A developed version of Generalized Differential Evolution, GDE3, is proposed. GDE3 is an extension of Differential Evolution (DE) for global optimization with an arbitrary number of objectives and constraints. In the case of a problem with a single objective and without constraints GDE3 falls back to the original DE. GDE3 improves earlier GDE versions in the case of multiobjective problems by giving a better distributed solution. Performance of GDE3 is demonstrated with a set of test problems and the results are compared with other methods.

This study reports how the Differential Evolution (DE) algorithm performed on the test bed developed for the CEC05 contest for real parameter optimization. The test bed includes 25 scalable functions, many of which are both non-separable and highly multi-modal. Results include DE's performance on the 10 and 30-dimensional versions of each function.

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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.

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