  Multi-tasking optimization can usually achieve better performance than
traditional single-tasking optimization through knowledge transfer between
tasks. However, current multi-tasking optimization algorithms have some
deficiencies. For high similarity problems, the knowledge that can accelerate
the convergence rate of tasks has not been fully taken advantages of. For low
similarity problems, the probability of generating negative transfer is high,
which may result in optimization performance degradation. In addition, some
knowledge transfer methods proposed previously do not fully consider how to
deal with the situation in which the population falls into local optimum. To
solve these issues, a two-stage adaptive knowledge transfer evolutionary
multi-tasking optimization algorithm based on population distribution, labeled
as EMT-PD, is proposed. EMT-PD can accelerate and improve the convergence
performance of tasks based on the knowledge extracted from the probability
model that reflects the search trend of the whole population. At the first
transfer stage, an adaptive weight is used to adjust the step size of
individual's search, which can reduce the impact of negative transfer. At the
second stage of knowledge transfer, the individual's search range is further
adjusted dynamically, which can improve the diversity of population and be
beneficial for jumping out of local optimum. Experimental results on
multi-tasking multi-objective optimization test suites show that EMT-PD is
superior to other six state-of-the-art evolutionary multi/single-tasking
algorithms. To further investigate the effectiveness of EMT-PD on
many-objective optimization problems, a multi-tasking many-objective test suite
is also designed in this paper. The experimental results on the new test suite
also demonstrate the competitiveness of EMT-PD.
