Evolutionary computation has long promised to deliver both high-performance optimization tools as well as rigorous scientific simulations of Darwinian evolution. However, modern algorithms frequently abandon evolutionary fidelity for physics-inspired heuristics or superficial biological metaphors. This paper derives a suite of advanced gradient-based optimization algorithms directly from evolutionary first principles. We introduce Darwinian Lineage Simulations (DLS) to prove that, in an asexual context, Fisher's and Wright's historically opposed views of evolution are actually formally equivalent; One can partition Fisher's deterministically-evolving total population into Wright's randomly-drifting sub-populations. We prove that proper bookkeeping requires introducing a specific kind of structured noise (the DLS noise relation). Crucially, any bookkeeping choices which satisfy this relation will yield a faithful simulation of evolution. Using this vast representational freedom, we prove that a broad family of battle-tested optimization algorithms are already perfectly compatible with evolutionary dynamics. These include: Stochastic Gradient Descent as well as many regularizations/approximations of Newton's method and Natural Gradient Descent. By simply adding DLS noise (i.e., evolutionarily faithful genetic drift), these algorithms become scientifically valid in silico simulations of Darwinian evolution. Finally, we demonstrate that even the state-of-the-art Adam optimizer can be brought into evolutionary compliance through a minor mathematical surgery.
Baldwinian and Lamarckian evolution have existed for a long time in evolutionary algorithms (EAs) without ever dominating the academic literature or practical applications. In this work, we use modern empirical and theoretical methods to revisit Lamarckian and Baldwinian evolution and rigorously compare them with the generic Darwinian evolution. On the empirical side, we run a comprehensive suite of experiments on graphs from six different datasets from the recent GraphBench benchmark on Maximum Independent Set and Maximum Cut problems. Our results show that Baldwinian and Lamarckian evolution consistently outperform Darwinian evolution, confirming the great potential of local search augmented evolutionary algorithms. Notably, in the great majority of cases, all EAs outperform recent deep learning baselines and approach the performance of highly specialised heuristic and exact solvers. We furthermore report a high-performing set of generalist parameters for all studied evolution types that we hope will be of use to practitioners in future. On the theoretical side, we extend the existing DeceptiveLeadingBlocks benchmark to arbitrary block length k. For all constant k, we then prove asymptotically tight runtime bounds for the (1+1) EA in the three evolution types on this benchmark. For Baldwinian evolution, these are independent of k, whereas for the other two evolution types, the runtimes steeply increase with growing value of k.
Probabilistic model-based evolutionary algorithms are promising for black-box optimization. Specifically, the adaptive stochastic natural gradient (ASNG) adaptively updates its learning rate, a typical hyperparameter in probabilistic model-based evolutionary algorithms, thereby realizing efficient and robust optimization. Although weight parameters are common hyperparameters, with the increasing demand for parallel evaluation of time-consuming tasks, it remains unclear how to set suitable weights for larger population sizes. In this paper, we propose Weight Adaptation ASNG (WA-ASNG), which incorporates a weight adaptation mechanism into ASNG. We calculated the estimated signal of the update direction from the accumulations of the natural gradient. Then, to maximize the signal, WA-ASNG adaptively updates its weight parameters by a gradient ascent over the optimization. While the learning rate adaptation plays a role in satisfying a sufficient condition for monotonic improvement of the expected objective value, the mechanism of weight adaptation is intended to maximize this improvement. The experimental results demonstrate that WA-ASNG outperforms PBIL and ASNG across various settings with population sizes ranging from 25 to 100 for binary optimization problems. Furthermore, WA-ASNG can perform efficiently in the presence of strong noise. Our code is available at https://github.com/shiralab/WA-ASNG .
Would experience designing faster GPU kernels also help close in on a long-standing open mathematical conjecture? Large Language Models (LLMs) integrated into evolutionary search have recently produced state-of-the-art solutions on optimization tasks, including open mathematical conjectures, GPU kernel design, scientific law discovery, and combinatorial puzzles. To achieve this, prior work applied search scaffolds to one target task at a time, so every new problem is approached from scratch and the experience accumulated during search is discarded once the model finishes its attempt. This leaves the capability of iteratively evolving a solution (e.g., knowing which part to mutate and how, deciding when to backtrack) entirely in the scaffold rather than in the model itself. Whether the model itself could acquire this capability and reuse it across different tasks has been largely unexamined. To address this, we introduce Evolution Fine-Tuning (EFT), a mid-training paradigm that teaches LLMs to evolve solutions across tasks by converting evolutionary search trajectories into supervision. We construct Finch Collection, a 156K-trajectory dataset spanning 10 domains and 371 optimization tasks, and fine-tune open-source LLMs from 2B to 9B parameters. Empirically, EFT confers cross-task generalization: across 22 held-out tasks, our models surpass their base counterparts by 10.22% on average. Furthermore, when paired with test-time RL, our model matches state-of-the-art performance on two circle-packing tasks and outperforms its base-model counterpart on the Erdős minimum-overlap problem. EFT thus serves as a "practice phase" for general-purpose discovery agents that do not solve new problems from scratch.