A novel algorithm for fast representation of a Pareto front with adaptive resolution: Application to multi-objective optimization of a chemical reactor

- A novel algorithm for the representation of the Pareto front is presented.
- Large overhead of the smart filter approach is avoided.
- Algorithm revolves around a divide and conquer approach.
- Decision maker can decide a priori the resolution of the Pareto front.
- Illustrated with multi-objective bench mark problems.

Solving a multi-objective optimization problem yields an infinite set of points in which no objective can be improved without worsening at least another objective. This set is called the Pareto front. A Pareto front with adaptive resolution is a representation where the number of points at any segment of the Pareto front is directly proportional to the curvature of this segment. Such representations are attractive since steep segments, i.e., knees, are more significant to the decision maker as they have high trade-off level compared to the more flat segments of the solution curve. A simple way to obtain such representation is the a posteriori analysis of a dense Pareto front by a smart filter to keep only the points with significant trade-offs among them. However, this method suffers from the production of a large overhead of insignificant points as well as the absence of a clear criterion for determining the required density of the initial dense representation of the Pareto front. This paper's contribution is a novel algorithm for obtaining a Pareto front with adaptive resolution. The algorithm overcomes the pitfalls of the smart filter strategy by obtaining the Pareto points recursively while calculating the trade-off level between the obtained points before moving to a deeper recursive call. By using this approach, once a segment of trade-offs insignificant to the decision maker's needs is identified, the algorithm stops exploring it further. The improved speed of the proposed algorithm along with its intuitively simple solution process make it a more attractive route to solve multi-objective optimization problems in a way that better suits the decision maker's needs.