Multi-objective test problems, linkages, and evolutionary methodologies

Existing test problems for multi-objective optimization are criticized for not having ade-quate linkages among variables. In most problems, the Pareto-optimal solutions correspond to a xed value of certain variables and diversity of solutions comes mainly from a random vari-ation of certain other variables. In this paper, we introduce explicit linkages among variables so as to develop dicult 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. 1 introduction There exists a number of test problems for multi-objective optimization in the evolutionary multi-objective evolutionary optimization (EMO) literature [1, 16, 6, 13, 8]. The reason for developing controllable yet challenging test problems for optimization and using them to test an optimization methodology is to investigate the problem diculties, for which a method performs well an