6.2.4. Others

Thanks to the effectiveness of MTEC algorithms, they have been successfully applied to tackle other real-world problems in the literature, such as mobile robot path planning [44,107,108], search-based software test data generation [139], the cloud computing service composition problem [74,179], HIV-1 protease cleavage sites prediction [180], and the double-pole balancing problem [61–63].

#### **7. Future Works**

Although multi-task optimization methodology in the evolutionary community has been a tremendous success, compared with other well-known evolutionary and swarm intelligent methods, it is just at the stage of discipline creation and preliminary exploration in a so far unexplored research direction. Many challenges are ye<sup>t</sup> to be discovered and overcome in the future in theoretical models, efficient algorithms, and engineering applications of this promising paradigm. Based on the literature analysis in the past five years, some opportunities and challenges of MTO and MTEC are summarized as follows [11,184].

#### *7.1. Explore Mechanism of Knowledge Transfer*

One of the main features of MTEC algorithms is knowledge transfer from one task to help solve other tasks, which greatly affects the optimization process and algorithm performance. Considering the general process of transfer learning, there are three key issues to be solved serially: (1) when to transfer; (2) what to transfer; (3) how to transfer.

As the original, the first question is to answer when the knowledge transfer is triggered. Theoretically, it is initiated at any stage of optimization process. Thus, the straightforward answer is executing it periodically in a fixed generation interval [21,102]. However, this trial-and-error approach does not properly explain or define the true transfer demands, leading to resource waste. Therefore, we should carefully strike a good balance between transfer cost and transfer effect. One possible and reasonable attempt in the literature is the knowledge transfer across tasks being triggered when the best solutions found so far stagnate for successive generations [88,97].

The second question might seem simple, but it is deceptively difficult. Intuitively, the best solutions found so far are good choices to be transferred. However, it might be counter-productive due to distinctly different search spaces of constitutive tasks. Inspired by biomes symbiosis, three relationships between source tasks and target tasks (mutualism, parasitism, and competition) were summarized in [83] by Li et al. Xu et al. [144] also provided a negative case when the optimal solutions were located in different positions in the unified search space. A potential approach is using the distribution characteristics of population or fitness landscape characteristics of task, instead of a special solution. These characteristics represent a full view of population or task, guiding to the global optimal solutions of each task. More importantly, the MTEC algorithm can learn these characteristics online and then adjust knowledge transfer strategy in a timely manner and properly. As a result, an important research topic is the formulation of approximate online models that can make use of the data generated during the optimization process to somehow quantify the relatedness between tasks.

The research findings of the third question are the most fruitful among three issues. In general, there are two knowledge transfer schemes in multi-task scenario in the literature: implicit transfer and explicit transfer, which are systematically discussed in Section 4.3. Although the experimental results of these schemes are encouraging, it must be kept in mind that the transfer of genetic material across tasks may be pessimistic or negative in some cases. Therefore, the mechanism of knowledge transfer across tasks should be further explored. Only by fully understanding internal mechanisms and external connections of knowledge transfer can we construct novel and positive knowledge transfer strategies.

#### *7.2. Balance Theoretical Analysis and Practical Application*

At present, most scholars concentrated mainly on algorithmic advancement and practical application. The superiority of MTEC algorithms is, in most cases, illustrated by simulation results, not by mathematical analysis with some pertinent mathematical concepts and tools. On the other hand, the researchers and practitioners ignore further study on the theoretic analysis of MTO and MTEC, either consciously or unconsciously. The most representative results focused on convergence performance [37,41] and time complexity [46,47] of simplified MFEA, which theoretically explains the superiority of the

MTEC algorithm compared with traditional single-task EAs. Comparatively speaking, other theoretical analysis (stability, diversity, etc.) of the MTEC algorithm is very limited and the distinct theoretical framework has not been assessed so far.

As a novel evolution computation paradigm, MTEC has distinct characteristics, such as a unified search space, assortative mating, and selective evaluation, to distinguish it from the single-task EAs. The intensive research of the theoretical models and functioning mechanisms of these key stone characteristics is infrequent. For this reason, the essential and fundamental development of MTO and MTEC has been hard to obtain until now.

#### *7.3. Enhance Effectiveness and Efficiency of MTEC Algorithms*

To optimize multiple tasks simultaneously, the effectiveness and adaptation of MTEC algorithm is especially important for a practitioner. In addition to canonical genetic operators (crossover, mutation, and selection), individuals encoding schemes in the unified genotype space and the implicit genetic transfer (via assortative mating and vertical cultural transmission) are the most critical ingredients of the original MFEA [18]. To improve the effectiveness and efficiency, more existing encoding schemes and genetic operators available in the literature need to be tested in a multi-task setting.

