When designing a system to transmit satellite images, it is important to balance the need for a high compression rate with the ability to accurately reconstruct them. The discrete wavelet transform (DWT) can be used to compress images and can be fine-tuned for specific classes of images, but it requires substantial hardware resources to perform floating-point multiplications. Separate research efforts to evolve wavelets and hardware multipliers have been performed, but not together. This work explores the use of several evolutionary and coevolutionary algorithms to address this gap, focusing on different ways of combining wavelets and hardware. The first algorithm evolves them in two separate stages, a second evolves them in pairs, and the third algorithm cooperatively coevolves two populations of wavelets and hardware. The results indicate that problem decomposition is most beneficial when evolution allows individual components to be optimized separately. Additionally, our evolved wavelets show improved accuracy over existing wavelets at high compression ratios, and the evolved hardware uses four times fewer components as a human-designed approach. This work demonstrates strong potential for effective image compression and, more broadly, the use of coevolutionary algorithms to fine-tune circuit design alongside secondary systems defining the needs of those circuits.
Electroencephalography (EEG) data is highly sensitive, requiring strong privacy protection in brain–computer interfaces and neurological diagnosis. Homomorphic encryption enables secure EEG classification with deep neural networks, but standard activation functions (e.g., ReLU) are incompatible with encrypted arithmetic, causing severe computational overhead. Polynomial approximations mitigate this issue yet fail to capture EEG’s distinctive spectral patterns, temporal dynamics, and inter-subject variability. We propose a surrogate-assisted genetic algorithm (SA-GA) to optimize activation function approximations for encrypted deep learning models. SA-GA uses fixed-length chromosome encoding and a Gaussian Process surrogate to efficiently search the approximation space while avoiding costly encrypted evaluations. Applied to motor imagery classification (BCI Competition IV Dataset 2a), our method achieves 89.7
Single Image Super-Resolution reconstructs high-fidelity images from low-resolution inputs under tight computational budgets, essential in fields like medical diagnostics, remote sensing, surveillance, and aerospace imaging. To ease manual network design, Neural Architecture Search is a key AutoML tool, though its effectiveness hinges on often costly and imperfect performance evaluations. This paper compares two efficient predictors: (i) SynFlow, a zero-cost method, and (ii) an XGBoost regressor, a model-based approach. Both are integrated into NSGA-III, a multi-objective evolutionary algorithm, to explore Super-Resolution architectures optimizing three objectives: maximizing PSNR while minimizing parameter count and floating-point operations. We analyze each method’s impact on final architecture quality. SynFlow offers faster and more reliable estimations compared to XGBoost, which is slower and less accurate. However, XGBoost enables broader approximations of the Pareto front, making it suitable for more comprehensive trade-off exploration. Therefore, we recommend using SynFlow in scenarios where quick and resource-constrained searches are required, while XGBoost is more appropriate when the benefits of a wider trade-off analysis outweigh the additional computational cost.
Surrogate-assisted evolutionary algorithms (SAEAs) are a representative approach for expensive optimization problems, as solutions for expensive function evaluations (FEs) are prescreened or iteratively improved with the surrogate model of objective functions. These days, SAEAs are often designed to enhance convergence speed by utilizing previously evaluated solutions with good function values. Although this convergence-first design enables SAEAs to find relatively better solutions quickly at the beginning of the search, SAEAs tend to select quite similar solutions to each other for expensive FEs in the middle to the end of the search, resulting in the waste of expensive FEs. Accordingly, this work first incorporates a principle of tabu search into existing SAEAs as well as observes the behavior of the existing SAEAs and their extension. Tabu search extended for continuous optimization prevents to evaluation of similar solutions to previously evaluated ones. This promotes a variety of solution choices in SAEAs and realizes a sustainable performance improvement toward the end of the search. In the experiments held in this work, some SAEAs that have different search strategies and machine learning models for surrogate models are selected, and their extended versions incorporating tabu search are tested in a suite of single-objective continuous optimization benchmarks under an expensive scenario.
