Evolutionary Multitasking

• Evolutionary multitasking is an optimization paradigm that simultaneously tackles multiple tasks by leveraging shared search spaces and adaptive knowledge transfer.
• It employs multifactorial, multi-population, and cellular methods along with learned transfer mechanisms to enhance convergence and reduce negative transfer.
• This approach is applied across continuous, combinatorial, and real-world problems, where task engineering and adaptive transfer yield improved solution quality.

Searching arXiv for recent and foundational papers on evolutionary multitasking to ground the article. Evolutionary multitasking is a paradigm in evolutionary computation and transfer optimization concerned with solving multiple optimization tasks simultaneously through a shared or coordinated search process, so that knowledge discovered for one task can benefit the others (Osaba et al., 2021). In the multitask optimization setting, one considers tasks $\{T_k\}_{k=1}^K$, each with its own search space $\Omega_k$ and objective function $f_k$, and seeks task-wise optima rather than a single trade-off set (Osaba et al., 2021). Within this paradigm, the central technical issue is knowledge transfer: when tasks exhibit similarities, latent complementarities, or overlap in useful structure, joint search can improve convergence or final quality, whereas poorly aligned transfer can induce negative transfer and degrade performance (Gupta et al., 2016). The literature has developed from foundational multifactorial frameworks to multi-population, mapping-based, cellular, swarm-based, and learning-based systems, and more recently to multifidelity task construction, application-specific task engineering, and automated transfer-model design (Li et al., 2023).

1. Historical framing and conceptual foundations

Evolutionary multitasking emerged within the broader framework of transfer optimization, which the literature distinguishes into sequential transfer, multitasking, and multiform optimization (Osaba et al., 2021). In the multitasking case, multiple optimization problems are solved simultaneously rather than sequentially, and the intended advantage is dynamic exploitation of complementarities among tasks through the exchange of valuable knowledge (Osaba et al., 2021). The formal multitask setting is usually written in terms of $K$ tasks $\{T_k\}_{k=1}^K$, each with search space $\Omega_k$ and objective $f_k : \Omega_k \rightarrow \mathbb{R}$, with the goal of finding one optimum per task (Osaba et al., 2021). A related formulation used in platform-oriented work writes multitask optimization as

$$(\bm{x}_{1}^\ast,\bm{x}_{2}^\ast,...,\bm{x}_{K}^\ast) = \arg\min \Big[F_1(\bm{x}_1),F_2(\bm{x}_2),...,F_K(\bm{x}_K)\Big], \quad \bm{x}_k \in \Omega_k,\ k=1,2,...,K,$$

thereby emphasizing that each task may have its own decision space and objective structure (Li et al., 2023).

A foundational conceptual debate concerns why multitasking works when it does. The paper "Genetic Transfer or Population Diversification? Deciphering the Secret Ingredients of Evolutionary Multitask Optimization" (Gupta et al., 2016) argues that implicit genetic transfer is the more fundamental explanatory principle. It shows empirically that diversity and transfer are often tightly coupled, but that diversification alone cannot explain both broad exploratory behavior and rapid entropy collapse toward good regions. This argument is significant because later EMT work repeatedly treats positive transfer and negative transfer as primary algorithm-design concerns.

The methodological-overview literature also separates evolutionary multitasking from adjacent paradigms. It is distinct from multiobjective optimization because multitask optimization seeks one best solution per task rather than a Pareto trade-off set, and tasks may inhabit different search spaces $\Omega_k$ rather than sharing a single objective domain (Osaba et al., 2021). It is also distinct from multitask learning, although the two can intersect when model parameters are treated as optimization variables (Osaba et al., 2021). The position paper "Evolutionary Multitask Optimization: Fundamental Research Questions, Practices, and Directions for the Future" (Osaba et al., 2021) further argues that the field should not assume task synergy by construction, and that strong evidence is needed for practical applicability, genuine novelty, and fair evaluation.

2. Core mechanisms: representation, transfer, and task relatedness

The two major methodological families identified in surveys are multifactorial optimization and multi-population multitasking (Osaba et al., 2021). In the multifactorial family, a single population evolves in a unified search space $\Omega_U$, and task-specific search spaces are related to $\Omega_k$0 by encoding/decoding mappings $\Omega_k$1 (Osaba et al., 2020). In the multi-population family, each task has its own population and explicit transfer occurs through migration, mapping, archive injection, or other inter-population interactions (Osaba et al., 2021).

