Differential Evolution

Also known as DE

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2 papers in the last four weeks, with none the four weeks before. 0.0% of all new papers.

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Sep 28, 2026cs.LG

EvE: An Alternate Optimizer to Adam

Adam and its variants dominate neural network training, but a single run only reveals whether a configuration works well after most of its budget is spent, a poor fit for hyperparameter or architecture search, where configurations must be ranked cheaply and pruned early. We introduce EvE (Evolutionary Explorer), a steady-state, population-of-four differential evolution (DE) optimizer with a targeted Adam fallback: each iteration proposes one candidate via DE, running a short burst of gradient descent only if the DE step fails to improve on the incumbent. Selection is greedy, so on a deterministic objective the best-so-far value is provably monotone non-increasing, and since gradients are used only as a targeted rescue, per-iteration cost stays within a constant factor of a single Adam step regardless of dimension. Under a fixed, evaluation-cost-matched budget, EvE wins or ties Adam on 76% of 70 (problem, dimension) cells across seven scalable benchmarks up to one million variables. On three real neural-network tasks (an MLP on MNIST, and LoRA fine-tuning of a 1.5B-parameter language model on two datasets) EvE finishes the same charged budget 1.7-3.9x faster, at a modest cost in final quality (about one accuracy point on MNIST, 9-11% higher relative test loss on the two fine-tuning tasks; on GSM8K, Adam is about 5 accuracy points more accurate, and fine-tuning lowers accuracy below the base model for both). Inside successive halving on UCI Adult, EvE completes hyperparameter and architecture searches 3.1-3.5x faster, ranking configurations about as consistently with Adam as Adam does with itself across seeds (Kendall's tau 0.66-0.69). EvE is not a total replacement for Adam as a final-stage trainer, but a fast, gradient-aware proxy for the search-heavy, budget-constrained regime one level up.

Shashank Raj, Kalyanmoy Deb

Department of Computer Science The University of Alabama Tuscaloosa, AL 35487, USA

Deep Learning OptimizationDifferential EvolutionEvolutionary Optimization
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Sep 15, 2026cs.NE

LLMDE: A Large Language Model-Driven Differential Evolution Algorithm for Portfolio Optimization

This study proposes a Large Language Model-Driven Differential Evolution (LLMDE) algorithm to reduce the reliance on handcrafted hyperparameter design. The proposed algorithm leverages a prompt engineering strategy, allowing large language models (LLMs) to dynamically select mutation strategies and configure control parameters guided by optimization feedback, thus enhancing the performance of the DE algorithm. We evaluate the performance of LLMDE on the CEC2022 benchmark suite, comparing it with standard DE and representative metaheuristics. Furthermore, we employ factor analysis and K-means clustering for stock selection, and then apply LLMDE to solve the Conditional Value at Risk (CVaR) portfolio optimization problem using the selected stocks, subject to budget and minimum expected return constraints. Experimental results demonstrate that LLMDE achieves competitive performance on the benchmark suite while continuously generating high-quality solutions for complex constrained optimization tasks. These outcomes successfully demonstrate the viability of embedding LLMs within metaheuristics, paving a promising path toward the design of advanced LLM-assisted optimization techniques.

Rong Chai, Vaclav Snasel, Xiaopeng Wang +2

Faculty of Electrical Engineering and Computer Science, VŠB-Technical University of Ostrava, Ostrava, Czech Republic · Centre for Artificial Intelligence Research and Optimisation, Torrens University Australia, Brisbane, Australia · Digital Health and Applied Technology Assessment, King’s College London, London, UK

Differential EvolutionLarge Language Model-Guided OptimizationPortfolio Optimization
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Jul 31, 2026cs.NE

Linear Proposal Operators and Stochastic Search Geometry in SOMA and Differential Evolution

