Cooperative and Distributed Multiobjective Optimization for Heterogeneous Belief Rule Base

So far, there has been only oneoptimization objective in belief rule base (BRB) learning-related studies, either modeling accuracy via parameter learning, modeling complexity via structure learning, or a unified objective representing them both. This article proposes a new cooperative and distributed multiobjective approach for heterogeneous BRB (CDMO-BRB) to simultaneously optimized its structure and parameters. The new CDMO-BRB approach is implemented in a parent–child framework. In the parent process, cooperative optimization is equipped with a multipopulation strategy and another redundant-gene strategy to simultaneously optimize the structure and parameters of BRBs in heterogeneous structures. In the child process, distributed learning is designed to improve optimization efficiency and avoid early convergence and overfitting. A benchmark case on pipeline leakage detection is studied. Case study results show that the structure and parameters of BRB can be optimized simultaneously by pushing forward the Pareto front. In comparison with previous studies, CDMO-BRB has produced superior performance. Moreover, distributed learning is also separately validated.