The classic multifactorial formalism uses factorial cost, factorial rank, skill factor, and scalar fitness. For an individual $\Omega_k$2 and task $\Omega_k$3, the skill factor is

$\Omega_k$4

and scalar fitness is

$\Omega_k$5

with $\Omega_k$6 denoting factorial rank on task $\Omega_k$7 (Wang et al., 2022). Closely related definitions recur in combinatorial and continuous EMT work (Gupta et al., 2016). These constructs allow task-agnostic selection while preserving task specialization within a shared population.

Task relatedness is central but difficult. A common theoretical intuition is that if two tasks have high ordinal correlation, then improvements in one imply improvements in the other in the unified space (Gupta et al., 2016). However, later work emphasizes that similarity is not reducible to superficial closeness. "Genetic Transfer or Population Diversification?" (Gupta et al., 2016) distinguishes complementarity from mere similarity, showing that cloned tasks need not yield the strongest benefits. In combinatorial multitasking, "On the Transferability of Knowledge among Vehicle Routing Problems by using Cellular Evolutionary Multitasking" (Osaba et al., 2020) argues that positive transfer depends more on overlap in best-solution structure than on raw instance overlap. The paper reports empirically that intersection degrees greater than $\Omega_k$8 are enough to ensure at least some positive transfer activity (Osaba et al., 2020). Likewise, "AT-MFCGA" (Osaba et al., 2020) reports that overlap in optimal permutations is more predictive of transfer than superficial overlap in nodes or weights, and notes that overlaps above roughly $\Omega_k$9 between optimal solutions appear sufficient to induce at least some positive transfer.

Negative transfer is the complementary phenomenon. It is especially problematic when tasks are weakly aligned, when unified representations impose bias, or when transfer operators are too indiscriminate (Wu et al., 2018). The field has therefore developed a large variety of mechanisms for controlling transfer intensity, task pairing, source-task choice, and representation alignment (Li et al., 2023).

3. Canonical frameworks and major methodological families

The classical baseline is the Multifactorial Evolutionary Algorithm, which introduced single-population multitasking with implicit transfer in a unified space (Osaba et al., 2021). Much subsequent work either extends this line or departs from it. Platform-oriented summaries classify EMT algorithms into multifactorial methods and multi-population methods, and catalog a large set of transfer paradigms including unified search space, autoencoding, affine transformation, adversarial generative models, similarity judgment, knowledge selection, and historical feedback (Li et al., 2023).

A representative multi-population alternative is the "Multi-Tasking Genetic Algorithm (MTGA)" (Wu et al., 2018). MTGA does not use a unified population with skill factors. Instead, it keeps separate populations, estimates task bias from elite means, and performs bias-corrected elite transfer: $f_k$0 and for transfer from task 2 to task 1,

$f_k$1

This makes transfer explicitly compensate for spatial offset between tasks (Wu et al., 2018). The paper reports that MTGA performed second best early and best overall late on nine multitask benchmarks, and after 100,000 evaluations it achieved the best performance score on eight of the nine benchmarks (Wu et al., 2018).

Another major line is cellular and coevolutionary multitasking in combinatorial optimization. "AT-MFCGA" (Osaba et al., 2020) extends a multifactorial cellular genetic algorithm by organizing the population on a 2D grid with Moore neighborhoods and an adaptive transfer layer. It defines a global transfer matrix $f_k$2, where entry $f_k$3 counts successful positive transfers from task $f_k$4 to task $f_k$5, and uses this matrix to rebuild the grid so that synergistic tasks become adjacent (Osaba et al., 2020). The method achieved the best average result on all 20 instances in the hardest $f_k$6 scenario, with Friedman ranks $f_k$7, $f_k$8, $f_k$9, and $K$0 for MFEA, MFEA-II, MFCGA, and AT-MFCGA respectively (Osaba et al., 2020).

"COEBA: A Coevolutionary Bat Algorithm for Discrete Evolutionary Multitasking" (Osaba et al., 2020) represents a different discrete design philosophy: one deme per task, task-specialized search, and periodic migration-based transfer. On 15 multitasking TSP scenarios, COEBA was better than MFEA on all but 4 jointly evolved TSP-instance results, and in the 8-task case it beat MFEA on all 8 tasks (Osaba et al., 2020). This line shows that EMT is not confined to MFEA-style unified-population schemes.

At the infrastructure level, "MToP: A MATLAB Optimization Platform for Evolutionary Multitasking" (Li et al., 2023) marks the field’s maturation into a platform-based discipline. It introduces an open-source environment with over 40 MTEAs, more than 150 problem cases with real-world applications, multiple metrics, and adapted single-task baselines (Li et al., 2023). This platformization is methodologically important because EMT performance is highly sensitive to evaluation protocol and baseline quality.

