单目标景观对多目标优化的影响
Impacts of Single-objective Landscapes on Multi-objective Optimization
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中文总结 AI 辅助
该研究揭示多目标优化问题与其内嵌单目标问题的关联，通过分析两类网络结构，发现多数帕累托最优解可从单目标局部最优解获得，为多目标优化提供了新线索。
中文摘要 AI 辅助
本研究揭示了多目标优化问题与其中包含的单目标优化问题之间的关系，聚焦于组合问题，探究了单目标问题的局部最优网络与多目标问题的帕累托最优网络之间的联系，两类网络均具有图结构，研究者将整个网络划分为子图，每个子图称为一个组件，其特征是单目标局部最优网络与多目标帕累托最优网络之间的重叠关系。在多目标景观问题上的结果表明，大多数帕累托最优解可从单目标局部最优解中获得，且该趋势随目标数量增加和目标相关性增强而更显著，共变量的数量会影响单目标局部最优网络与多目标帕累托最优网络之间的交叉链接关系数量，研究结果表明，对单目标问题的搜索是解决多目标优化问题的线索。
英文摘要
This work revealed a relationship between a multi-objective optimization problem and single-objective optimization problems that exist in the multi-objective problem. This work focused on combinatorial problems and investigated the relations between the local optima networks of the single-objective problems and the Pareto optima network of the multi-objective problem. Each of their networks has a graph structure. We divided the entire network into subgraphs. Each subgraph was called a component and characterized by overlapping relations between the single-objective local optima networks and the multi-objective Pareto optima network. Results on multi-objective landscape problems showed that most Pareto optimal solutions were reachable from the single-objective local optimal solutions. This tendency was emphasized by increasing the number of objectives and the objective correlation. The number of co-variables impacted the number of cross-link relations between the single-objective local optima networks and the multi-objective Pareto optima network. The results suggested that searching for single-objective problems is a clue to multi-objective optimization.
