**8. Conclusions**

As a novel optimization paradigm proposed five years ago, with the increasing complexity and volume of data collected in the data-driven world of today, multi-task optimization appears to be an indispensable and competitive tool for the future. Since it has been proposed by Ong in 2015 [24], it has gradually attracted the attention of scholars in the community of evolutionary computation and many good results have been obtained.

To the best of our knowledge, this paper is the first literature review devoted to multitask optimization and multi-task evolutionary computation. This overview introduced the basic definition of MTO and several confusing concepts of MTO, such as multi-objective optimization, sequential transfer optimization, and multi-form optimization. Some bold theoretical conclusions are also provided, mainly in terms of convergence performance and time complexity of some simplified forms of MFEA. Its goal is theoretically explaining the superiority of the existing MTEC algorithm compared with traditional single-task EAs.

As the core of this review article, a variety of implementation approaches of key components of MTEC are described in Section 4, including a chromosome encoding and decoding scheme, intro-population reproduction, inter-population reproduction, balance between intra-population reproduction and inter-population reproduction, and evaluation and selection strategy. In particular, we provided a clear description of inter-population

reproduction, dealing with the when, what, and how of achieving positive knowledge transfer. Further, other related extension issues of MTEC were summarized in Section 5, but they are just preliminary, fragmentary attempts and lack systematization. Next, the applications of MTEC in science and engineering were reviewed, highlighting the theoretical meaning and practical value of each problem.

Finally, a number of trends for further research and challenges that can be undertaken to help move the field forward are discussed. In a word, the future work in MTO and MTEC includes but is not limited to (1) exploring a novel mechanism of positive knowledge transfer, (2) strengthening the theoretical research to set a solid foundation, (3) enhancing the effectiveness and efficiency of MTEC algorithms by various advanced technologies, (4) extend MTEC algorithms in more complex scenarios, such as many-task or uncorrelated optimization problems under uncertainties, (5) developing real-world applications of MTEC, e.g., in machine learning, smart manufacturing [191], and smart logistics [192], and (6) comparing disparate MTEC algorithms under different scenarios.

In short, the purpose of this review article is twofold. For researchers in the evolution computation community, it provides a comprehensive review and examination of MTEC. Further, we hope to encourage more practitioners working in the related fields to become involved in this fascinating territory.

**Author Contributions:** Conceptualization, methodology, Q.X.; formal analysis, investigation, supervision, project administration, funding acquisition, Q.X., N.W., and L.W.; resources, data curation, W.L. and Q.S.; writing—original draft preparation, Q.X., N.W., L.W., and W.L.; writing—review and editing, Q.X. and L.W. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was partially supported by the National Science Foundation of China 61773314, Natural Science Basic Research Program of Shaanxi 2019JZ-11 and 2020JM-709, Scientific Research Project of Education Department of Shaanxi Provincial Government 19JC011, and Research Development Foundation of Test and Training Base 23.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
