Organizations: College of Computing & Data Science, Nanyang Technological University, Singapore · School of Computer Science, China University of Geosciences · School of Intelligent Rail Transportation, Dalian Jiaotong University · School of Mechanical Sciences, Indian Institute of Technology, Goa, India
Evolutionary multitasking (EMT) has shown strong capability in solving multiple optimization problems simultaneously by exploiting latent inter-task consistency, such as similarities in promising solutions or search directions. However, most existing EMT studies remain focused on objective-driven optimization, where such consistency is mainly used to accelerate convergence toward predefined optima. In this paper, we move EMT from consistency to collaborative discovery and propose a multifactorial evolutionary algorithm with collaborative discovery (MFEA-CoD) for multitask novelty search. Unlike conventional EMT, MFEA-CoD coordinates multiple novelty search tasks to collaboratively discover behaviorally novel solutions rather than merely transferring consistent search information for faster convergence. Specifically, a multitask repulsion operator encourages different tasks to explore distinct regions of the unified search space, thereby reducing redundant behavioral discoveries. Meanwhile, an adaptive inter-task transfer mechanism exploits shared discovery opportunities in overlapping novelty-improving regions by adjusting the transfer probability according to the online contribution of transferred information. Furthermore, MFEA-CoD is extended to multitask novelty-augmented optimization, where behavioral novelty is jointly considered with objective information to alleviate premature convergence caused by deceptive objectives. Experiments on synthetic basin-type problems, deceptive maze navigation problems, MuJoCo policy optimization problems, and generative novelty search problems demonstrate that MFEA-CoD improves the efficiency of discovering diverse novel solutions and shows clear advantages in deceptive objective landscapes.
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.
Evolutionary multitasking is a recent approach that solves multiple related optimization problems within a single evolutionary run, rather than addressing each problem separately. We consider monotone submodular optimization problems with dynamic knapsack constraints and study a multitasking formulation in which all tasks share a common monotone submodular function f, but differ in their constraints. We focus on the case where elements within each constraint have uniform cost and show that this structure leads to small Pareto fronts in the multitasking formulation. This enables solution sharing across tasks and can improve performance compared to running standard evolutionary approaches independently, depending on the constraint regime. Using rigorous runtime analysis, we analyze the expected time until the proposed multitasking algorithms obtain a (1−1/e)-approximation for each task. Experimental results for the Maximum Coverage problem complement the theoretical analysis and provide further insight into the practical behavior of the approach across different budget settings.
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.