Hypervolume Indicator Gradient Ascent Multi-objective Optimization

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• 关键词：Set ; based scalarization ; Hypervolume indicator ; Gradient ascent ; Non ; dominated sorting ; Cumulative step ; size control
• 刊名：Lecture Notes in Computer Science
• 出版年：2017
• 出版时间：2017
• 年：2017
• 卷：10173
• 期：1
• 页码：654-669
• 丛书名：Evolutionary Multi-Criterion Optimization
• ISBN：978-3-319-54157-0
• 卷排序：10173

文摘

Many evolutionary algorithms are designed to solve black-box multi-objective optimization problems (MOPs) using stochastic operators, where neither the form nor the gradient information of the problem is accessible. In some real-world applications, e.g. surrogate-based global optimization, the gradient of the objective function is accessible. In this case, it is straightforward to use a gradient-based multi-objective optimization algorithm to achieve fast convergence speed and the stability of the solution. In a relatively recent approach, the hypervolume indicator gradient in the decision space is derived, which paves the way for the method for maximizing the hypervolume indicator of a fixed size population. In this paper, several mechanisms which originated in the field of evolutionary computation are proposed to make this gradient ascent method applicable. Specifically, the well-known non-dominated sorting is used to help steering the dominated points. The principle of the so-called cumulative step-size control that is originally proposed for evolution strategies is adapted to control the step-size dynamically. The resulting algorithm is called Hypervolume Indicator Gradient Ascent Multi-objective Optimization (HIGA-MO). The proposed algorithm is tested on ZDT problems and its performance is compared to other methods of moving the dominated points as well as to some evolutionary multi-objective optimization algorithms that are commonly used.