Swarm and evolutionary algorithms are usually analyzed as complete procedural systems in which nonlinear selection, replacement, and adaptation obscure simpler structure within candidate generation. This paper introduces an operator--selection factorization that separates objective-independent variation from boundary repair and fitness-dependent selection, and uses it to study the proposal geometry of the Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE). The canonical SOMA proposal is shown to be affine in the search space and exactly linear in an augmented migrant--leader state. In leader-relative coordinates, the resulting operator provides a direct interpretation of interpolation, projection, overshooting, and coordinate masking. Under Bernoulli perturbation masks, we derive closed-form expressions for the proposal mean, covariance, expected squared step length, expected squared distance from the leader, active dimensionality, and coordinate coverage. For canonical DE/rand/1/bin, we derive the finite-population moments of differential mutation and characterize the additional covariance and coordinate dependence induced by forced-coordinate binomial crossover. Exact enumeration and Monte Carlo experiments verify the analytical identities and quantify the effects of mask conditioning, boundary repair, and fitness-based selection. The analysis further motivates geometry-controlled and rotation-aware SOMA variants, together with an adaptive population-reducing extension of iSOMA. Experiments on the complete noiseless BBOB benchmark show that these operator-guided variants substantially improve upon canonical SOMA and are competitive with established DE methods in several dimension--budget regimes. The results demonstrate how proposal-level operator analysis can support both the interpretation and design of population-based optimizers.

Vojtěch Novák, Ivan Zelinka

Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VSB - Technical University of Ostrava, Ostrava, Czech Republic · IT4Innovations National Supercomputing Center, VSB - Technical University of Ostrava, 708 00 Ostrava, Czech Republic · Department of Informatics and Statistics, Marine Research Institute, Klaipeda University, Lithuania

Differential EvolutionEvolutionary OptimizationBlack-Box OptimizationMetaheuristic Optimization
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Jul 20, 2026cs.RO

Polar Coordinate-based Differential Evolution for Moving Target Search Using Vision Sensor on Unmanned Aerial Vehicles

In search and rescue operations, there is a period known as the "golden time" during which the probability of finding the target alive is highest. The objective of this work is to propose a new search algorithm for unmanned aerial vehicles (UAVs) with a focus on improving the detection probability and execution time. We approach this problem by first modeling target dynamics as a Markov process and the detection likelihood as a function of image quality and the observer's vision. We then employ Bayesian theory to derive a fitness function representing the probability distribution of the target's location over the search area. Finally, we introduce a new algorithm named polar coordinate-based differential evolution (PDE) to generate a UAV search path that maximizes this fitness function. The PDE algorithm utilizes polar coordinates to incorporate kinematic constraints and maneuver properties of the UAV, allowing for better exploration of the solution space. A series of simulations and comparative analyses have been conducted to evaluate the performance of the proposed algorithm. Experiments involving a real UAV have also been conducted. Results demonstrate that the PDE algorithm outperforms state-of-the-art algorithms in terms of detection probability and execution time across diverse search scenarios while remaining practical for real-world applications. The source code of the algorithm is available at https://github.com/thuhangkhuat/PDE_target_search.

Thu Hang Khuat, Duy-Nam Bui, Thuy Ngan Duong +1

1VNU University of Engineering and Technology, Vietnam National University, Hanoi, Vietnam. · Department of Electrical Engineering, Ulsan National Institute of Science and Technology, Ulsan, Korea. · College of Engineering and Computer Science and Smart Green Transformation Center (GREEN-X), VinUniversity, Hanoi, Vietnam.

Differential EvolutionUAV NavigationDisaster Response
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Jul 7, 2026cs.AI

Multi-Agent Deep Reinforcement Learning for Multi Objective Battery Management in Dairy Farms

The dairy industry in Ireland has a large potential for the integration of renewable energy and the reduction of carbon emissions. However, researchers of distributed generation control are mainly focused on residential and commercial applications. To contribute to the effective integration of renewable energy in the dairy sector, this paper presents a multi-objective optimisation control system based on differential evolution and multi agent Deep Reinforcement Learning. The proposed control is organised in two layers: the upper layer uses dynamic pricing, and the lower layer is based on multi-agent reinforcement learning for battery management. This paper also simulates the electrical response of the proposed control system in a rural distribution circuit. The simulation results show that the proposed control framework can improve profits from energy arbitrage up to 18% compared to using Rule-based models, increase the use of distributed generation without significantly increasing cost, and comply with the Irish grid code in terms of voltage variation.

