Hamid Reza Yousefzadeh - Department of Mathematics, Payame Noor University (PNU), P.O. BOX ۱۹۳۹۵-۴۶۹۷, Tehran, Iran.
Elham Zahiri - Department of Mathematics, Payame Noor University (PNU), P.O. BOX ۱۹۳۹۵-۴۶۹۷, Tehran, Iran.
Aghileh Heydari - Department of Mathematics, Payame Noor University (PNU), P.O. BOX ۱۹۳۹۵-۴۶۹۷, Tehran, Iran.

The existence of different solution approaches that generate approximations to the optimal Pareto frontiers of a multi-objective optimization problem lead to different sets of non-dominated solutions. To evaluate the quality of these solution sets, one requires a comprehensive evaluation measure to consider the features of the solutions. Despite various  valuation measures, the deficiency caused by the lack of such a comprehensive measure is  visible. For this reason, in this paper, by considering some evaluation measures, first we evaluate the quality of the approximations to the optimal Pareto front resulting from the decomposition-based multi-objective evolutionary algorithm equipped with four decomposition approaches and investigate the related drawbacks. In the second step, we use the concept of Gaussian degree of closeness to combine the evaluation measures, and hence, we propose a new evaluation measure called the quasi-Gaussian integration measure. The numerical results obtained from applying the proposed measure to the standard test functions confirm the effectiveness of this measure in examining the quality of the non-dominated solution set in a more accurate manner.

Multi-objective optimization‎, Evolutionary algorithm‎, Evaluation measure‎, ‎Pareto frontier‎, Decomposition