Optimization Toolbox

Multiobjective Optimization

The rigidity of the mathematical problem posed by the general optimization formulation given in GP (Eq. 3-1) is often remote from that of a practical design problem. Rarely does a single objective with several hard constraints adequately represent the problem being faced. More often there is a vector of objectives

that must be traded off in some way. The relative importance of these objectives is not generally known until the system's best capabilities are determined and tradeoffs between the objectives fully understood. As the number of objectives increases, tradeoffs are likely to become complex and less easily quantified. There is much reliance on the intuition of the designer and his or her ability to express preferences throughout the optimization cycle. Thus, requirements for a multiobjective design strategy are to enable a natural problem formulation to be expressed, yet to be able to solve the problem and enter preferences into a numerically tractable and realistic design problem.

This section includes

• An introduction to multiobjective optimization, which looks at a number of alternative methods
• A discussion of the Goal Attainment method, which can be posed as a nonlinear programming problem
• Algorithm improvements to the SQP method, for use with the Goal Attainment method

SQP Implementation

Introduction