Marcos Eduardo Cruz Victorio, Karl Mason

University of Galway, Ireland

Multi-Objective Reinforcement LearningDifferential EvolutionMulti-Agent Reinforcement LearningPower Systems
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Jun 26, 2026cs.NE

DE-2LS: Differential Evolution with Lightweight Late Local Search for Constrained Numerical Optimization

Constrained single-objective numerical optimization requires a careful balance among feasibility, objective convergence, and computational efficiency under a fixed function-evaluation budget. This paper proposes DE-2LS, a late-stage, locally search-enhanced variant of differential evolution built on the RDEx framework. The proposed method preserves the original RDEx components, including mutation and crossover operators, success-history adaptation, archive mechanism, population-size reduction, and εε-based constraint handling. A lightweight coordinate-pattern local search is added as a guarded polishing component around the current best solution. It is activated only in the late stage of the run, uses a small evaluation budget, and accepts candidates through a feasibility-aware comparison rule. Ablation results show that the finalized DE-2LS configuration achieves the best U-score among all tested variants, confirming that controlled late-stage refinement is more effective than aggressive or premature local search. In the direct comparison with RDEx, DE-2LS achieves a 5.58% gain in U-score. In the four-algorithm comparison, DE-2LS obtains the highest overall U-score of 80968 and the best total rank of 48 among RDEx, CL-SRDE, and UDE-III. These results indicate that DE-2LS improves the exploitation capability of the RDEx-based search framework while preserving its speed advantage under the combined speed-accuracy scoring criterion. The source code of DE-2LS is available at https://github.com/ChauhanDikshit?tab=repositories.

Dikshit Chauhan, Anupam Trivedi

Department of Electrical and Computer Engineering, National University of Singapore

Differential EvolutionEvolutionary OptimizationLocal SearchConstrained Optimization
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Jun 26, 2026cs.NE

DE-2LS: Differential Evolution with Late-Stage local-search for Unconstrained Single-Objective Numerical Optimization

Unconstrained single-objective numerical optimization requires a careful balance among global exploration, late-stage exploitation, and function-evaluation efficiency. This paper presents DE-2LS, a late-stage, local-search-enhanced differential evolution framework built on RDEx for unconstrained single-objective optimization with variable bounds. The proposed method preserves the original RDEx evolutionary search engine and introduces two conservative refinements: a smoothed exploitation-biased branch-rate update in the late search stage and a guarded coordinate-pattern local-search that serves as a budget-aware refinement mechanism. Since the considered setting is unconstrained apart from variable bounds, all selection and local-search acceptance decisions are based solely on objective values. To determine the final algorithm configuration, we conduct a staged ablation study by testing multiple settings of the EB-rate smoothing mechanism, the initial EB-rate, the standard-branch Gaussian sampling scale, the selection-pressure parameters, and the local-search coefficients. The final configuration is selected using a U-score-based evaluation that jointly reflects solution quality and convergence speed. Experimental results show that DE-2LS consistently improves the original RDEx in direct head-to-head comparison. In particular, DE-2LS increases the U-score from 33602.033602.0 to 37448.037448.0, corresponding to an improvement of 11.45%11.45\%. Moreover, compared with several competitive and IEEE CEC-winning algorithms, DE-2LS achieves the best overall U-score of 178966.5178966.5, outperforming the others by 34.43%34.43\%. These results show that a carefully designed late-stage local-search strategy can improve both convergence speed and the final objective quality of the algorithm. The source code of DE-2LS is available at https://github.com/ChauhanDikshit?tab=repositories.

