I have doubt in computing IGD value in multi-objective optimization. In IGD, Euclidean distance is computed. My doubt is that Euclidean distance is computed between what? whether compute Euclidean distance between Pareto optimal solutions(denoted by PS*={x| x is a Pareto optimal solution}) and obtained set (ours) or between Pareto front (denoted PF*={(f1(x),f2(x),....,fM(x))|x is Pareto optimum}) and our obtained Pareto front PF.
Dear Yenugula RAMU Naidu,
Look the link. May be useful.
http://www.sciencedirect.com/science/article/pii/S1568494614003913
http://e-collection.library.ethz.ch/eserv/eth:25454/eth-25454-01.pdf
Regards, Shafagat
Dear Yenugula RAMU Naidu
The following links may be useful in this case.
http://e-collection.library.ethz.ch/eserv/eth:25454/eth-25454-01.pdf
http://www.iaeng.org/publication/WCE2008/WCE2008_pp1155-1159.pdf
If I understand the question correctly then you want to know whether to calculate the IGD value in objective space or decision space. Then the answer is in objective space. So the IGD values are calculated between your obtained Pareto front and the reference Pareto front. It can be confusing because Pareto front and Pareto set are sometimes used as synonyms but sometimes Pareto set means optimal decision variables and Pareto front optimal objective values. Hope this helps.
Regards,
Miha
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