機率分配導引式仿水流演算法：應用於類神經網路之參數訓練

Abstract

本研究展示以母水流流域及子水流代理人架構的新式仿水流演算法 (Probability Distributioin-Guided Water Flow-like Algorithm，PWFA)。PWFA的主要特色是利用連續型機率分配仿傚水流分流、匯流、及降水，使水流代理人的解朝優演化。效能驗證的求解對象是單一目標的連續型優化問題及前饋式類神經網路的權重參數優化問題，共有29個標竿優化函數及五個UCI資料集。實例測試時，比較本法與倒傳遞演算法、共軛梯度法、兩種仿水流演算法、三種遺傳演算法、及四種粒子群演算法的求解效能。數值結果顯示PWFA求解僅具單一全域最佳解的單峰型及多峰型優化函數的效能優於其他優化演算法；而求解具多個全域最佳解的多峰型函數時，PWFA與三種粒子群演算法在不同函數下各有優勢。此外，前饋式類神經網路參數優化問題的實測結果顯示，PWFA與粒子群演算法的優化效能皆屬最佳者。

Water flow-like algorithm (WFA) is inspired by the nature of water flow during circulating in the physical space. Initailly, WFA was developed to be a heuristic algorithm for combinatorial optimization. Thanks to WFA’s underlying ideal, this work propose a novel version of WFA for continuous optimization, called probability distribution-guided water flow-like algorithm (PWFA). In PWFA, basins are conceptualized as subspaces in the solution space, which help subflows to stochastically move toward the lowest position (the global optimum). To imitate the behavior of water flow heuristically, the flows perform spltting and moving, merging and precipitation operation to traverse in the space. Moreover, for evaluating PWFA’s performance, a large set of benchmark test functions and other basic optimization techiques from the literature are adopted for numerical test. In addition, the application to the training of feed-forward neural network (FNN) for pattern classification is also present as a test case for this algorithm. For the reason, a system prototype for solving continuous optimization problem and FNN parameter optimization is implemented by this work. The results show, first, that PWFA has a better performance than other optimization methods on uni-modal functions and multi-modal functions with single one optimum, and second, that this algorithm represents a competitive performance to other basic methods as solving multi-modal functions with many optimums. Additionally, the results of the application show PWFA is comparable to several optimization techniques included as well.