害蟲擴散對農業生產與作物收成造成持續且嚴重之威脅。過度依賴化學農藥雖可於短期內抑制蟲害，卻亦可能伴隨環境污染、生態失衡及農產品安全等問題。相較之下，透過投放害蟲天敵進行生物防治，不僅可降低化學藥劑之使用，亦有助於兼顧農業經濟效益與環境永續。因此，如何在有限防治資源下，決定天敵之投放位置、時機與數量，以抑制害蟲擴散、維持作物完整度並提升整體農業利潤，為一項具有實務意義之資源配置與排程決策問題。
本研究建構一套整合空間害蟲擴散、生物防治及作物生長之多期最佳化架構。研究中將農地表示為方格網路，以節點描述各區域之害蟲數量、天敵存量及作物完整度，並考量害蟲族群成長、擴散閾值、鄰近節點遷徙、天敵捕食與留存，以及作物受害與恢復等動態機制。在此基礎上，本研究建立多期混合整數規劃模型，以各節點與期別之天敵投放量為主要決策變數，並以期末可收成作物之總價值扣除天敵投放成本後的整體利潤最大化為目標，同時納入最低與最高投放量、可投放期別及全規劃期總投放量上限等管理限制。
由於本問題同時包含整數投放決策、期末收成門檻、不可逆作物毀損、害蟲空間擴散及跨期生態動態，使其解空間呈現離散門檻、時空耦合、全域資源限制及搜尋路徑依賴等特性。當問題規模增加時，混合整數規劃模型之求解負擔亦隨之上升。為提升大規模實例之求解效率，本研究提出貪婪建構啟發式演算法（GreedyConstruction Heuristic, GCH）與模型導向空間基因演算法（Model-Aware Spatial Genetic Algorithm, MA-SGA）。GCH 由高防治覆蓋之最大投放配置出發，依序執行收成數保留式反向縮減、整數劑量精煉、離散邊際損失導向之總投放量修復、目標節點救援交換、劑量與期別改善搜尋，以及時間限制下之擾動與重啟搜尋。MA-SGA則透過生態參數與空間錨點建立問題特化初始族群，並結合競賽選擇、矩形區塊交配、兩點交配、混合突變、總投放量修復、菁英保留及建構式移入個體，以群體式搜尋探索不同的時空投放配置。
數值實驗針對不同問題規模比較混合整數規劃模型、GCH與MA-SGA之解品質及計算效率，並以混合整數規劃所得之最佳解或最佳界作為相對差距之計算基準。實驗結果顯示，隨著節點數量增加，精確求解所需之計算負擔明顯提高；相較之下，GCH與MA-SGA均能於限定計算時間內產生滿足投放限制之可行解，提供大規模天敵投放排程問題之近似求解方法。兩種演算法分別透過單一目前解之集中改善與多個候選解之群體式探索處理解空間特性，呈現不同的搜尋行為與解品質表現。
此外，本研究透過單參數敏感度分析，探討害蟲成長率、作物損害率、作物生長率、天敵捕食率與留存率、單位投放成本、期末收成閾值、投放量上下界及全規劃期總投放量上限等參數對系統利潤與投放決策之影響。分析結果顯示，生態條件、經濟參數及管理限制均可能改變天敵投放之空間與時間配置，反映生物防治決策須同時考量害蟲風險、天敵控制效能、作物恢復能力及可用防治資源。
本研究之主要貢獻在於整合空間化害蟲擴散、生物防治、作物生長與管理限制，建立可描述多期生態動態及天敵投放決策之混合整數規劃模型；並針對問題之離散門檻與時空耦合特性，提出具不同搜尋架構之GCH與MA-SGA，以支援大規模實例之近似求解。研究結果可作為農業管理者進行害蟲防治規劃、天敵資源配置及相關管理政策評估之決策參考。

Pest diffusion poses a persistent threat to agricultural production and crop harvests. Biological control through the release of natural enemies provides an alternative toexcessive reliance on chemical pesticides. This study develops a multi-period optimization framework integrating spatial pest diffusion, biological control, and crop growth. A mixed-integer programming (MIP) model is formulated to determine the locations, timing, and quantities of natural-enemy releases with the objective of maximizing total profit. To improve computational scalability, a Greedy Construction Heuristic (GCH) and a Model-Aware Spatial Genetic Algorithm (MA-SGA) are developed. Numerical experiments show that both methods can generate feasible solutions within limited computation time as problem size increases. Sensitivity analysis further demonstrates that ecological, economic, and operational factors affect system performance and release decisions. The proposed framework provides quantitative decision support for pest control planning and natural-enemy resource allocation.

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