A Sequential Comparison Procedure for Bi-Objective Simulation Optimization Problem

[[abstract]]隨著科技的進步，電腦運算快速及軟體的普及化，商業模擬軟體開始結合最佳化技術以進行最佳化分析，如模擬軟體ARENA與最佳化軟體OptQuest結合，但是仍無法解決多目標最佳化問題。雖有許多論文發展出求解多目標問題的演算法，但是僅有少數研究使用模擬估算函數值，主因不外乎使用模擬需要長時間實驗，若實驗時間太短可能會造成模擬誤差過大，而演算法本身搜尋較佳解需花費許多時間，若模擬時間太長而導致搜尋次數不足，可能無法找到品質良好的解。 目前與模擬結合的演算法是依據平均數來衡量，忽略模擬結果存在著隨機誤差，容易造成演算法求解過程有誤判的情形，因此在選擇與比較時，無法精確的認定搜尋到的解為較佳解。一般利用執行更多replications的方式來解決模擬存在隨機誤差的問題，以降低隨機誤差所造成誤判的情況，相對地，此方法需耗費相當多的時間。因此本研究針對模擬解的比較與如何選擇較佳模擬解提出新的構想。 本研究簡化Boesel et al.（2003）發展出的Ranking and Selection搜尋流程方式來解決模擬最佳化存在的隨機誤差問題。本演算法主要分成兩階段，第一階段篩選作業先執行較少replications的模擬實驗，利用比較機制刪除明顯較差的解；倖存的解便進入第二階段，執行更多replications的模擬實驗以獲得較精確的結果，然後進行統計比較以產生母代與更新非凌駕解集合。經數學與模擬範例結果發現，本研究之構想確實能降低隨機誤差對搜尋解造成的干擾，較精確地執行優劣判斷，同時亦可減少不必要系統的模擬，減少模擬所需耗費大量的時間。[[abstract]]As computer technology advances, commercial simulation packages can solve simulation optimization problems using optimization techniques. For example, Arena combining with OptQuest provides a powerful tool. However, none is capable of handling multi-objective optimization problems. Although there are numerous studies on multi-objective optimization, few perform functional evaluation via simulation. Simulation optimization is difficult because both simulation and search algorithm are time-consuming. If simulation time is not enough, simulation results would have large random error and the algorithm could miss quality solutions. This research revises the ranking and selection procedure designed for single-objective optimization problems by Boesel et al.(2003). The algorithm first performs a fixed number of replications for each offspring solution. A subset selection procedure screens out noncompetitive solutions. Then the algorithm performs more replications for the remaining solutions to produce more accurate results. Mathematical examples and simulation experiments suggest that this procedure can save simulation time, reduce random error that interferes with the search process, and improve the effectiveness of the algorithm