  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.
