非線性規劃問題之視覺搜尋法 - 以行銷組合之最佳化為例

Abstract

非線性整數規劃（Nonlinear Integer Programming）問題，是指目 標函數或限制式中存在有非線性項，而且某些變數為整數。在傳統非線性 整數規劃問題的求解，甚少利用圖形作為輔助工具，也未能充分利用人眼 視覺的優點。人眼視覺的主要優點是能夠在短時間內辨識出大量的資訊， 由於人眼對圖形變化的敏感性，可以很快速的在一個空間中，找到所想要 的解答。因此如果能將非線性整數規劃問題的求解過程以圖形的方式呈現 出來，就可以透過人機互動（Human-Machine Interactive）的方式，藉 由人眼迅速找到所要的解。 因此，本研究將提出視覺搜尋法的演算流 程與其理論基礎，並發展一套可供使用者與機器作互動式調整的視覺化搜 尋系統，以協助使用者從求解的過程中瞭解目標式與限制式間、變數間的 關係。最後以實際管理案例加以解析，說明視覺搜尋法在管理議題上的應 用性。 Nonlinear integer programming (NIP) problems are the problems with nonlinear terms and some variables are integers. In traditional NIP methods, visual ways are seldom used as auxiliary tools and advantages of human eyes are often ignored. A main advantage of human eyes is that it can recognize much information simultaneously. Owing to the sensitivity of human eyes to graphics changing, people can find their solutions in solution space immediately. By displaying the related information visually of NIPproblems, people would be able to find their solutions rapidly. This study proposes an algorithm of visual search method for solving NIP problems. We also develop a prototype system for this method to provide users to find solutions by interactive adjusting. Users can obtain a lot of information from relationships between the objective function and constraints or from relationships among variables. A realistic management case is also taken as an example to illustrate the practicability of our visual search method.