A new approach for solving vector optimization problems

A method is presented to solve parametric vector optimization problems. Vector optimization problems consist of n objectives (at least two) which are concurrently improved. The new approach is based on a stochastic search algorithm, and solves the problem directly without any transformation into scalar subproblems. The solution set describes a (n-1)-dimensional hyper plane, which is approximated by a finite number of points, being uniformly distributed among the hyper plane. As a practical application, the method is applied to optimize a 6-pole permanent magnet synchronous machine. The machine design is optimized with respect to two objectives, the internal power and the magnet volume. Objective 1 is maximized and objective 2 is minimized. The two design parameters “magnet width” and “magnet height” are variable between defined upper and lower bounds