The divide-and-conquer strategy has been widely used in cooperative co-evolutionary algorithms to deal with large-scale global optimization problems, where a target problem is decomposed into a set of lower-dimensional and tractable subproblems to reduce the problem complexity. However, such strategy usually demands a large number of function evaluations to obtain an accurate variable grouping. To address this issue, a merged differential grouping method is proposed in this paper based on subset-subset interaction and binary search. In the proposed method, each variable is firstly identified as either a separable variable or a non-separable variable. Afterward, all separable variables are put into the same subset, and the non-separable variables are divided into multiple subsets using a binary-tree-based iterative merging method. With the proposed algorithm, the computational complexity of interaction detection is reduced to O(max{n, nns ×log2 k}), where n, nns(≤n), and k(<n) indicate the numbers of decision variables, non-separable variables, and subsets of non-separable variables, respectively. The experimental results on benchmark problems show that merged differential grouping is very competitive with the other state-of-the-art methods in terms of efficiency and accuracy of problem decomposition.

Evolutionary multitasking (EMT) is an emerging research direction in the field of evolutionary computation. EMT solves multiple optimization tasks simultaneously using evolutionary algorithms with the aim to improve the solution for each task via intertask knowledge transfer. The effectiveness of intertask knowledge transfer is the key to the success of EMT. The multifactorial evolutionary algorithm (MFEA) represents one of the most widely used implementation paradigms of EMT. However, it tends to suffer from noneffective or even negative knowledge transfer. To address this issue and improve the performance of MFEA, we incorporate a prior-knowledge-based multiobjectivization via decomposition (MVD) into MFEA to construct strongly related meme helper-tasks. In the proposed method, MVD creates a related multiobjective optimization problem for each component task based on the corresponding problem structure or decision variable grouping to enhance positive intertask knowledge transfer. MVD can reduce the number of local optima and increase population diversity. Comparative experiments on the widely used test problems demonstrate that the constructed meme helper-tasks can utilize the prior knowledge of the target problems to improve the performance of MFEA.

Multiobjectivization has emerged as a new promising paradigm to solve single-objective optimization problems (SOPs) in evolutionary computation, where an SOP is transformed into a multiobjective optimization problem (MOP) and solved by an evolutionary algorithm to find the optimal solutions of the original SOP. The transformation of an SOP into an MOP can be done by adding helper-objective(s) into the original objective, decomposing the original objective into multiple subobjectives, or aggregating subobjectives of the original objective into multiple scalar objectives. Multiobjectivization bridges the gap between SOPs and MOPs by transforming an SOP into the counterpart MOP, through which multiobjective optimization methods manage to attain superior solutions of the original SOP. Particularly, using multiobjectivization to solve SOPs can reduce the number of local optima, create new search paths from local optima to global optima, attain more incomparability solutions, and/or improve solution diversity. Since the term “multiobjectivization” was coined by Knowles et al. in 2001, this subject has accumulated plenty of works in the last two decades, yet there is a lack of systematic and comprehensive survey of these efforts. This article presents a comprehensive multifacet survey of the state-of-the-art multiobjectivization methods. Particularly, a new taxonomy of the methods is provided in this article and the advantages, limitations, challenges, theoretical analyses, benchmarks, applications, as well as future directions of the multiobjectivization methods are discussed.