Multi-speed Gearbox Synthesis Using Global Search and Non-convex Optimization

This paper applies generative design to multi-speed gear box, a type of complex mechanical system. The research investigates various techniques to solve a bi-level, combinatorial optimization problem, including non-convex optimization, graph isomorphism algorithm, best-first search, and estimation of distribution algorithm. These techniques could be also applied in the future to solve many relevant bi-level and combinatorial problems that our customer faces in both AEC and MFC domains.

Abstract

Multi-speed Gearbox Synthesis Using Global Search and Non-convex Optimization

Chiara Piacentini, Hyunmin Cheong, Mehran Ebrahimi, Adrian Butscher

CPAIOR 2020

We consider the synthesis problem of a multi-speed gearbox, a mechanical system that receives an input speed and transmits it to an outlet through a series of connected gears, decreasing or increasing the speed according to predetermined transmission ratios. Here we formulate this as a bi-level optimization problem, where the inner problem involves non-convex optimization over continuous parameters of the components, and the outer task explores different configurations of the system. The outer problem is decomposed into sub-tasks and optimized by a variety of global search methods, namely simulated annealing, best-first search and estimation of distribution algorithm. Our experiments show that a three-stage decomposition coupled with a best-first search performs well on small-size problems, and it outmatches other techniques on larger problems when coupled with an estimation of distribution algorithm.