@inproceedings{2006001, abstract = {Existing test problems for multi-objective optimization are criticized for not having adequate linkages among variables. In most problems, the Pareto-optimal solutions correspond to a fixed value of certain variables and diversity of solutions comes mainly from a random variation of certain other variables. In this paper, we introduce explicit linkages among variables so as to develop difficult two and multi-objective test problems along the lines of ZDT and DTLZ problems. On a number of such test problems, this paper compares the performance of a number of EMO methodologies having (i) variable-wise versus vector-wise recombination operators and (ii) spatial versus unidirectional recombination operators. Interesting and useful conclusions on the use of above operators are made from the study. Copyright 2006 ACM.}, author = {Deb, Kalyanmoy and Sinha, Ankur and Kukkonen, Saku}, booktitle = {GECCO 2006 - Genetic and Evolutionary Computation Conference}, doi = {10.1145/1143997.1144179}, isbn = {1595931864}, keywords = {Evolutionary Multi-objective optimization,Generalized differential evolution,Linkages,NSGA-II,Recombination operator,Test problems}, pages = {1141--1148}, title = {{Multi-objective test problems, linkages, and evolutionary methodologies}}, volume = {2}, year = {2006} }