A novel non-gradient optimization methodology with application to mechanical design and scheduling in production and healthcare.

摘要

Modern engineering design optimization, scheduling in industrial engineering featuring combinatorial optimization, and appointment optimization in healthcare share some common challenges, i.e., they all demand methods that can handle often expensive black-box objective functions, work without function gradients, and locate the optima efficiently and robustly. Meta-modeling techniques arise from the field of design optimization, as well as meta-heuristics or stochastic search approaches in combinatorial optimization are non-gradient methodologies that have been developed to solve simulation (black-box)-based optimization problems. There lacks of a methodology, however, that is capable of efficiently solving problems of no-gradient and (expensive) black-box functions originated from above-mentioned different areas. This thesis proposes such a methodology that consists of a series of methods rooted in Mode Pursuing Sampling (MPS) (Wang et al. (2004a)). In its original form, MPS only solves continuous global optimization problems. In this work, MPS has been extended to design problems involving discrete variables, as well as combinatorial problems with a large search space. Correspondingly four variants of algorithms have been developed, namely, D-MPS for discrete-variable global optimization, Co-MPS for combinatorial optimization, TSP-MPS for the well-known Traveling Salesman Problem, and AS-MPS for appointment scheduling in healthcare. All of the algorithms have achieved better or comparable results with the state-of-the-art. The work contributes significantly by bringing the core concept of MPS into the discrete and combinational optimization domains and by developing a novel Double Sphere Method that is common in all the algorithms. The developed methods have high potential to be used in industrial practice.