A Multifactorial Evolutionary Algorithm for Multitasking Under Interval Uncertainties

Various real-world applications with interval uncertainty, such as the path planning of mobile robot, layout of radio frequency identification readers and solar desalination, can be formulated as an interval multiobjective optimization problem (IMOOP), which is usually transformed into one or a series of certain problems to solve by using evolutionary algorithms. However, a definite characteristic among them is that only a single optimization task can be catched up at a time. Inspired by the multifactorial evolutionary algorithm (MFEA), a novel interval MFEA (IMFEA) is proposed to solve IMOOPs simultaneously using a single population of evolving individuals. In the proposed method, the potential interdependency across related problems can be explored in the unified genotype space, and multitasks of multiobjective interval optimization problems are solved at once by promoting knowledge transfer for the greater synergistic search to improve the convergence speed and the quality of the optimal solution set. Specifically, an interval crowding distance based on shape evaluation is calculated to evaluate the interval solutions more comprehensively. In addition, an interval dominance relationship based on the evolutionary state of the population is designed to obtain the interval confidence level, which considers the difference of average convergence levels and the relative size of the potential possibility between individuals. Correspondingly, the strict transitivity proof of the presented dominance relationship is given. The efficacy of the associated evolutionary algorithm is validated on a series of benchmark test functions, as well as a real-world case of robot path planning with many terrains that provides insight into the performance of the method in the face of IMOOPs.