Parallel Differential Evolution Algorithms for Stackelberg-Nash Bilevel Optimization Problems

The Bilevel Programming Problems with interdependent followers are characterized by three or more optimization problems nested in a hierarchical structure of the type leader-followers whose solution configures a Stackelberg-Nash equilibrium game. Their complexity and structure make many of them almost impracticable for solving via classical deterministic methods. Thus, population-based metaheuristics have been used to handle this class of problems. However, while the meta-models-based implementations are not indicated to tackle the inter-dependent followers BLPs, their nested structure can greatly increment the already high computational cost of the metaheuristics. Thus, we offer and study the three first parallel models for solving Stackelberg-Nash equilibrium BLPs via metaheuristics. All our parallel approaches are scalable and can be efficiently executed in individual multi-cores computing nodes and in high-distributed computational clusters. We reported relevant speedups for different computing architectures, which endorsed the potential of the proposals of this work as relevant tools to enable the study of increasingly larger and complex inter-dependent followers BLPs.