4. Task construction and multifidelity formulations

A major development in EMT has been the recognition that tasks need not be given externally; they can be constructed from a single hard problem to induce useful auxiliary searches. A clear example is "Evolutionary Multitasking AUC Optimization" (Wang et al., 2022), which formulates large-scale AUC maximization as an expensive task and a sampled AUC problem on a subset as a cheap task. For binary training data

$K$1

with linear scorer $K$2, empirical AUC is

$K$3

and one evaluation costs $K$4 (Wang et al., 2022). EMTAUC defines the expensive task on the full dataset and a cheap task on a sampled subset $K$5 with sampling ratio $K$6, yielding a cost ratio

$K$7

The paper validates that runtime on a9a scales approximately as $K$8 (Wang et al., 2022). It further reports that cheap and expensive fitness landscapes have average Spearman correlation above 0.5 on most datasets, supporting transfer (Wang et al., 2022).

EMTAUC’s most distinctive feature is dynamic cheap-task adjustment. Using the current best expensive-task classifier $K$9, it defines difficulty scores

$\{T_k\}_{k=1}^K$0

$\{T_k\}_{k=1}^K$1

and rebuilds the cheap task from hard instances (Wang et al., 2022). This means task relatedness is treated as something that can be improved during search, not merely assumed.

A related task-engineering principle appears in "Evolutionary Multitasking with Solution Space Cutting for Point Cloud Registration" (Yue et al., 2022). There, a full 6D rigid-registration task is paired with a 3D rotation-only helper task obtained by cutting the solution space. The full task uses a robust M-estimator Chamfer objective,

$\{T_k\}_{k=1}^K$2

while the helper task optimizes only rotation using translation invariant measurements (Yue et al., 2022). The reported average success ratio is $\{T_k\}_{k=1}^K$3, compared with $\{T_k\}_{k=1}^K$4 for DEORA, $\{T_k\}_{k=1}^K$5 for EMFPCR, and $\{T_k\}_{k=1}^K$6 for MFEA-II (Yue et al., 2022). This application exemplifies how EMT can be used to improve success ratio by pairing a hard task with an easier structurally aligned helper.

Feature-selection work generalizes this principle to high-dimensional search. "An Evolutionary Multitasking Algorithm with Multiple Filtering for High-Dimensional Feature Selection" (Li et al., 2022) constructs one original task plus three auxiliary tasks from Relief-F, term variance, and Pearson correlation coefficient filtering. The generic multitask formulation is

$\{T_k\}_{k=1}^K$7

and the transfer operator uses an aggregated cross-task exemplar

$\{T_k\}_{k=1}^K$8

with $\{T_k\}_{k=1}^K$9 and $\Omega_k$0 (Li et al., 2022). The paper reports 84 wins, 8 losses, and 34 ties against seven EA-based feature-selection methods (Li et al., 2022). "Towards Multi-Objective High-Dimensional Feature Selection via Evolutionary Multitasking" (Feng et al., 2024) pushes this further by combining multiple task formulations, task-specific solvers, and explicit task-specific transfer in a multiobjective setting.

5. Applications and empirical patterns across domains

EMT has been applied across continuous, combinatorial, learning-oriented, and engineering domains. The semantic web service composition work (Wang et al., 2019) treats multiple QoSM preference intervals as related tasks sharing repository, inputs, and outputs. It uses a permutation-based multifactorial EA with task neighborhoods defined by adjacent QoSM intervals. The neighbor-evaluation variant PMFEA-NT achieves better solution quality than both inherited-only PMFEA and all-task PMFEA-AT, while requiring roughly 23%–29% of the runtime of a single-task fixed-length GA baseline (Wang et al., 2019). This supports the broader principle that structured transfer can outperform both no transfer and indiscriminate global transfer.

In fuzzy-system optimization, MTGA is applied to simultaneous optimization of type-1 and interval type-2 fuzzy logic controllers for coupled-tank water level control (Wu et al., 2018). The task pair differs in parameter dimension, but domain knowledge provides fixed semantic gene matching. The results indicate that multitasking with bias-corrected transfer improves both controller designs relative to SOEA and MFEA (Wu et al., 2018). This is an example of explicit transfer across heterogeneous but semantically aligned tasks.

