Evolutionary Multitasking With Global and Local Auxiliary Tasks for Constrained Multi-Objective Optimization

Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.

Effect of substrate type on Ni self-assembly process

Ni self-assembly has been performed on Ga N(0001), Si(111) and sapphire(0001) substrates. Scanning electron microscopy(SEM) images verify that the Si(111) substrate leads to failure of the Ni assembly due to Si–N interlayer formation; the GaN(0001) and sapphire(0001) substrates promote assembly of the Ni particles. This indicates that the GaN/sapphire(0001) substrates are fit for Ni self-assembly. For the Ni assembly process on Ga N/sapphire(0001) substrates,three differences are observed from the x-ray diffraction(XRD) patterns:(i) Ni self-assembly on the sapphire(0001) needs a 900?C annealing temperature, lower than that on the GaN(0001) at 1000?C, and loses the Ni network structure stage;(ii) the Ni particle shape is spherical for the sapphire(0001) substrate, and truncated-cone for the GaN(0001) substrate; and(iii) a Ni–N interlayer forms between the Ni particles and the GaN(0001) substrate, but an interlayer does not appear for the sapphire(0001) substrate. All these differences are attributed to the interaction between the Ni and the Ga N/sapphire(0001) substrates. A model is introduced to explain this mechanism.

Differential Evolution with Level-Based Learning Mechanism

To address complex single objective global optimization problems,a new Level-Based Learning Differential Evolution(LBLDE)is developed in this study.In this approach,the whole population is sorted from the best to the worst at the beginning of each generation.Then,the population is partitioned into multiple levels,and different levels are used to exert different functions.In each level,a control parameter is used to select excellent exemplars from upper levels for learning.In this case,the poorer individuals can choose more learning exemplars to improve their exploration ability,and excellent individuals can directly learn from the several best individuals to improve the quality of solutions.To accelerate the convergence speed,a difference vector selection method based on the level is developed.Furthermore,specific crossover rates are assigned to individuals at the lowest level to guarantee that the population can continue to update during the later evolutionary process.A comprehensive experiment is organized and conducted to obtain a deep insight into LBLDE and demonstrates the superiority of LBLDE in comparison with seven peer DE variants.