Rank-density-based multiobjective genetic algorithm and benchmark test function study

Concerns the use of evolutionary algorithms (EA) in solving multiobjective optimization problems (MOP). We propose the use of a rank-density-based genetic algorithm (RDGA) that synergistically integrates selected features from existing algorithms in a unique way. A new ranking method, automatic accumulated ranking strategy, and a "forbidden region" concept are introduced, completed by a revised adaptive cell density evaluation scheme and a rank-density-based fitness assignment technique. In addition, four types of MOP features, such as discontinuous and concave Pareto front, local optimality, high-dimensional decision space and high-dimensional objective space are exploited and the corresponding MOP test functions are designed. By examining the selected performance indicators, RDGA is found to be statistically competitive with four state-of-the-art algorithms in terms of keeping the diversity of the individuals along the tradeoff surface, tending to extend the Pareto front to new areas and finding a well-approximated Pareto optimal front.