Applying knowledge transfer across multiple optimization tasks, multitask optimization (MTO) emerges as a promising approach to solving synergistic optimization tasks simultaneously. However, the development of effective knowledge transfer mechanisms in MTO fundamentally relies on aligning elite solution distributions across tasks. This dependency creates a critical bottleneck in few-shot optimization regimes, as restricted evaluation budgets impede the identification of elite solution distributions required for beneficial transfer. This challenge is exacerbated in multiobjective multitask problems, where each optimizer must approximate a continuous Pareto manifold rather than a single optimal point. This paper introduces Iterative Sequential Transfer (IST) to circumvent this bottleneck. We model MTO as a sequence of sequential transfer optimization problems, concentrating evaluations on a single target per iteration. We propose a likelihood-informed task prioritization mechanism to maximize transfer utility by identifying the task most likely ready for knowledge integration. Empirical results on benchmark and real-world problems verify the effectiveness of the proposed method under tight budgets.
Multi-task optimization (MTO) addresses a set of optimization tasks simultaneously, often suffering from inaccurate inter-task relationship estimation under limited evaluation budgets, leading to negative transfer. This paper introduces In-Context Guidance Multitask Optimization (ICG-MTO), a novel framework that leverages numerical foundational models to improve inter-task coupling estimation in few-shot scenarios. Unlike conventional methods that rely solely on scarce observed data, ICG-MTO employs a frozen foundational model to infer auxiliary guidance through in-context learning. The framework operates through three stages: constructing an algorithm-specific in-context query from evaluated solutions, using the foundational model to infer a guidance signal characterizing predictive relationships among tasks, and translating this signal into algorithm-specific guidance for maximum-a-posteriori coupling estimation. This approach provides regularization during the early, data-scarce stages of optimization and gradually relinquishes control as task-specific observations accumulate. We instantiate the framework in multitask Bayesian optimization as ICG-MTBO, using directional fitness-class queries to guide inter-task coupling estimation, and further instantiate it in MFEA-II using decision-space-overlap queries to guide random mating probability estimation. Experiments across synthetic benchmarks and a real-world robot arm control problem, together with evaluations under different acquisition functions and evolutionary multitasking, demonstrate the effectiveness and generality of ICG-MTO for few-shot multitask optimization.
Multi-task optimization is typically characterized by a fixed and finite set of tasks. The present paper relaxes this condition by considering a non-fixed and potentially infinite set of optimization tasks defined in a parameterized, continuous and bounded task space. We refer to this unique problem setting as parametric multi-task optimization (PMTO). Assuming the bounds of the task parameters to be (θl, θu), a novel (θl, θu)-PMTO algorithm is crafted to operate in two complementary modes. In an offline optimization mode, a joint search over solution and task spaces is carried out with the creation of two approximation models: (1) for mapping points in a unified solution space to the objective spaces of all tasks, which provably accelerates convergence by acting as a conduit for inter-task knowledge transfers, and (2) for probabilistically mapping tasks to their corresponding solutions, which facilitates evolutionary exploration of under-explored regions of the task space. In the online mode, the derived models enable direct optimization of any task within the bounds without the need to search from scratch. This outcome is validated on both synthetic test problems and practical case studies, with the significant real-world applicability of PMTO shown towards fast reconfiguration of robot controllers under changing task conditions. The potential of PMTO to vastly speedup the search for solutions to minimax optimization problems is also demonstrated through an example in robust engineering design.
Pareto set learning (PSL) is an emerging paradigm in multi-objective optimization that trains neural networks to map preference vectors to Pareto optimal solutions. However, existing PSL methods primarily focus on solving a single multi-objective optimization problem at a time. This limitation not only increases computational costs in multi-objective multitask optimization scenarios by requiring a separate model for each task, but also fails to exploit the inter-task correlations across tasks. To address this, we propose a Cross-tAsk correlation-aware Pareto Set Learning (CoAction) framework, which leverages task-aware transformer to handle multiple tasks simultaneously. Specifically, by assigning task-specific embedding vectors to individual tasks, the model effectively distinguishes between tasks while facilitating knowledge sharing among them. We utilize a Transformer encoder as the backbone architecture to leverage its self-attention mechanism for capturing complex task dependencies. The proposed approach is evaluated on comprehensive multitask test suites covering both benchmark problems and real-world applications, demonstrating effectiveness and competitive performance in Hypervolume, Range, and Sparsity.