Response surface approximation of pareto optimal front in multi-objective optimization

Many engineering design problems have multiple objectives. The optimal solutions to these problems are known as Pareto optimal solutions and their function space representation is called the Pareto optimal front. The Pareto optimal front can help the designer visualize the trade-offs between different objectives and select an appropriate compromise design. In this paper, a systematic approach is presented to approximate the Pareto optimal front using a response surface. The Pareto optimal solutions are obtained using a combination of an evolutionary algorithm (elitist non-dominated sorting genetic algorithm NSGA-II) and a local search (ε-constraint strategy). This solution set is used for approximating the Pareto optimal front by a response surface. The proposed method is applied to a rocket injector design problem where the surrogate models are used to evaluate the design objectives of the injector. Insight into the trade-offs between different objectives is obtained from the Pareto optimal solutions and the approximated Pareto optimal front.