  Multi-task optimization (MTO) studies how to simultaneously solve multiple
optimization problems for the purpose of obtaining better performance on each
problem. Over the past few years, evolutionary MTO (EMTO) was proposed to
handle MTO problems via evolutionary algorithms. So far, many EMTO algorithms
have been developed and demonstrated well performance on solving real-world
problems. However, there remain many works to do in adapting knowledge transfer
to task relatedness in EMTO. Different from the existing works, we develop a
self-adaptive multi-task particle swarm optimization (SaMTPSO) through the
developed knowledge transfer adaptation strategy, the focus search strategy and
the knowledge incorporation strategy. In the knowledge transfer adaptation
strategy, each task has a knowledge source pool that consists of all knowledge
sources. Each source (task) outputs knowledge to the task. And knowledge
transfer adapts to task relatedness via individuals' choice on different
sources of a pool, where the chosen probabilities for different sources are
computed respectively according to task's success rate in generating improved
solutions via these sources. In the focus search strategy, if there is no
knowledge source benefit the optimization of a task, then all knowledge sources
in the task's pool are forbidden to be utilized except the task, which helps to
improve the performance of the proposed algorithm. Note that the task itself is
as a knowledge source of its own. In the knowledge incorporation strategy, two
different forms are developed to help the SaMTPSO explore and exploit the
transferred knowledge from a chosen source, each leading to a version of the
SaMTPSO. Several experiments are conducted on two test suites. The results of
the SaMTPSO are comparing to that of 3 popular EMTO algorithms and a particle
swarm algorithm, which demonstrates the superiority of the SaMTPSO.
