A Homotopy Method for Large-Scale Multi-Objective Optimization

A homotopy method for multi-objective optimization that produces uniformly sampled Pareto fronts by construction is presented. While the algorithm is general, of particular interest is application to simulation-based engineering optimization problems where economy of function evaluations, smoothness of result, and time-to-solution are critical. The presented algorithm achieves an order of magnitude improvement over other geometrically motivated methods, like Normal Boundary Intersection and Normal Constraint, with respect to solution evenness for similar computational expense. Furthermore, the resulting uniformity of solutions extends even to more difficult problems, such as those appearing in common Evolutionary Algorithm test cases.