Dikshit Chauhan

Department of Electrical and Computer Engineering, National University of Singapore

Differential EvolutionEvolutionary OptimizationBlack-Box OptimizationGlobal OptimizationLocal Search
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Jun 17, 2026cs.NE

Constraint-aware Optimization in Auto-Tuning

Automatic performance tuning, or auto-tuning, is a key technique in high-performance computing, enabling applications to adapt to complex and evolving hardware architectures. A central challenge is the need to optimize over large discrete, constrained parameter spaces, where many candidate configurations are invalid due to hardware or software correctness constraints. Traditional evolutionary algorithms, such as Differential Evolution, Particle Swarm Optimization, and Genetic Algorithms, are not inherently constraint-aware and thus often waste computational resources evaluating invalid solutions. In this work, we present and evaluate constraint-aware variants of four evolutionary algorithms for auto-tuning. Through extensive experiments on a representative benchmark suite, we show that constraint-aware optimization leads to faster convergence and improved performance over unconstrained methods. Furthermore, we demonstrate that our methods outperform the pyATF methods, a state-of-the-art framework for constraint-based auto-tuning. Our results demonstrate that incorporating constraint-awareness into the optimization process significantly enhances their applicability and effectiveness in real-world auto-tuning problems. Constraint-awareness improved algorithm efficiency by ~39 on average, correlated with search space sparsity. The algorithms developed in this study are publicly available as open-source contributions to the Kernel Tuner framework, facilitating future research and benefitting users.

Floris-Jan Willemsen, Stijn Heldens, Rob V. van Nieuwpoort +1

LIACS, Leiden University, the Netherlands · Netherlands eScience Center, Amsterdam, the Netherlands

Differential EvolutionEvolutionary OptimizationConstrained OptimizationParticle Swarm OptimizationGenetic Algorithms
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Jun 3, 2026cs.LG

Hyperparameter Learning for Latent Factorization of Tensors for Representation Learning to Large-scale Dynamic Weighted Directed Network

Large-scale dynamic weighted directed networks (DWDNs) are widely used to model time-varying interactions among nodes. Latent factorization of tensors (LFT) extracts target knowledge from DWDNs via low-rank embedding. However, similar to many machine learning models, the performance of LFT heavily depends on the selection of hyperparameters. In practice, these parameters are often tuned manually or through grid search, which requires significant computational resources and human effort. Motivated by this challenge, this paper proposes an automated hyperparameter optimization framework based on Differential Evolution (DE) for LFT (DE-LFT). The proposed method integrates DE into the training process of the LFT model to automatically learn optimal regularization parameters λ1λ_1, λ2λ_2 and λ3λ_3. As a result, the model can adaptively search the hyperparameter space and improve prediction accuracy. Experimental results on four real-world datasets demonstrate that the proposed approach achieves lower MAE and RMSE compared with manually tuned baselines while reducing the need for extensive parameter tuning.

Yaqian Zhan, Jialan He, Tianzhu Chen

College of Computer and Information Science Southwest University Chongqing, China

Differential EvolutionGraph Representation LearningDynamic Graph LearningHyperparameter Optimization
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Jun 3, 2026cs.LG

An Ensembled Latent Factor Model via Differential Evolution and Gradient Descent Optimization

High-dimensional and incomplete (HDI) data are prevalent in many real-world big data scenarios. Latent factor models serve as a common representation learning approach, capable of uncovering informative latent factors from such data. Nevertheless, most existing latent factor models rely solely on gradient descent for optimization, which may lead to insufficient and biased representations, particularly when dealing with heterogeneous HDI data. Thus, this study proposes an Ensembled Latent Factor Model via Differential Evolution and Gradient Descent Optimization (ELFM-DEGDO) with two-fold designed: 1) two diverse latent factor models are independently modeled via differential evolution and gradient descent optimization, respectively, and 2) the two diverse latent factor models are combined via a customized self-adaptive weighting mechanism to effectively fuse their strengths. By leveraging the complementary advantages of both optimization paradigms, ELFM-DEGDO is able to produce more comprehensive and less biased representations for HDI data. Three HDI datasets are tested to show that ELFM-DEGDO consistently performs better than related several latent factor models.

