Visualising the landscape of multi-objective problems using local optima networks
Visualising the landscape of multi-objective problems using local optima networks
复制标题
使用局部最优网络可视化多目标问题的情况
DOI：
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发表时间：
2019
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通讯作者：
Khulood AlYahya
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文献类型：
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作者：
J. Fieldsend;Khulood AlYahya
局部最优网络（隆恩）代表了优化问题的景观。在LON中，图顶点表示搜索域中的局部最优，它们的半径表示盆地大小，顶点之间的有向边表示从一个盆地过渡到另一个盆地的能力（边宽度表示这有多容易）。最近，一个网络的建设方法的启发隆恩已被提出的多目标问题，它使用无向图，表示相互非主导的解决方案和相邻的链接，但不是盆地的大小。相比之下，在这里，我们介绍了两个配方的多/多目标的问题，这是类似于传统的LON，使用优势为基础的爬山搜索域。每个顶点表示一组局部最优解，并显示了盆地和它们之间的过渡。这些隆恩取决于是否使用基于点（支配中性最优）或基于集合（帕累托局部最优）的表示来定义模式构造。我们说明这些替代配方上的一些说明性的问题。我们讨论了一些基本的计算问题，在构建隆恩在一个多目标，而不是单目标的问题域，沿着固有的问题的中立性-在这些图中的每个顶点几乎总是代表一组在我们提出的构造。
Local optima networks (LONs) represent the landscape of optimisation problems. In a LON, graph vertices represent local optima in the search domain, their radii the basin sizes, and directed edges between vertices the ability to transit from one basin to another (with the edge width denoting how easy this is). Recently, a network construction approach inspired by LONs has been proposed for multi-objective problems which uses an undirected graph, representing mutually non-dominating solutions and neighbouring links, but not basin sizes. In contrast, here we introduce two formulations for multi/many-objective problems which are analogous to the traditional LON, using dominance-based hill-climbing to characterise the search domain. Each vertex represents a set of locally optimal solutions, with basins and ease of transition between them shown. These LONs vary depending on whether a point-based (dominance neutral optima) or set-based (Pareto local optima) representation is used to define mode construction. We illustrate these alternative formulations on some illustrative problems. We discuss some of the underlying computational issues in constructing LONs in a multi-objective as opposed to uni-objective problem domain, along with the inherent issue of neutrality - as each a vertex in these graphs almost invariably represents a set in our proposed constructs.