AN INTERACTIVE APPROACH FOR SOLVING MULTI-OBJECTIVE OPTIMIZATION PROBLEMS (INTERACTIVE COMPUTER, NELDER-MEAD SIMPLEX ALGORITHM, GRAPHICS)
WOODS, DANIEL JOHN
Doctor of Philosophy
Multi-objective optimization problems are characterized by the need to consider multiple, and possibly conflicting, objectives in the solution process. We present an approach based on the use of interactive computer graphics to obtain qualitative information from a user about approximate solutions. We then use this qualitative information to transform the multi-objective optimization problem into a single-objective optimization problem that we may solve using standard techniques. Preliminary convergence results for the Nelder-Mead simplex algorithm are presented. Techniques for updating the single-objective problem after each piece of information is obtained from the user are described. These techniques are based on the duality theory for linear and quadratic programming. A software system for the subclass of 1-dimensional curve-fitting problems is also described.