atmosphere. To lessen effects of global warming, this work investigates the spatial forest thinning planning problem that takes into account carbon sequestration and emission simulta-neously, which were never considered in previous studies. The problem is to decide different forest thinning schedules at different planning periods. Forest thinning is the selective removal of forests. Appropriate forest thinning is beneficial for continuing forest growing, increasing forest timber harvested, and protecting eco-logical envi-ronments, to achieve cycling and sustainability of forest resources. This work first es-tablishes a mathematical programming model for solving small-scale problems, in which the model with carbon sequestration, carbon emission, and forest thinning is increasingly complex. Furthermore, to solve large-scale problems, this work proposes an improved simulated annealing algorithm. The first improvement in the proposed algorithm is to additionally consider a spatial-operator-based local search scheme, which searches solutions based on the spatially neighboring idea that a certain forest block may adopt the same forest thinning schedule with its neighboring forest blocks. The second improvement in the proposed algorithm is to filter the solution that is the same as the current solution to avoid the time wasted for searching repetitive solutions, when searching a neighboring solution during algorithm process. Simulation results for 300 forest instances show that the proposed algorithm has a statistically remarkably better performance than conventional algorithms. Additionally, the decision with carbon considerations is also verified to be obviously beneficial to the environment.