Solving interval many-objective optimization problems by combination of NSGA-III and a local fruit fly optimization algorithm

Abstract

Interval many-objective optimization problems (IMaOPS) are ubiquitous in practical applications. Therefore, it is of great significance to study the solving method for IMaOPS. However, there are fewer solving methods due to the uncertain interval of the objective function. In this paper, an improved NSGA-III algorithm (named LFOA-NSGA-III) is proposed to effectively solve these problems. Due to the uncertain interval in the IMaOPs, the original NSGA-III algorithm can ineffectively evaluate the relationship between the interval solution set and the reference point. So the matter-element extension model is introduced, which can make the optimized solution set close to the Pareto optimal solution. Furthermore, in order to improve the optimization performance and population diversity of the improved algorithm, the K-mean algorithm is used to solve the initial solution set, as well as a local fruit fly optimization algorithm (FOA) is combined with the genetic algorithm (GA). Finally, the LFOA-NSGA-III algorithm is empirically evaluated on eleven interval benchmark test problems and an unmanned aerial vehicles (UAVs) path planning problem. Through simulation comparisons with other different algorithms, it is concluded that the hyper-volume value, the imprecision value and the IGD value indicators are significantly better than other comparison algorithms. In addition, from a simulation experiment in application of the multi-UAVs path planning problem, it can be seen that the LFOA-NSGA-III algorithm is more effective and applicative in the IMaOPs.