An Application of BnB-NSGAII: Initializing NSGAII to Solve 3 Stage Reducer Problem

TL;DR

This paper introduces BnB-NSGAII, a hybrid method combining branch and bound with NSGAII, to improve initial population quality for solving complex 3-stage reducer problems constrained by ISO standards.

Contribution

The paper proposes a novel hybrid initialization method, BnB-NSGAII, with a legacy feature for inheritance, enhancing NSGAII performance on complex multi-criteria engineering problems.

Findings

BnB-NSGAII with legacy feature outperforms standard NSGAII.

The hybrid method improves solution quality for constrained reducer problems.

Results show competitive performance of the proposed approach.

Abstract

The 3 stage reducer problem is a point of interest for many researchers. In this paper, this problem is reformulated to a bi-objective problem with additional constraints to meet the ISO mechanical standards. Those additional constraints increase the complexity of the problem, such that, NSGAII performance is not sufficient. To overcome this, we propose to use BnB-NSGAII method - a hybrid multi-criteria branch and bound with NSGAII - to initialize NSGAII before solving the problem, seeking for a better initial population. A new feature is also proposed to enhance BnB-NSGAII method, called the legacy feature. The legacy feature permits the inheritance of the elite individuals between - branch and bound - parent and children nodes. NSGAII and BnB-NSGAII with and without the legacy feature are tested on the 3 stage reducer problem. Results demonstrate the competitive performance of BnB-NSGAII with the legacy feature.