Combinatorial routing and assignment have been especially important testbeds. CVRP multitasking via MFCGA (Osaba et al., 2020) and larger combinatorial suites via AT-MFCGA (Osaba et al., 2020) both show that transfer is highly structured and often cluster-specific. Strong transfer occurs within problem families or among tasks with overlapping best-solution structure, while unrelated tasks exhibit negligible or harmful exchange (Osaba et al., 2020). "Multitasking Evolutionary Algorithm Based on Adaptive Seed Transfer for Combinatorial Problem" (Lv et al., 2023) addresses many-task cross-domain combinatorial multitasking by combining greedy dimension unification, similarity-based source-task selection, and corrected seed transfer. It reports better or tied performance against STO on 79 of 80 cross-domain task outcomes, with especially strong gains on TSP and CVRP (Lv et al., 2023). This suggests that explicit seed-based transfer with source filtering is effective in heterogeneous combinatorial environments.

The modern program-synthesis setting extends EMT beyond vector optimization. "Evolutionary Multi-Task Optimization for LLM-Guided Program Discovery" (Gozeten et al., 21 May 2026) introduces EMO-STA, a shared-then-adapt framework in which a shared archive of programs is first evolved across a family of tasks and then adapted per task. It uses family-level score

$\Omega_k$1

with matched-compute budgeting $\Omega_k$2 between multitask and single-task evolution (Gozeten et al., 21 May 2026). Across eight task families, at least one EMO-STA variant beats single-task evolution in 38/40 cells, with Best-Local best in 23/40 cells and Best-Shared strongest on held-out tasks (Gozeten et al., 21 May 2026). This shows that EMT ideas can be reformulated as archive-based transfer in open-ended program spaces.

6. Adaptive, learned, and automated transfer

A major recent trend is moving from hand-crafted transfer rules toward adaptive or learned transfer control. "A Two stage Adaptive Knowledge Transfer Evolutionary Multi-tasking Based on Population Distribution for Multi/Many-Objective Optimization" (Liang et al., 2020) proposes EMT-PD, which models task populations with per-dimension probability models $\Omega_k$3, computes task centers $\Omega_k$4, and extracts shared knowledge from the product distribution via

$\Omega_k$5

For an individual $\Omega_k$6, it defines distances

$\Omega_k$7

and stage-1 transfer

$\Omega_k$8

Stage 2 then adds dynamic perturbation

$\Omega_k$9

to maintain diversity (Liang et al., 2020). The reported results show EMT-PD outperforming strong multitask and single-task baselines on MTMOPs, CEC2019-CMO, and a new many-objective suite (Liang et al., 2020).

"Learning to Transfer for Evolutionary Multitasking" (Wu et al., 2024) goes further by casting transfer in implicit EMT as a sequential decision problem optimized by reinforcement learning. It decomposes transfer into “when to transfer” and “how to transfer” via a continuous action vector $f_k : \Omega_k \rightarrow \mathbb{R}$0 for each task. For DE-based multitasking, generalized mutation is

$f_k : \Omega_k \rightarrow \mathbb{R}$1

subsuming several classic transfer operators (Wu et al., 2024). The framework uses state features describing generation progress, inter-task distances, stagnation, transfer quality, and prior actions, and optimizes reward terms for convergence and transfer-efficiency gain (Wu et al., 2024). Across synthetic and real multitask problems, learned transfer outperforms a wide range of implicit EMT baselines (Wu et al., 2024).

"Advancing Automated Knowledge Transfer in Evolutionary Multitasking via LLMs" (Huang et al., 2024) automates transfer-model design itself. It uses an LLM-assisted optimization framework to generate Knowledge Transfer Models as code, evaluate them on multitask benchmarks, and optimize them jointly for fitness $f_k : \Omega_k \rightarrow \mathbb{R}$2 and runtime $f_k : \Omega_k \rightarrow \mathbb{R}$3, with dominance defined by

$f_k : \Omega_k \rightarrow \mathbb{R}$4

On 10 WCCI-style many-task benchmarks with 50 tasks each, the best generated KTM is better than both vertical crossover and solution mapping baselines in both normalized fitness and runtime on WCCI1, WCCI2, WCCI4, WCCI6, WCCI9, and WCCI10 (Huang et al., 2024). This line reframes EMT transfer as an object of automated design rather than fixed human engineering.

