A Bi-Level Multi-Objective Optimization Algorithm with a Bounded Multi-Variate Conjugate Gradient Method.

Abstract

Designing any complex system requires engaging many areas. Thus, it is necessary for engineers from multiple disciplines, such as hydrodynamics, structures, etc., to collaborate. Although this increased collaboration across multiple disciplines has yielded tremendous benefit, it makes the design process substantially more difficult. Engineers must communicate frequently across all the disciplines, and they can no longer design in isolation. Therefore, efficient algorithms that are capable of facilitating interaction across multiple engineering disciplines are required. Moreover, the collaboration across multiple disciplines tends to increase the size of the optimization problems. When multiple disciplines are considered, more elements of the system have to be accounted with greater accuracy. As a result, size of engineering optimization problems has increased exponentially in recent years. However, many classical optimization algorithms are not suited to solve optimization problems with a large number of design variables (large-scale). The goal of this research is to create a flexible multidisciplinary optimization algorithm that is capable of solving large-scale optimization problem by improving known optimization techniques. First, a new bi-level multi-objective optimization algorithm is developed. Engineering systems are designed in a distributed environment where multiple departments design each respective sub-system. However, these departments often have mutually conflicting objectives, and it is necessary to measure the trade- off between different objectives that the system needs to achieve. The new bi-level multi-objective optimization framework finds the trade-off of multiple objectives in a distributed environment. A numerical optimization method called ‘Conjugate Gradient (CG) method’ is modified to solve optimization problems with a large number of design variables. The CG method is known for its low memory requirement and strong convergence properties. It is one of the earliest large-scale optimization algorithms; the modifications are made to improve its computing time and the rate of convergence for large-scale optimization problems. In the last phase of research, the bi-level multi-objective optimization algorithm and the modified conjugate gradient method are combined to create a multi-disciplinary optimization capability suitable for solving problems with a large number of design variables.