Rui Zhang, Jinhang Liu, Wenbo Zhang

Chongqing Academy of Economics Research Chongqing, China · College of Computer and Information Science, Southwest University Chongqing, China

Representation LearningLatent Variable ModelsDifferential EvolutionEnsemble Learning
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May 12, 2026cs.NE

A Family of Quaternion-Valued Differential Evolution Algorithms for Numerical Function Optimization

The numerical optimization of continuous functions is a fundamental task in many scientific and engineering domains, ranging from mechanical design to training of artificial intelligence models. Among the most effective and widely used algorithms for this purpose is Differential Evolution (DE), known for its simplicity and strong performance. Recent research has shown that adapting AI models to operate over alternative number systems-such as complex numbers, quaternions, and geometric algebras-can improve model compactness and accuracy. However, such extensions remain underexplored in bio-inspired optimization algorithms. In particular, the use of quaternion algebra represents an emerging area in computational intelligence. This paper introduces a family of novel Quaternion-Valued Differential Evolution (QDE) algorithms that operate directly in the quaternion space. We propose several mutation strategies specifically designed to exploit the algebraic and geometric properties of quaternions. Results show that our QDE variants achieve faster convergence and superior performance on several function classes in the BBOB benchmark compared to the traditional real-valued DE algorithm.

Gerardo Altamirano-Gomez, Álvaro Gallardo, Carlos Ignacio Hernández Castellanos

Instituto de Investigaciones en Matem´aticas Aplicadas y Sistemas, Universidad Nacional Aut´onoma de M´exico, M´exico · Universidad Iberoamericana, M´exico

Differential EvolutionEvolutionary OptimizationBlack-Box Optimization
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May 10, 2026cs.NE

RDEx-CASK: Cauchy Mutation, Archive, and Stagnation Kick for RDEx-CSOP

We extend RDEx-CSOP with 3 changes that target stagnation & late-stage variance, plus minor parameter tuning. The second scale factor in the standard branch is sampled independently from a truncated Cauchy. A small feasible-only JADE-style archive (|A|_max = 50) is added & sampled with probability |A|/(|A|+|P|). Per-individual stagnation counter triggers, after 180 no-improvement generations, three local overrides on standard branch: pull toward the global best, lift the archive sampling floor to 0.65, & saturate CR to 0.95 when population success rate is below 0.10. The exploitation biased branch & every other RDEx component are left untouched. On CEC CSOP suite (D=30, 25 runs), RDEx-CASK is competitive with RDEx, UDE-III, & CL-SRDE in feasibility-aware quality & improves time-to-target on most problems.

Dikshant, Dikshit Chauhan, Chen Hao +3

Differential EvolutionEvolutionary OptimizationGlobal OptimizationConstrained Optimization
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May 9, 2026cs.NE

ARES-LSHADE: Autoresearch-Enhanced LSHADE with Memetic Polish for the GNBG Benchmark

We present ARES-LSHADE, a memetic differential-evolution variant submitted to the GECCO 2026 competition on LLM-designed evolutionary algorithms for the Generalized Numerical Benchmark Generator (GNBG). The algorithm builds on the LLM-LSHADE 2025 winner, contributing two new components: (a) a scout-augmented mutation operator with adaptive CMA-ES integration, produced by an autonomous research loop across approximately thirty LLM-driven design experiments, and (b) a multi-start L-BFGS-B polish phase that respects strict blackbox treatment of the benchmark. On the official 31-run-per-function evaluation with the competition-specified function-evaluation budgets, ARES-LSHADE obtains 510 of 744 wins (per-function gap below 1e-8), reaching machine precision on 18 of 24 functions. The remaining six functions exhibit characteristic plateau signatures consistent with GNBG's compositional structure, and were independently identified by the autoresearch loop as the hardest of the suite. Beyond the result itself, this report documents two methodological observations: (i) an LLM-driven research loop with operator-only edit surface and fitness-only observation space converges to a characteristic plateau on this benchmark; (ii) when we initially widened the observation space to include the benchmark's compositional metadata, the resulting algorithm trivially solved all 24 functions but violated the competition's blackbox rule, which we identified before submission. We discuss this tension between LLM capability and benchmark integrity as a design consideration for future LLM-driven optimization-algorithm research. Code and reproducibility artifacts are available at https://github.com/anaeem1/ARES-LSHADE.

Abdullah Naeem, Md Wasi Ul kabir, Manish Bhatt +3

University of New Orleans · Amazon†

Differential EvolutionEvolutionary OptimizationBlack-Box OptimizationLarge Language Model-Guided Optimization
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