In multi-objective optimization, designing good benchmark problems is an important issue for improving solvers. Controlling the global location of Pareto optima in existing benchmark problems has been problematic, and it is even more difficult when the design space is high-dimensional since visualization is extremely challenging. As a benchmarking with explicit local Pareto fronts, we introduce a benchmarking based on basin connectivity (3BC) by using basins of attraction. The 3BC allows for the specification of a multimodal landscape through a kind of topological analysis called the basin graph, effectively generating optimization problems from this graph. Various known indicators measure the performance of a solver in searching global Pareto optima, but using 3BC can make us localize them for each local Pareto front by restricting it to its basin. 3BC's mathematical formulation ensures the accurate representation of the specified optimization landscape, guaranteeing the existence of intended local and global Pareto optima.

翻译：在多目标优化中，设计良好的基准测试问题是提升求解器性能的关键。现有基准测试问题在控制帕累托最优解集的全局位置方面存在困难，当设计空间为高维时，由于可视化极其困难，这一问题更为突出。我们提出了一种基于盆地区域连通性的显式局部帕累托前沿基准测试方法（3BC）。该方法通过一种称为盆地图的拓扑分析来指定多模态景观，并据此有效生成优化问题。各类已知指标可度量求解器搜索全局帕累托最优解的性能，但通过3BC方法将搜索范围限制在各自盆地区域内，即可定位出每个局部帕累托前沿的相应解。3BC的数学公式确保了所指定优化景观的精确表征，并保证了预期的局部与全局帕累托最优解的存在性。