A Robust Proportion-Preserving Composite Objective Function for Scale-Invariant Multi-Objective Optimization

Abstract

This paper aims at introducing a proportion-preserving composite ob-jective function for multi-objective optimization, namely, PPCOF, and validating its e ciency through demonstrating its applicability to opti- mization of the kinetostatic performance of planar parallel mechanisms. It exempts the user from both specifying preference factors and conduct- ing decision-making. It consists of two terms. The rst one adds the normalized objective functions up, where the extrema are resulted from single-objective optimization. To making the composite objective func- tion steer the variations of the objective functions while preserving ra- tional proportions between them, as the main contribution of the paper, it is sought that the normalized objective functions take closely similar values, to which end, they are juxtaposed inside a vector, which is then scaled such that its Euclidean norm-2 is equal to that of the vector of all ones with the same dimensions, and then the second term is constructed as the addition of penalty factors standing for the absolute value of the di erence between each element of the foregoing vector from 1. Based on the experimental results, with a considerably smaller computational cost, the PPCOF obtains an optimal solution that is not dominated by any point from a set of Pareto-optimal solutions o ered by NSGA-II.