Pareto local optimal solution networks (PLOS-nets) model fitness landscapes as graphs where nodes are Pareto local optima and edges account for standard neighbourhood relationships. PLOS-nets capture the global structure of multi-objective combinatorial landscapes and provide a rich set of features. Published results so far focus on small problems. This article proposes new modelling and sampling methodologies to scale up PLOS-nets to larger problem sizes. Our sampling approach is based on the effective multi-objective random one-bit climber (moRBC). In our coarse-grained model, nodes are sets of Pareto local optimal solutions grouped according to the logarithm of their Pareto rank (following non-dominated sorting). For modelling edges, we consider the original neighbourhood edges, but also propose a new definition representing soft-restarts from Pareto local optima. We analyse and visualise our models on a set of combinatorial landscapes with tuneable ruggedness and number of objectives (MNK-landscapes). The models provide landscape features that correlate with the performance of multi-objective optimisation algorithms, and can be used in algorithm recommendation settings. The model with neighbour edges slightly outperforms the soft-restart model (in terms of predictive power), but its substantial computational overhead makes the soft-restart model a promising approximation.
To solve constrained optimization problems (COPs) with genetic algorithms, different methods have been proposed to handle constraints, but none of them are specifically designed for model-building genetic algorithms (MBGAs). This paper presents a three-population scheme, abbreviated as B-3Pop, which features three populations: a feasible one, an infeasible one, and a third one to explore the boundary between the feasible and infeasible spaces with MBGAs. The core idea is to learn how to combine feasible and infeasible solutions to evolve optimal solutions near the boundary. Empirically, B-3Pop outperforms five widely used constraint-handling methods—elimination, dominance concept, penalization, adaptive segregational constraint-handling methods, and the feasible-infeasible two-population scheme—in terms of the number of function evaluations on all six tested COPs: dimensional knapsack, uncapacitated warehouse location, Steiner tree, capacitated minimum spanning tree, capacitated p-median, and weighted maximum-2-satisfiability problems.
Particle Swarm Optimization (PSO) performance relies heavily on interaction topology. Our prior work, Self-Evaluated Topology Particle Swarm Optimization (SET-PSO), achieved high accuracy and stability through self-evaluated dynamic topology, but suffered from significant computational inefficiency due to global topological changes and multi-run evaluations. To solve this problem, this paper proposes the Grouping and Mediator Self-Evaluating Topology Particle Swarm Optimization (GMSET-PSO). GMSET-PSO incorporates a novel Grouping and Mediator model, organizing particles into localized Von Neumann groups with virtual mediator particles facilitating hierarchical, inter-group communication. This design effectively blocks global information propagation, localizing search and reducing computational burden. Furthermore, dynamic topology adaptation becomes group-specific, and topology evaluation is streamlined to a single-run assessment with immediate rollback if no improvement. On the CEC2020 and CEC2022 benchmark function set, GMSET-PSO was compared with SET-PSO and other PSO variants equipped with adaptive mechanisms. The results show that GMSET-PSO largely retains the accuracy of the original algorithm while improving stability by 46.08
Real-valued optimization has attracted considerable interest because of its wide-ranging applications in areas such as control system design, circuit design, and hyperparameter tuning for machine learning. In this paper, we propose the skew multidimensional split-on-demand (smSoD), an extension of multidimensional split-on-demand (mSoD). mSoD serves as a discretization interface that enables discrete model-building genetic algorithms to tackle continuous-domain problems; smSoD further improves split-point selection by leveraging the sample distribution. We then embed smSoD into the integer version of the extended compact genetic algorithm (ECGA) and evaluate it on two benchmark suites: decomposable linkage problems and an extended version of the CEC2014 benchmark with additional subproblems. We compare smSoD+ECGA against bothmSoD+ECGA and L-SHADE. According to statistical tests, under high-dimensional scenarios, our method outperforms the other two methods on more than 50
Cartesian Genetic Programming (CGP) is a graph-based evolutionary representation in which candidate solutions are encoded as directed acyclic grid of computational nodes. In standard CGP, only the output of the full graph is considered for fitness evaluation, although all intermediary (active) node outputs are computed during execution. We introduce Iterative Subgraph Assessment CGP (ISA-CGP), a straightforward extension that treats every active node output as a potential solution: during each individual’s evaluation, all subgraph outputs are assessed alongside the full graph, and the best-performing expression is selected. Favourably, in Symbolic Regression (SR) fitness measurements are usually inexpensive. To validate ISA-CGP, we conduct experiments on eight benchmark problems drawn from the Feynman symbolic regression suite, comparing convergence speed, final model error, and computational effort against standard CGP. Experimental results on the eight Feynman problems demonstrate that ISA-CGP converges more rapidly and attains superior fitness values in most cases. Furthermore, ISA-CGP creates smaller solution programs, indicating less bloated phenotypes which saves computational efforts. These findings suggest that ISA-CGP offers a simple yet effective enhancement to CGP, achieving faster search and better solutions with minimal overhead.
