1. Design Optimization School of Engineering University of Bradford 1 Formulation of a multi-objective problem Pareto optimum set consists of the designs which cannot be improved with respect to all criteria at the same time MULTI-OBJECTIVE PROBLEMS A general multi-objective optimization problem

2. Design Optimization School of Engineering University of Bradford 2 A multi-objective problem MULTI-OBJECTIVE PROBLEMS Pareto optimum solutions correspond to the AB part of the contour

3. Design Optimization School of Engineering University of Bradford 3 Formulation of a multi-objective problem Basic approaches to the formulation of a combined criterion 1. Select the most important criterion and treat it as a single criterion. Impose constraints on the values of all remaining criteria. 2. Linear combination of all criteria. It is important to normalise the criteria using the best values of corresponding individual criteria. 3. The minimax criterion MULTI-OBJECTIVE PROBLEMS where F k * is the desirable value of the criterion F k.