Adaptive Epsilon dominance in decomposition-based multiobjective evolutionary algorithm

Complicated geometric shapes of Pareto fronts can cause difficulties for multiobjective evolutionary algorithms. To deal with these difficulties, efficient diversity strategies must be highly addressed in order to obtain a set of representative Pareto solutions. In decomposition-based multiobjective evolutionary algorithms, this is often done by optimizing multiple single objective subproblems defined by a set of weight vectors. For complicated Pareto fronts with extreme convexity, disconnection or degeneracy, however, it is nontrivial to set these weight vector properly. To overcome this shortcoming, we propose a new decomposition-based multiobjective evolutionary algorithm based on a hybrid weighting strategy, which optimizes both random subproblems and fixed subproblems. To maintain diversity of nondominated solutions stored in external population, a new archiving strategy based on adaptive Epsilon dominance is also suggested in our proposed algorithm. Our experimental results have showed that our proposed algorithm is superior to several other state-of-the-art multiobjective evolutionary algorithms on a set of benchmark multiobjective test problems with different challenging difficulties regarding the geometric shapes of Pareto fronts.