Real-world optimization applications in complex systems always contain multiple factors to be optimized, which can be formulated as multi-objective optimization problems. These problems have been solved by many evolutionary algorithms like MOEA/D, NSGA-III, and KnEA. However, when the numbers of decision variables and objectives increase, the computation costs of those mentioned algorithms will be unaffordable. To reduce such high computation cost on large-scale many-objective optimization problems, we proposed a two-stage framework. The first stage of the proposed algorithm combines with a multi-tasking optimization strategy and a bi-directional search strategy, where the original problem is reformulated as a multi-tasking optimization problem in the decision space to enhance the convergence. To improve the diversity, in the second stage, the proposed algorithm applies multi-tasking optimization to a number of sub-problems based on reference points in the objective space. In this paper, to show the effectiveness of the proposed algorithm, we test the algorithm on the DTLZ and LSMOP problems and compare it with existing algorithms, and it outperforms other compared algorithms in most cases and shows disadvantage on both convergence and diversity.

复杂系统中的实际优化应用程序总是包含多个要优化的因素，可以将其表述为多目标优化问题。这些问题已通过许多进化算法（如MOEA / D，NSGA-III和KnEA）解决。但是，当决策变量和目标的数量增加时，这些算法的计算成本将无法承受。为了减少大规模多目标优化问题的高计算成本，我们提出了一个两阶段框架。该算法的第一阶段结合了多任务优化策略和双向搜索策略，其中原始问题在决策空间中被重新表述为多任务优化问题，以增强收敛性。为了提高多样性，在第二阶段，所提出的算法基于目标空间中的参考点将多任务优化应用于多个子问题。在本文中，为了证明所提算法的有效性，我们在DTLZ和LSMOP问题上对该算法进行了测试，并将其与现有算法进行了比较，在大多数情况下其性能均优于其他比较算法，并且在收敛性和多样性上都表现出劣势。