The Core is a unique competitive co-evolution algorithm that allows agents to evolve autonomous control without utilizing a traditional fitness function. The agents evolve via local interactions through tournament selection, crossover, and mutation, producing offspring by evolving better controllers. Previous works have shown The Core’s ability to evolve agents capable of combat and navigation in the Xpilot video game. This research expands upon that premise by niching agents to specific subsets of the original environment The Core was tested in. Our results demonstrate the niched agents capacity for success over agents niched to the entire system and agents niched to different sub-environments.
Bilevel optimization, a class of hierarchical optimization problems with broad applications in machine learning and engineering, presents a significant research challenge due to its inherent NP-hard nature in the non-convex optimization problems. In this paper, we address the limitations of existing solvers. Classical, gradient-based methods are inapplicable to the non-convex and non-differentiable landscapes, common in practice. On the other hand, derivative-free methods like nested evolutionary algorithms are rendered intractable by a prohibitively high query complexity. To this end, we propose a novel framework, the Surrogate Assisted Co-evolutionary - Evolutionary Strategy (SACE-ES), which synergizes the global search capabilities of evolutionary computation with the data-driven efficiency of surrogate modeling. The core innovation of our framework is a multi-surrogate, constraint-aware architecture that decouples the complex bilevel problem by using separate Gaussian Process models to approximate the lower-level optimal solution vector and its corresponding constraint violations. We conducted a comprehensive empirical study on a suite of challenging benchmarks, including the standard SMD problems. We demonstrate empirically that on complex constrained problems, SACE-ES discovers solutions that are upto two orders of magnitude superior upper-level fitness values to those found by exhaustive search baselines. Furthermore, on a range of unconstrained, non-convex problems, our approach achieves statistically comparable solution quality while reducing the required computational cost by approximately upto 96
The Electric Vehicle Routing Problem (EVRP) has gained increasing attention with the growing adoption of electric vehicles, driven by the global shift towards reducing the negative environmental impact. This paper addresses the EVRP with Time Windows (EVRPTW), incorporating nonlinear charging functions that are often overlooked in existing models. Traditional EVRP approaches typically assume linear charging functions, which can lead to imprecise solutions due to unrealistic charging time estimations. However, real-world charging behaviour is nonlinear, and since recharging significantly affects total travel time, it is essential to account for more realistic charging dynamics. The objective of this paper is to solve the EVRPTW while minimizing both the total number of vehicles and the overall delay, using a more accurate representation of the charging process. To further assess adaptability, several recharging policies are examined, including minimal recharging, fixed-level recharging, and an adaptive policy that adjusts based on vehicle load. The proposed approach uses genetic programming as a hyper-heuristic to evolve routing policies that construct solutions while accounting for nonlinear charging behaviour. This work combines automatically evolved routing policies via genetic programming with both nonlinear charging models and different partial recharging strategies, providing a more realistic EVRPTW formulation.
