Multi-Objective Optimisation Problems: A Symbolic Algorithm for Performance Measurement of Evolutionary Computing Techniques

In this paper, a symbolic algorithm for solving constrained multi-objective optimisation problems is proposed. It is used to get the Pareto optimal solutions as functions of KKT multipliers (lambda) over bar for multi-objective problems with continuous, differentiable, and convex/pseudo-convex functions. The algorithm is able to detect the relationship between the decision variables that form the exact curve/hyper-surface of the Pareto front. This algorithm enables to formulate an analytical form for the true Pareto front which is necessary in absolute performance measurement of evolutionary computing techniques. Here the proposed technique is tested on some test problems which have been chosen from a number of significant past studies. The results show that the proposed symbolic algorithm is robust to find the analytical formula of the exact Pareto front.