利用多目標差分演化的距離最小化與多樣性最大化來找出柏雷多最佳解

Multi-objective Differential Evolution Based on Minimizing the Distance and Maximizing the Diversity to Find Pareto Optimal Solutions

林豐澤(Feng-Tse Lin) ； 黃介鴻(Chieh-Hung Huang)

《智慧科技與應用統計學報》 14卷1期 (2016/06) Pp. 35-46

摘要

現實世界中有許多問題是屬於多目標最佳化問題，這類問題有多個相互衝突的目標函數，若要改進一個目標，勢必要犧牲掉其他目標，因此欲找尋的最佳解不是滿足所有目標函數的最佳解，而是稱為柏雷多的折衷解。柏雷多最佳解是具有連續性質相當多個解，這些解所構成的圖形曲面稱為柏雷多前線。傳統的最佳化技巧不能夠順利將原技巧延伸到求解柏雷多最佳解，而演化式計算因為群體中的個體可同時並行搜尋，根據 schemata 理論，它能夠找到具有相似結構的多組可能解。差分演化是近年來被廣泛使用的一種演化式計算，文獻上已證明於求解某些最佳化問題其效能與收斂速度均勝過基因演算法，因此被視為是一種有效率、隨機性，可求解連續空間複雜問題的最佳化方法。本論文的研究重點在於 (1) 能夠做產生解與柏雷多最佳解集合的距離最小化，(2) 對發展中的柏雷多集合做多樣性的最大化，來設計一個有效率的差分演化演算法找出柏雷多最佳解，未來可用來求解多目標最佳化問題。

關鍵字

多目標最佳化問題 ； 柏雷多最佳化 ； 柏雷多最佳解集合 ； 柏雷多前線 ； 差分演化

並列摘要

Many real-world optimization problems are posed as multi-objective optimization problems. The multi-objective optimization has conflicting situations so that no one can be made one objective better off without making other objectives worse off. Therefore, the optimal solution obtained is not the true optimal solution which optimizes all objective functions simultaneously; it is a compromise solution called Pareto optimal solution. Pareto optimal solution is not unique there exists a set of solutions known as the Pareto optimal set. A plot of entire Pareto set in the design objective space, with design objectives plotted along each axis, gives a Pareto front. Conventional optimization techniques are difficult to extend to the true multi-objective case, because they were not designed with multiple solutions in mind. Evolutionary algorithms (EAs), however, have been recognized to be possibly well-suited to multi-objective optimization since they can search for multiple solutions in parallel. According to the schemata theory, EAs can find any similarities available in the family of possible solutions to the problem. Differential evolution (DE) is an EA that has been widely applied on a plethora of applications. DE is regarded as one of the most powerful stochastic population-based optimization methods. DE has a great probability to obtain the global optimum for multi-dimensional functions and has been proven it outperforms Genetic Algorithms in terms of efficiency and convergence in solving single objective optimization problem. The main focuses of this paper are (1) to minimize the distance of the generated solutions to the Pareto set, and (2) to maximize the diversity of the developed Pareto set.

並列關鍵字

Multi-objective optimization problems ； Pareto optimal ； Pareto optimal set ； Pareto front ； Differential evolution