Pareto local optimal solution networks (PLOS-nets) model fitness landscapes as graphs where nodes are Pareto local optima and edges account for standard neighbourhood relationships. PLOS-nets capture the global structure of multi-objective combinatorial landscapes and provide a rich set of features. Published results so far focus on small problems. This article proposes new modelling and sampling methodologies to scale up PLOS-nets to larger problem sizes. Our sampling approach is based on the effective multi-objective random one-bit climber (moRBC). In our coarse-grained model, nodes are sets of Pareto local optimal solutions grouped according to the logarithm of their Pareto rank (following non-dominated sorting). For modelling edges, we consider the original neighbourhood edges, but also propose a new definition representing soft-restarts from Pareto local optima. We analyse and visualise our models on a set of combinatorial landscapes with tuneable ruggedness and number of objectives (MNK-landscapes). The models provide landscape features that correlate with the performance of multi-objective optimisation algorithms, and can be used in algorithm recommendation settings. The model with neighbour edges slightly outperforms the soft-restart model (in terms of predictive power), but its substantial computational overhead makes the soft-restart model a promising approximation.

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Scaling Up Pareto Local Optimal Solutions Networks: Modelling Multi-objective Landscapes

  • Gabriela Ochoa,
  • Hernan Aguirre,
  • Arnaud Liefooghe,
  • Sébastien Verel

摘要

Pareto local optimal solution networks (PLOS-nets) model fitness landscapes as graphs where nodes are Pareto local optima and edges account for standard neighbourhood relationships. PLOS-nets capture the global structure of multi-objective combinatorial landscapes and provide a rich set of features. Published results so far focus on small problems. This article proposes new modelling and sampling methodologies to scale up PLOS-nets to larger problem sizes. Our sampling approach is based on the effective multi-objective random one-bit climber (moRBC). In our coarse-grained model, nodes are sets of Pareto local optimal solutions grouped according to the logarithm of their Pareto rank (following non-dominated sorting). For modelling edges, we consider the original neighbourhood edges, but also propose a new definition representing soft-restarts from Pareto local optima. We analyse and visualise our models on a set of combinatorial landscapes with tuneable ruggedness and number of objectives (MNK-landscapes). The models provide landscape features that correlate with the performance of multi-objective optimisation algorithms, and can be used in algorithm recommendation settings. The model with neighbour edges slightly outperforms the soft-restart model (in terms of predictive power), but its substantial computational overhead makes the soft-restart model a promising approximation.