On the other hand, the performance of MTEC algorithm mainly depends on the tasks to be optimized. If the adopted methodology does not appropriately suit the behavior or feature of optimization tasks, the optimization process may be counterproductive. Therefore, we should accurately depict and deeply understand the optimization problem we face. As a critical problem to be solved urgently, based on the key feature of each task, a variety of novel encoding schemes and genetic operators can be designed to achieve the active controlling of population diversity and adaptive adjustment over the search direction of the population.

More fundamentally, we can try to modify the basic structure of the MTEC algorithm [185,186]. For instance, Chen et al. [129] introduced a local search strategy based on quasi-Newton, a re-initialization technique of worse individuals, and a self-adapt parent selection strategy to obtain better solutions. Due to the grea<sup>t</sup> success of memetic algorithms, incorporating local search to MTEC can also be another possible orientation. The new algorithm framework discussed in Section 5.1 can be seen as a certain positive attempt for this research topic.

#### *7.4. Extend MTEC Algorithmic Advancements*

In addition to the core demands of having suitable individuals encoding and the knowledge transfer, the advancements of peripheral elements will certainly play a crucial role in the future progress of MTO and MTEC. In this regard, some potential research prospects are in (a) the many-task optimization problem, (b) uncorrelated optimization tasks, (c) heterogeneous optimization tasks, (d) adaptively selecting the most appropriate genetic operators, (e) the multi-task optimization problem under uncertainties, (f) developing hyper-heuristic MTEC algorithms, and (g) exploring an effective approach to construct auxiliary tasks, as discussed in Section 5.

Without a doubt, these examples studied so far are just the tip of the iceberg. They are simply divided into two groups: issues similar to single-task EAs, such as (e), (f), and (g), and distinct issues in a multi-task scenario, such as (a), (b), (c), (d), and (h). Further, inspired by the single-task EAs, a good deal of similar algorithmic advancements will be explored in a multi-task scenario. For instances, adaptive MTEC is capable of adapting core mechanisms such as genetic operators, population size, and a choice of local search steps. On the other hand, several distinct forms of research in a multi-task scenario should be also conducted in the near future. For example, a natural extension of canonical MTO is effective handling of many tasks or heterogeneous tasks at a time.

#### *7.5. Develop New Science and Engineering Applications*

Finally, we believe that the notion of MTO provides a fresh perspective in terms of available knowledge transfer for improved problem solving. Several complex problems in science, engineering, operations research, etc. benefit immensely from the proposed ideas. At present, most applications focus on traditional continuous or discrete optimization fields. Thus, there is still a big gap between MTEC and the practical applications in the real world. As a preliminary attempt in the community of multi-task optimization, Prof. Ong et al. [135,187] have designed two MTO test suites for single-objective and multiobjective continuous optimization tasks, respectively. The test suite for single-objective and multi-objective MTO both contains 10 MTO complex problems, and 10 50-task MTO benchmark problems. Note that the MTO benchmark problems feature different degrees of latent synergy between their involved two component tasks.

Up to now, MTEC has not gained international recognition in community of evolutionary computation, and the reason for this might be just a lack of inspiring results in fundamental, subversive, and pioneering fields. What is more to the point, nobody has carefully and deeply considered why no breakthrough has occurred in such fields, or even summarized the basic features of MTO and MTEC.

#### *7.6. Compare Disparate Algorithms under Different Scenarios*

The No Free Lunch (NFL) theory proposed by Wolpert and Macready states that all algorithms are equivalent when their performance is evaluated over all possible problems [188]. Accordingly, each MTEC algorithm with its unique structure and operation strategy always shows different algorithm performance under different scenarios. Although some similar results have been repeatedly confirmed experimentally, it is not enough to draw a conclusion. In order to investigate the sense of the relative strengths and weaknesses of MTEC approaches, disparate strong algorithms based on a novel strategy should be compared directly and thoroughly [189].

As we all know, the overall performance of EAs more or less depends on the tested benchmark problems. Therefore, it is necessary for design diverse benchmark problems to receive a thorough investigation or evaluation. Similarly to the classical EAs, the benchmark problems for MTEC algorithms can be continuous and discrete, unimodal and multimodal, low and high dimension, static and dynamic, non-adaptive and adaptive, and with and without noise instances [152,190]. More importantly, the deviation and complementarity between any two problems should be taken into consideration. Ideally, the benchmark problems should contain various features mentioned above.
