Gradient-based multi-objective optimization with applications to waterflooding optimization

We consider problems where it is desirable to maximize multiple objective functions, but it is impossible to find a single design vector (vector of optimization variables) which maximizes all objective functions. In this case, the solution of the multi-objective optimization problem is defined as the Pareto front. The defining characteristic of the Pareto front is that, given any specific point on the Pareto front, it is impossible to find another point on the Pareto front or another feasible point which yields a greater value of all objective functions. The focus of this work is on the generation of the Pareto front for bi-objective optimization problems with specific applications to waterflooding optimization.