Deriving Functions for Pareto Optimal Fronts Using Genetic Programming

Genetic Programming is a specialized form of genetic algorithms which evolve trees. This paper proposes an approach to evolve an expression tree, which is an N-Ary tree that represents a mathematical equation and that describes a given set of points in some space. The points are a set of trade-off solutions of a multi-objective optimization problem (MOOP), referred to as the Pareto Optimal Front (POF). The POF is a curve in a multi-dimensional space that describes the boundary where a single objective in a set of objectives cannot improve more without sacrificing the optimal value of the other objectives. The algorithm, proposed in this paper, will thus find the mathematical function that describes a POF after a multi-objective optimization algorithm (MOA) has solved a MOOP. Obtaining the equation will assist in finding other points on the POF that was not discovered by the MOA. Results indicate that the proposed algorithm matches the general curve of the points, although the algorithm sometimes struggles to match the points perfectly.