Explainable data-driven optimization for complex systems with non-preferential multiple outputs using belief rule base

Abstract

To better handle problems with non-preferential multi-outputs (NPMO), a new approach is proposed in this study by employing the belief rule base (BRB) to provide a superior nonlinearity modeling ability as well as good explainability. The new approach is thus called NPMO–BRB. First, a new optimization model is constructed where the optimization objective is the integration of multi-outputs and respective constraints are designed. Then, a new optimization algorithm with a new customized gene makeup is designed where the NPMO–BRB inferencing process is embedded in the fitness calculation procedure. A practical case study on Changsha Metro Line 4 is studied to use multiple geological parameters to infer multiple operational parameters. Case study results show that NPMO–BRB has shown superior performance in comparison with the random forest (RF), the backpropagation neural network (BPNN), the Gradient Gaussian Process (GPR), as well as multiple separate BRBs. Owing to the explainability provided by the NPMO–BRB approach, further investigations into the belief distribution comparison reveal more information that can be used as practical work guidelines.