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

Document Type : Research Note


1 iCV Group, Institute of Technology, University of Tartu, Tartu 50411, Estonia

2 Human and Robot Interaction Laboratory, Faculty of New Sciences and Technologies, University of Tehran, Tehran, Iran

3 Mechanical Engineering Department, Colorado School of Mines, USA

4 Telecom ParisTech, Paris, France


This paper aims at introducing a proportion-preserving composite ob-jective function for multi-objective optimization, namely, PPCOF, and  validating its eciency 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.


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