Numerical Study for Discrete Optimization Problems --- Combining Particle Swarm Optimization with Successive Taguchi Method

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Project title

Code/計畫編號

NSC100-2221-E019-014

Translated Name/計畫中文名

離散問題之最佳化數值研究-啟發式演算法與循序式田口試驗法之整合

Project Coordinator/計畫主持人

Jeun-Len Wu

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Systems Engineering and Naval Architecture

Website

https://www.grb.gov.tw/search/planDetail?id=2336280

Year

2011

Start date/計畫起

01-08-2011

Expected Completion/計畫迄

01-07-2012

Bugetid/研究經費

368千元

ResearchField/研究領域

機械工程

"本計劃主要發展一套非連續變數問題之最佳化求解方法。本方法架構為整合兩個不同數值最佳解搜尋方法而成。第一個方法乃是引用啟發式演算法理論，先行於實數領域找尋所求問題之最佳解所座落區域。第二個方法為進行迭代式因子實驗篩選最佳值，參酌所求問題之非連續變數界限範圍，藉由第一啟發式演算法所求之最佳解座落區域，分別選取各變數之有限個數目值，進行因子實驗以決定問題最佳解。針對以啟發式演算法搜尋問題最佳解，本研究將以粒子群演算法[1]為基礎，融合搜尋系統過程之資料儲存、分析、及引用區域鑑定法逐步判定最優搜尋區域，以利最佳解求取。本研究稱此演算法為MPSO。我們將以MPSO求解一些單極點或多極點之標竿函數[2]，以驗證MPSO之效益。至於因子試驗法，本計劃將延伸循序式田口試驗法[3]，考量變數交戶作用之求解技巧，以擴充循序式田口試驗法之可用性，本研究稱此因子試驗法為NSTP。本計劃將選取球曲面函數、二次曲面函數、及Rosenbrock函數，以驗證新發展之因子試驗法，所得結果預期與其它因子試驗法所求結果比較。接著我們將MPSO及NSTP整合，以為離散問題最佳化之求解。本研究將以本數值方法求解兩著名之工程標竿問題，齒輪組之最佳齒輪數組配及十桿桁架於最小重量為目標之最佳桁架組配，以驗證方法之可效性。所得結果預期與其它方法所求結果比較[4-7]。整合啟發式演算法與因子試驗法，以求解非連續變數最佳化問題之觀念，目前並無相關文獻有此研究，祇要是往昔因子試驗法所能求解並非全域最佳解。由於我們所發展之循序式田口試驗法可得到全域最佳解，因此產生本計劃研究之構想。從邏輯觀點而言，本構想應為可行，本方法用於求解非連續變數最佳化問題預期將可解決目前以啟發式演算法求解過程，用於耗費驗證變數值域滿足條件[7]所遭遇之大量數值計算時間。" "A numerical method is going to be developed for optimizing discrete problems. The proposed numerical algorithm is established through the integration of two different numerical goal-searching processes. The first is applying a heuristic evolution method to search in real domain the region where the global optimum might stay. Secondly, the final solution is then determined by employing design of experiments, which the levels of variables are chosen based on the numerical result from the first numerical method. The heuristic evolution computational algorithm is developed on the basis of the population-based particle swarm optimization (PSO) [1]. The newly modified PSO algorithm is named in the study as MPSO, which is built through stages of data collection, analysis, identification of the most promising region, and zero in the optimum. The performance of MPSO will be verified through several benchmark problems possessing single-mode or multi-modes and compared with results from other methods [2]. As to design of experiment, a newly successive Taguchi process [3] is to be introduced to deal with a problem presenting strong interaction among its variables concerned. Three benchmark functions, the Sphere, the Quadric and the Rosenbrock will be taken to verify the developed method and also the results are going to compare with those obtained from other methods. After finishing the verification of the two different numerical schemes, we will incorporate both together in solving the optimization of discrete problems. In the study, we will take the two well-known benchmark practical problems, design of a gear train and design of ten-bar truss to verify the numerical method. The determined results will be compared with those of literatures from different methods [4-7]. The idea of combining heuristic evolution computation and design of experiments in optimizing discrete problems so far has never found in literatures. In applying the proposed method, one can avoid spending a considerable amount of effort in evaluating non-feasible solutions [7] when other methods are applied."

Keyword(s)

循序式直交表法
遺傳演算法
多極值
單極值
successive orthogonal array method
genetic computation algorithm
multi-modal
single modal

DSpace CRIS

Numerical Study for Discrete Optimization Problems --- Combining Particle Swarm Optimization with Successive Taguchi Method

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