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MPCS: Neuroplastic Continual Learning via Multi-Component Plasticity and Topology-Aware EWC Combining Trained Models in Reinforcement Learning Training Non-Differentiable Networks via Optimal Transport ShiftLIF: Efficient Multi-Level Spiking Neurons with Power-of-Two Quantization Probe-Geometry Alignment: Erasing the Cross-Sequence Memorization Signature Below Chance Benchmarking local Hebbian learning rules for memory storage and prototype extraction Robust volatility updates for Hierarchical Gaussian Filtering Spiking Sequence Machines and Transformers Affinity Is Not Enough: Recovering the Free Energy Principle in Mixture-of-Experts Scalable Learning in Structured Recurrent Spiking Neural Networks without Backpropagation Geometric and dynamical analysis of attractor boundaries and storage limits in kernel Hopfield networks Attractor FCM Physical Foundation Models: Fixed hardware implementations of large-scale neural networks When Does Structure Matter in Continual Learning? Dimensionality Controls When Modularity Shapes Representational Geometry Learning to Forget: Continual Learning with Adaptive Weight Decay Causal Learning with Neural Assemblies NORACL: Neurogenesis for Oracle-free Resource-Adaptive Continual Learning Text-Utilization for Encoder-dominated Speech Recognition Models EdgeSpike: Spiking Neural Networks for Low-Power Autonomous Sensing in Edge IoT Architectures EvoTSC: Evolving Feature Learning Models for Time Series Classification via Genetic Programming Analysis and Explainability of LLMs Via Evolutionary Methods Deployment-Aligned Low-Precision Neural Architecture Search for Spaceborne Edge AI SeaEvo: Advancing Algorithm Discovery with Strategy Space Evolution Primitive Recursion without Composition: Dynamical Characterizations, from Neural Networks to Polynomial ODEs MAEO: Multiobjective Animorphic Ensemble Optimization for Scalable Large-scale Engineering Applications Necessary and sufficient conditions for universality of Kolmogorov-Arnold networks Learn&Drop: Fast Learning of CNNs based on Layer Dropping Architecture-Induced Recoverability Bias in Differentiable Symbolic Regression Collocation-based Robust Physics Informed Neural Networks for time-dependent simulations of pollution propagation under thermal inversion conditions on Spitsbergen Structure-Guided Diffusion Model for EEG-Based Visual Cognition Reconstruction
Proven Runtime Guarantees for How the MOEA/D Computes the...
Benjamin Doerr, Martin S. Krejca, Noé Weeks · 2024-05-02 · via cs.NE updates on arXiv.org

The decomposition-based multi-objective evolutionary algorithm (MOEA/D) does not directly optimize a given multi-objective function $f$, but instead optimizes $N + 1$ single-objective subproblems of $f$ in a co-evolutionary manner. It maintains an archive of all non-dominated solutions found and outputs it as approximation to the Pareto front. Once the MOEA/D found all optima of the subproblems (the $g$-optima), it may still miss Pareto optima of $f$. The algorithm is then tasked to find the remaining Pareto optima directly by mutating the $g$-optima. In this work, we analyze for the first time how the MOEA/D with only standard mutation operators computes the whole Pareto front of the OneMinMax benchmark when the $g$-optima are a strict subset of the Pareto front. For standard bit mutation, we prove an expected runtime of $O(n N \log n + n^{n/(2N)} N \log n)$ function evaluations. Especially for the second, more interesting phase when the algorithm start with all $g$-optima, we prove an $Ω(n^{(1/2)(n/N + 1)} \sqrt{N} 2^{-n/N})$ expected runtime. This runtime is super-polynomial if $N = o(n)$, since this leaves large gaps between the $g$-optima, which require costly mutations to cover. For power-law mutation with exponent $β\in (1, 2)$, we prove an expected runtime of $O\left(n N \log n + n^β \log n\right)$ function evaluations. The $O\left(n^β \log n\right)$ term stems from the second phase of starting with all $g$-optima, and it is independent of the number of subproblems $N$. This leads to a huge speedup compared to the lower bound for standard bit mutation. In general, our overall bound for power-law suggests that the MOEA/D performs best for $N = O(n^{β- 1})$, resulting in an $O(n^β\log n)$ bound. In contrast to standard bit mutation, smaller values of $N$ are better for power-law mutation, as it is capable of easily creating missing solutions.