Optimizing over the Efficient Set of a Multi-Objective Discrete Optimization Problem

Satya Tamby, D. Vanderpooten
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Abstract

Optimizing over the efficient set of a discrete multi-objective problem is a challenging issue. The main reason is that, unlike when optimizing over the feasible set, the efficient set is implicitly characterized. Therefore, methods designed for this purpose iteratively generate efficient solutions by solving appropriate single-objective problems. However, the number of efficient solutions can be quite large and the problems to be solved can be difficult practically. Thus, the challenge is both to minimize the number of iterations and to reduce the difficulty of the problems to be solved at each iteration. In this paper, a new enumeration scheme is proposed. By introducing some constraints and optimizing over projections of the search region, potentially large parts of the search space can be discarded, drastically reducing the number of iterations. Moreover, the single-objective programs to be solved can be guaranteed to be feasible, and a starting solution can be provided allowing warm start resolutions. This results in a fast algorithm that is simple to implement. Experimental computations on two standard multi-objective instance families show that our approach seems to perform significantly faster than the state of the art algorithm.
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多目标离散优化问题的有效集优化
离散多目标问题的有效集优化是一个具有挑战性的问题。主要原因是,与在可行集上优化不同,有效集是隐式表征的。因此,为此目的设计的方法通过求解适当的单目标问题来迭代地生成有效的解。然而,有效解决方案的数量可能相当大,要解决的问题实际上可能很困难。因此,挑战在于最小化迭代次数和降低每次迭代要解决的问题的难度。本文提出了一种新的枚举方案。通过引入一些约束和优化搜索区域的投影,可能会丢弃大部分搜索空间,从而大大减少迭代次数。保证了所要求解的单目标方案的可行性,并提供了一个允许热启动的启动解。这就产生了一种易于实现的快速算法。在两个标准多目标实例族上的实验计算表明,我们的方法似乎比最先进的算法执行得快得多。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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