compactness for regionalization and its application in land-use planning

One of the most important and appealing subjects discussed and applied in many geographical studies is compactness. this is a geometrical notion and has applications far beyond the scope of its definition. besides the importance of measuring compactness in a single object, its study is significant in real-world applications, where the integration of items or objects in conjunction with each other is considered. regionalization is the term commonly used for this integrative perspective. although there are several methods to quantify compactness, this study tries to illustrate the simple way for its calculation. hence, this study is devised to apply with some modifications one of the methods that has been suggested for calculating single object compactness in regionalization domain. we attempt to propose a clear definition and to evaluate the computer implementation of the compactness in a land-use planning study. the ant colony algorithm as a heuristic approach was applied to measure compactness in an innovative manner and to incorporate this concept into a land-use planning case. results show that this method can be useful in achieving compactness in land-use planning.