分解多目标优化中的偏好集成
Integration of Preferences in Decomposition Multi-Objective Optimization
摘要：
现有的大多数进化多目标优化的研究集中在逼近整个帕累托最优前沿。尽管如此，而不是整个前线，这需要太多的点（特别是在高维空间中），决策者可能只对部分区域感兴趣，称为感兴趣区域。在这种情况下，该区域之外的解决方案可能会对决策过程造成干扰。更糟糕的是，在处理具有复杂性质或大量目标的问题时，无法保证我们可以找到首选的解决方案。在本文中，我们开发了一个系统的方法，将决策者的偏好信息分解为基础的进化多目标优化方法。一般来说，我们的基本思想是一个非均匀的映射方案，原来均匀分布的参考点在一个典型的单纯形可以映射到新的位置接近的愿望水平向量指定的决策者。通过这些手段，我们能够直接或以交互方式将搜索过程引导到感兴趣的区域，并且还处理大量的目标。同时，边界解可以根据决策者的要求进行近似。此外，感兴趣区域的范围是直观地可理解的，并且以封闭的形式是可控制的。广泛的实验，无论是证明的原则和3至10个目标的各种问题，充分证明了我们所提出的方法的有效性，在感兴趣的区域近似的首选解决方案。
英文摘要：
Most existing studies on evolutionary multi-objective optimization focus on approximating the whole Pareto-optimal front. Nevertheless, rather than the whole front, which demands for too many points (especially in a high-dimensional space), the decision maker might only interest in a partial region, called the region of interest. In this case, solutions outside this region can be noisy to the decision making procedure. Even worse, there is no guarantee that we can find the preferred solutions when tackling problems with complicated properties or a large number of objectives. In this paper, we develop a systematic way to incorporate the decision maker's preference information into the decomposition-based evolutionary multi-objective optimization methods. Generally speaking, our basic idea is a non-uniform mapping scheme by which the originally uniformly distributed reference points on a canonical simplex can be mapped to the new positions close to the aspiration level vector specified by the decision maker. By these means, we are able to steer the search process towards the region of interest either directly or in an interactive manner and also handle a large number of objectives. In the meanwhile, the boundary solutions can be approximated given the decision maker's requirements. Furthermore, the extent of the region of the interest is intuitively understandable and controllable in a closed form. Extensive experiments, both proof-of-principle and on a variety of problems with 3 to 10 objectives, fully demonstrate the effectiveness of our proposed method for approximating the preferred solutions in the region of interest.
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