A Projection-Based Approach for Constructing Piecewise Linear Pareto Front Approximations

Real-life design problems often require simultaneous optimization of multiple conflicting criteria resulting in a set of best trade-off solutions. This best trade-off set of solutions is referred to as Pareto optimal front (POF) in the outcome space. Obtaining the complete POF becomes impractical for problems where evaluation of each solution is computationally expensive. Such problems are commonly encountered in several fields, such as engineering, management, and scheduling. A practical approach in such cases is to construct suitable POF approximations, which can aid visualization, decision-making, and interactive optimization. In this paper, we propose a method to generate piecewise linear Pareto front approximation from a given set of N Pareto optimal outcomes. The approximations are represented using geometrical linear objects known as polytopes, which are formed by triangulating the given M-objective outcomes in a reduced $(M−1)$-objective space. The proposed approach is hence referred to as projection-based Pareto interpolation (PROP). The performance of PROP is demonstrated on a number of benchmark problems and practical applications with linear and nonlinear fronts to illustrate its strengths and limitations. While being novel and theoretically interesting, PROP also improves on the computational complexity required in generating such approximations when compared with existing Pareto interpolation (PAINT) algorithm.