坡地住宅社區開發之方格幾何多目標模式

Novel Grid-geometric Multi-objective Model for Residential Development on Hillsides

對於山地多平地少且地狹人稠的國度而言，為了擁有更多的居住空間，坡地建築一直是難 以避免的開發活動。坡地開發（hillside-land development）通常係透過將基地劃分為方格網 （gridded networks）來進行坡度分析。觀念上，不同的坡度（gradient/slope）計算方法搭配上 不同的方格網，可以產生許多不同的坡地開發方案。理論上，前述這些方案中應該存在最大與 最小可開發基地總面積的方案。如何有效地求得此二個方案，則是值得深入去探討。為此，本 研究應用多目標規劃（multiobjective programming）技術，納入可開發基地總面積及可建築樓 地板總面積二個目標，以建立坡地住宅社區開發之方格幾何多目標（grid-geometric multiobjective model for residential development, G2 M2 RD）模式。模式的建構係藉由將基地劃分 為方格網的方式，將前述二個目標轉化為 0-1 整數規劃問題，並以實務法規所規範的開發條 件，轉換成模式中的限制式。其次，藉由變動方格大小、方格座標原點、及座標軸旋轉角度來 建立方格幾何技術（grid-geometric technique, G2 T）法，以建立方格網產生的數學模式。最後， 結合多目標問題求解方法及 G2 T 方法來求解坡地住宅社區開發所關注的最佳可開發基地總面 積與區位問題。應用 1:1000 實測等高線圖實驗測試結果顯示，應用本研究所提出的 G2 T 法可 以精確地求得 G2 M2 RD 模式的最佳解，包含單一目標最大與最小可開發基地總面積、單一目 標最大與最小可建築樓地板總面積、多目標最佳折衷解（best compromise solution）、以及開發 區位。由於 G2 M2 RD 模式具備量化與可重複驗證的特性，對坡地開發實務所涉及的規劃與審 議作業具有高度的應用價值。若審議機關希望降低坡地開發致災的風險，確保更多的公共利 益，則可以採用 G2 M2 RD 模式的最小可開發基地總面積，或是最小多目標方案解來做為開發 的依據。

Preventing hillside development in countries with limited available land and high population density is difficult. The conventional method for hillside development is to partition sites into grid networks for gradient analysis. Different development alternatives can be created by fusing various grid networks and via gradient calculation methods. Among these development alternatives, solutions with maximum or minimum benefit have garnered considerable attention from the development and government sectors. How to obtain the optimal solution is a critical issue. This work applies a novel decision model, the grid-geometric multi-objective model for residential development (G2 M2 RD), for residential development on hillsides to assist in identifying optimal solutions. First, based on the grid networks, two objectives, total area of developed sites and total floor area of buildings, are considered in establishing the model. To formulate the model using multi-objective programming (MOP), two objectives are converted into a 0-1 integer programming problem and constraints are derived from regulations for hillside development. Second, to generate widely varying grid networks by altering factors, including origin shift, axis rotation, and grid size, a novel grid-geometric technique (G2 T) is applied. Finally, a two-stage approach that integrates G2 T and MOP techniques is applied to identify the optimal solutions of G2 M2 RD model. Experimental results for a 1:1000 scale contour map indicate that the proposed G2 T can identify the optimal solutions of G2 M2 RD model including optimal solutions for a single objective, the best compromise solution for multiple objectives, and identification of developable land on hillsides for residential development. For those advocating environmental protection and public welfare, hillside development should adopt the G2 M2 RD alternative with the highest restricted development ratio. The proposed G2 M2 RD and G2 T can serve as analytical tools to identify the most suitable hillside development alternative.