A robust proportion-preserving composite objective function for scale-invariant multi-objective optimization

This paper aims to introduce a proportion-preserving composite objective function for multi-objective optimization, namely, PPCOF, and validate its eciency through demonstrating its applicability to optimization of the kinetostatic performance of planar parallel mechanisms. It exempts the user from both specifying preference factors and conducting decision-making. It consists of two terms. The rst one adds the normalized objective functions up, where the extrema result from single-objective optimization. To make the composite objective function steer the variations of the objective functions while preserving rational 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. Then, the second term is constructed as the addition of penalty factors standing for the absolute value of the dierence between each element of the foregoing vector from 1. From the obtained results, with considerably smaller computational cost, the PPCOF obtains an optimal solution that is not dominated by any point from a set of Pareto-optimal solutions oered by NSGA-II.