An Improved Nondominated Sorting Multiobjective Genetic Algorithm and Its Application

The nondominated sorting genetic algorithm with elitism (NSGA-II) is widely used due to its good performance on solving multiobjective optimization problems. In each iteration of NSGA-II, truncation selection is performed based on the rank and crowding distance of each solution. There are, however, drawbacks in this process. These drawbacks to some extent cause overlapping solutions in the population and have an affection on the spread of nondominated solutions, which reduces the diversity of the obtained solution set. In this paper, 4 causes for generation of the overlapping solutions are investigated firstly. A new technique for alleviating this phenomenon is incorporated to enhance the capability of NSGA-II. The improved algorithm is referred to as NSGA-II+ in this paper. In NSGA-II+, overlapping solutions are removed during the truncation selection from the merged population (which is a combination of parent population and offspring population) after ranking in each iteration. The overlapping solutions and the ones with small crowding distance are removed one by one. The crowding distance is recalculated once a solution is removed. The performance of the improved algorithm is evaluated on four difficult test problems. Then NSGA-II+ is applied to the optimization of a composite wing structure with 2 objectives. Numerical results are reported which demonstrate the effectiveness of NSGA-II+. Keywords—nondominated sorting genetic algorithm, overlapping solutions, truncation selection, composite wing structure