7. Evaluation methodology, controversies, and open problems

A distinctive strand in the EMT literature is methodological critique. "Evolutionary Multitask Optimization: Fundamental Research Questions, Practices, and Directions for the Future" (Osaba et al., 2021) argues that the field has not yet fully resolved three questions: why simultaneous multitasking is practically necessary, what is genuinely novel in many multitasking algorithms, and how such algorithms should be evaluated. It stresses that feasibility is not enough; multitasking should demonstrate advantage over strong single-task baselines under matched computational budgets (Osaba et al., 2021). It also warns that many synthetic benchmarks encode favorable task relations by construction, which may exaggerate transfer benefits (Osaba et al., 2021).

The survey "Evolutionary Multitask Optimization: a Methodological Overview, Challenges and Future Research Directions" (Osaba et al., 2021) similarly emphasizes that task relatedness is representation- and operator-dependent, and that negative transfer remains a primary challenge. These critiques have influenced later infrastructure and benchmarking efforts, such as MToP’s inclusion of adapted single-task baselines and multiple performance metrics (Li et al., 2023).

Across application papers, several recurring open problems appear. Parameter sensitivity is common: EMTAUC depends materially on $f_k : \Omega_k \rightarrow \mathbb{R}$5, $f_k : \Omega_k \rightarrow \mathbb{R}$6, and $f_k : \Omega_k \rightarrow \mathbb{R}$7 (Wang et al., 2022); MO-FSEMT depends on task count, transfer probability, and formulation choices (Feng et al., 2024); and L2T still requires reward-weight tuning (Wu et al., 2024). Robustness under low similarity remains difficult. MTGA notes that its bias-correction assumption still requires some underlying similarity (Wu et al., 2018). MTEA-AST is strongest on TSP and CVRP but only modestly improved on low-similarity QAP and LOP (Lv et al., 2023). EMT-PD weakens on some many-objective cases where population distributions poorly summarize the search state (Liang et al., 2020).

Another recurrent issue is scalability beyond two or a handful of tasks. Many classical EMT formulations are strongest in paired-task settings, while later cellular, adaptive-seed, and LLM-based methods explicitly target many-task environments (Osaba et al., 2020, Lv et al., 2023, Huang et al., 2024). Cross-domain transfer and heterogeneous representations also remain challenging, motivating multi-population, mapping-based, or archive-based frameworks (Wu et al., 2018, Lv et al., 2023, Gozeten et al., 21 May 2026).

A plausible implication is that EMT research has progressively shifted from asking whether transfer can help at all to asking how transfer should be engineered, filtered, or learned under realistic heterogeneity. This suggests a maturation from foundational unified-population schemes toward task engineering, adaptive source selection, and policy-based transfer control.

8. Synthesis

Evolutionary multitasking has developed from the original insight that multiple optimization tasks can be solved within a shared evolutionary process into a broad methodological family spanning multifactorial optimization, multi-population multitasking, cellular and coevolutionary schemes, multifidelity task construction, swarm-based transfer, reinforcement-learned transfer control, and automated transfer-model generation (Osaba et al., 2021, Li et al., 2023). Its unifying principle is cross-task knowledge transfer, but the literature shows that transfer is beneficial only when task relations, representations, and operators align appropriately (Gupta et al., 2016).

The field’s most stable technical lessons are consistent across domains. First, transfer is usually more informative when tasks share either latent complementarity or overlap in good-solution structure rather than merely superficial similarity (Gupta et al., 2016, Osaba et al., 2020). Second, auxiliary tasks are often most useful when they are cheaper, simpler, or differently formulated views of the same hard problem, as in EMTAUC, solution-space cutting for registration, and high-dimensional feature selection (Wang et al., 2022, Yue et al., 2022, Li et al., 2022). Third, structured or adaptive transfer generally outperforms both indiscriminate transfer and no transfer, whether the control mechanism is cellular topology, bias correction, explicit seed filtering, distribution modeling, reinforcement learning, or LLM-generated code (Osaba et al., 2020, Wu et al., 2018, Lv et al., 2023, Liang et al., 2020, Wu et al., 2024, Huang et al., 2024). Fourth, rigorous evaluation against strong single-task baselines remains necessary if EMT is to establish practical rather than purely benchmark-level relevance (Osaba et al., 2021).

In this sense, evolutionary multitasking is not simply the simultaneous execution of multiple optimizers. It is a research program on how to construct related tasks, represent them compatibly, extract useful transferable structure, regulate positive and negative transfer, and allocate search effort across task families. Its modern trajectory suggests increasing emphasis on adaptive and learned transfer, richer task construction, and stronger empirical methodology, while its unresolved questions remain tied to robustness, real-world applicability, and scientifically defensible evaluation (Osaba et al., 2021, Osaba et al., 2021).