通常，在我們所取得的任意一組資料裡，由於內在特性的關係，往往會使資料自然形 成若干叢聚（Clusters）。叢聚分析（Cluster Analysis）的目的，就是如何藉由數 量的方法，找出這些自然形成的叢聚，俾便於往後資料的整理和分析。儘管界定叢聚 的角度，將因人、因事而有所不同。然而根本上，這就是一個尋找最佳解的方法，來 找出資料中的最理想分組，便成為一種自然而可行的嘗試。本文係就動態規劃、整數 規劃（整數規劃模式改以Subgradient Method求解）、暨分支定限法（Brandhand-bo und Method）如何處理叢聚分析問題，分別予以討論比較。

伴隨著永續發展思潮之興起，「大眾運輸導向發展（Transit-oriented development, TOD）」已成為都市規劃之重要理念。相關研究雖曾就TOD緊密、混合使用發展帶來之永續效益進行探討，然高密度之發展模式亦會加速都市內資源消耗，並影響生活環境品質。為解決前述課題，相關文獻因而提出「綠色大眾運輸導向發展（Green transit-oriented development, Green TOD）」理念，以期待在TOD與綠色都市主義（Green urbanism）之結合下，形塑更為友善環境發展之都市型態。國內外雖有相關研究對Green TOD之規劃理念進行探討，並建立評估架構與準則，然規劃上仍未以該理念建構土地使用規劃模式，以協助規劃者研擬規劃方案；此外傳統土地使用規劃模式建構亦較少將土地使用配置現況與變更限制納入考量，規劃模式因而無法反映實際之規劃問題，並使其應用受到限制。 　　基此，本研究係由通盤檢討面向切入建構「綠色大眾運輸導向土地使用規劃模式」，規劃上並以高密度發展、混合使用配置、親生物開放空間追求、非機動運具可及性提升、停車需求抑制、資源配置效益追求、都市機能健全發展為追求目標建構多目標規劃模式；模式考量限制則包含通盤檢討變更可行性、配置區位限制、規模與容量限制、預算限制、運輸場站自明性、自行車道連續性等；模式求解則修正最小偏差法，並設定不同之權重組合尋求非劣解集合；最後則模擬實例情境設計假想例，以測試模式之可用性，並透過敏感度分析探討規劃模式之應用特性。 　　研究結果發現，規劃模式部分目標因追求方向相同而不具有償付關係，然各目標規劃理念、衡量面向與決策內容皆有不同，規劃上因而有保留之必要性，規劃模式並可依據此特性追求整合性之規劃效益，且著重高密度發展策略之應用。而敏感度分析則顯示，預算額度多寡將影響模式之規劃彈性與償付關係之表現程度，規劃前應妥善分析土地使用配置現況後編列適當之預算資源，以確保規劃偏好達成。本研究建構之土地使用規劃模式可於Green TOD 理念下研提不同之替選方案，並輔助規劃單位進行土地使用、自行車路網、水資源配置之規劃作業。 / Transit-oriented development (TOD) has become a main concept of urban planning as the advocacy of sustainable development. Previous studies, though, have explored the benefit of TOD which features of compact development and mixed land use, excessive density would also accelerate the resources consumption in inner city and decrease the quality of living environment. To solve the aforementioned problems, studies have proposed the concept of “Green transit-oriented development (Green TOD)”, which combines the concepts of “TOD” and “Green Urbanism” in anticipation of shaping an environmentally friendly urban form. However, most of the studies about Green TOD mainly focus on defining the planning concept or establishing the evaluation framework and criteria of it, it still lacks a land use planning model for Green TOD which aims to generate planning alternatives objectively for planners. With regard to the land use planning model, prior studies seldom took the current zoning and rezoning restriction into consideration during the model formulation, which not only made the formulated model fail to represent the real planning problem but also decrease the application value. This study, therefore, develops a multi-objective land use planning model for Green TOD from the aspect of overall review of urban planning. The objectives of the model include “maximizing the development density”, “maximizing the mixed land use degree”, “maximizing the biophilic open space”, “maximizing the accessibility of non-motorized vehicle”, “minimizing the parking demand”, “maximizing the benefit of resource allocation” and “minimizing the rezoning scale of available land”. The constrains of the model include “the rezoning feasibility of overall review”, “the restriction of allocated location”, “the allocated restriction of minimum scale and maximum volume”, “budget limitation”, “identification of transit station area” and “connectivity of bikeway network”. The revised minimum deviation method with different weight settings was used to search the non-inferior solutions set for the simulated case to verify the applicability of the developed model. Besides, sensitivity analysis was used to explore the model characteristic. The result found that some of the objectives, which cannot be integrated due to the difference of planning concept, assessing aspect and decision contents, feature of non-trade-off relationship due to the same pursuing direction. The application of the model can therefore apply this characteristic to pursue the integrated benefit accordingly and focus on the planning approach of high density development. Besides, the sensitivity analysis showed that budget amount influences the planning flexibility and trade-off degree significantly. Budgeting should therefore be dealt appropriately after analyzing the current zoning to ensure the achievement of planning preference. The land use planning model developed by this study can be applied to generate planning alternatives under the planning concept of Green TOD and support the authorities for land use allocation, bikeway design and water resource allocation.

本論文係研究和發展平行疊代法（PARALLEL ITERATIVE METHOD ）以解決數學規劃（ MATHEMATICAL PROGRAMMING）中之互補問題（COMPLEMENTA-RITY PROBLEM）。互補問 題源自解決國防軍事、工程經濟及管理科學等領域之應用，而由於近年來各種超級或 平行電腦不斷地創新，使得發展平行演算法以充分並有效地應用超級或平行電腦來解 決大型科學計算的問題日趨重要。 在本篇論文中，我們分別探討線性互補問題以及非線性互補問題。首先我們發展出一 半非同步（SEMI-ASYNCHRONOUS ）法來解決線性互補問題，此法之特性在於其能大幅 地減低因同步法所造成處理機閒置（IDLING）之冗額成本（OVERHEAD）；同時，也放 寬了非同步法對問題所加諸之限制，因而擴大了半非同步法所能應用之範圍。我們也 建立了有關該法收斂性（CONVERGENCE ）之理論根據。此外，線性互補問題之探討， 實為進一步研究非線性互補問題之基礎。 其次，我們提出一個整體性之架構，探討平行牛頓法（NEWTON METHOD ）及其各種變 型（VARIATIONS）來解決各種非線性互補問題，比較並研究各種方法的特性、限制及 執行效率。 然後，針對上述各種演算法，我們在教育部電算中心之IBM ３０９０上發展並模擬各 該法之平行運算，經由廣泛地實驗測試，以獲得具體之數值結果，來檢驗其效率，並 比較研究各法之適用性與優劣。最後，我們也提出一些相關之問題，以供未來後續研 究之參考。