Engineering Optimization Using Improved Differential Evolution Algorithms

[[abstract]]對於許多實際工程最佳化的問題，如果同時考慮作業環境的噪音和製造的變異，要獲得精確的設計變數通常並不容易。為了克服這一困難，本論文利用田口外直交表(Taguchi outer array)來考量具有設計允差(噪音)的設計變數，提出兩個改進差分進化的方法解決混合離散連續與非線性，以及考慮設計變數允差的表面磨削最佳化的工程問題。本論文提出的第一種方法稱為田口滑動模式微分進化方法（TSBDEA），其中所謂的田口滑動水準方法（TSLM）係提供一個系統化的交叉運算，以取代傳統微分進化算法的交叉操作。以TSLM為基礎的交叉操作具有系統化的推理能力，利用滑動水準因子的影響，產生優秀的子代，再繁殖具有潛力的後代，有效提供多樣化的子代，避免陷入局部最佳解; 第二種方法命名為田口微分進化外陣列方法（TDEOA），延續 TSBDEA的方法，仿效外直交表存放噪音的方式，將設計變數的允差(容許變異)放置在外部陣列內，如此藉由TSLM滑動水準的多樣性交插運算、改良型微分進化快速穩健的收斂效能以及田口方法具有局部最佳解的穩健品質特性，得以求出適應環境噪音、容許設計允差的強健設計變數值。同時，本論文導入一估測設計變數可靠度的方式，在一般加工狀態或是不可預期干擾的環境下，或是在容許設計允差設定下，TDEOA的方法都被驗證其保有穩健的可靠性。本論文中應用不同的工程最佳化問題，結果顯示本論文改良型的微分演算方法同時具有全域最佳解的演算能力，以及強健的可靠度。[[abstract]]For many practical engineering optimization problems the exact design values of machining variables are not easy to be set because of both operating environmental noise and manufacturing variations To overcome this difficulty in this paper two improved differential evolution approaches are proposed to solve several mixed-discrete-continuous problems and the surface grinding process under considering the tolerances of machining variables The first approach is called as the Taguchi-sliding-based differential evolution algorithm (TSBDEA) where the Taguchi-sliding-level-method (TSLM) is applied to provide a new systematic crossover operation to replace the original crossover operation of differential evolution algorithm Then the systematic reasoning ability of the TSLM-based crossover operation with considering the influence of scaling factor is used to breed better individuals in order to generate the representative individuals to be the new potential offspring (or trial vectors) In addition the second approach is named as Taguchi differential evolution outer array (TDEOA) which is extending the methodology in TSBDEA and introducing the variable tolerances in an outer array is proposed to reduce the impact of variations of design variables Furthermore a distinct way has been introduced to estimate the reliability of a set of measurement from a surface grinding process and demonstrate that the reliability of the proposed TDEOA approach can perform and maintain its functions in routine circumstances as well as hostile or unexpected circumstances where some specific tolerances are considere