Interactive NBI and (E)NNC methods for the progressive exploration of the criteria space in multi-objective optimization and optimal control

•We introduce a novel interactive method for multi-objective optimization.•The method progressively explores the Pareto delivering a wider set of solutions.•The exploration of the extreme region of the set can generate valuable information.•The interactivity allows exploring only interesting extreme parts of the set.•The method is successfully applied on three scalar and two dynamic problems. A wide range of problems arising from real world applications present multiple and conflicting objectives to be simultaneously optimized. However, this multi-objective nature is too often neglected. Multi-objective optimization proved to be a powerful tool to correctly describe the trade-offs among conflicting objectives in a set of optimal solutions known as the Pareto set. This paper introduces an interactive method to solve multi-objective problems based on geometric considerations. The method returns a wider Pareto set, at a negligible computational cost, when compared to existing methods. The interactivity also allows the decision-maker to explore only relevant parts of the Pareto set. The extreme solutions yield insightful considerations on the generation of the scalarization parameters for the Normal Boundary Intersection and the Enhanced Normalized Normal Constraints methods. The proposed method is applied to: (i) three scalar multi-objective problems and (ii) the multi-objective optimal control of a tubular and a fed-batch reactor.