Genetic Algorithms (GA) have proven to be versatile tools for solving optimization problems in various domains. However, traditional reliance on fixed-size populations can impose constraints on storage, transmission, and adaptability, particularly in resource-limited or distributed systems. This paper introduces the Condensed Population Genetic Algorithm (CPGA), a novel approach that replaces traditional population storage with an integer-array representation, enabling efficient condensation and reconstruction of populations. By aggregating the population into a single integer array of bit-counts rather than a floating-point probability vector, the CPGA retains exact population statistics while drastically reducing its memory footprint. Compared to probabilistic model–based methods such as the Compact Genetic Algorithm (cGA) or Estimation of Distribution Algorithms (EDA), which require full floating-point probability distributions and often complex parameter updates, our integer-array scheme leverages simple, exact count updates. Through controlled modification and regeneration of individuals, the CPGA demonstrates improved scalability and adaptability, especially in distributed and embodied evolutionary systems. Benchmark results on the BBOB-17 suite show the CPGA matches or exceeds the performance of traditional GAs while offering significant gains in storage efficiency and communication overhead; experiments in the Atari ALE framework further validate its efficacy across disparate domains.
We generate all 160 valid solutions for the traveling tournament problem with 4 teams, and randomly select 10,000 valid solutions for 6, 8 and 10 teams. For every number of teams, the difference between any two valid solutions is taken an charted. It turns out these differences are very large, even when a key constraint, the home/away assignment, is completely ignored. These results might signal that the use of metaheuristic algorithms for this problem might be highly problematic.
This paper presents a novel approach to hexapod locomotion by evolving each leg’s gait independently through a decentralized evolutionary algorithm. Using the Webots simulator and the Mantis hexapod robot, we optimize individual leg controllers without centralized coordination, allowing emergent behaviors to drive the development of efficient, coordinated locomotion. Our decentralized method is benchmarked against cooperative coevolution, demonstrating improved efficacy in generating stable and adaptive gaits while showing interesting emergent coordination. By enabling independent evolution of leg controllers, this method reduces the complexity of gait optimization and highlights the potential of decentralized strategies for scalable and adaptive robotic systems.
The University Course Timetabling Problem (UCTP) is a well-known NP-hard multi-objective optimization problem influenced by variety of factors ranging from institutional policies and facilities, institutional facilities, course characteristics to instructor availability, instructor preferences and the diversity and variability of student registration behaviors. This paper introduces GADA, a novel approach to automate course timetabling. Unlike traditional models that mostly assume static, centralized scheduling, GADA is an adaptive geneticalgorithm-based approach tailored for decentralized, credit-based systems where students independently register for courses and instructors have diverse time preferences. GADA focuses on optimizing course-to-timeslot allocation while satisfying both hard institutional constraints and soft instructor preferences. By automating critical steps in the scheduling workflow, GADA significantly reduces manual effort, increases scheduling flexibility, and adapts efficiently to late-stage registration changes. It has been implemented and evaluated extensively in the real-world environment at the Faculty of Computer Science and Engineering at Ho Chi Minh City University of Technology (CSE@HCMUT). The experimental results demonstrate GADA’s effectiveness and practical applicability in generating conflict-free and operationally feasible schedules while addressing the complex constraints inherent in decentralized academic timetabling.
Traditional and high-level Petri nets are limited in representing adaptive or evolving distributed systems. We introduce a comprehensive definition of Reisig’s Algebraic Petri nets (APN) with active tokens, employing Maude, a declarative language with rewriting logic semantics. Reisig’s APN offers unmatched expressivity and analytical power, and with active tokens, they represent distributed components with internal logic naturally. Active tokens facilitate straightforward and efficient meta-modeling. Although rewriting logic was proposed as a unified logical framework for PNs two decades ago, ours is the first complete implementation of APNs (with active tokens) based on Maude. We tackle modeling challenges from Maude’s rewriting strategy relying on pattern-matching and coherence by proposing two alternative definitions. Our approach is illustrated with code snippets and examples, featuring an advanced model of an adaptive MLFQ algorithm.
Symbolic regression (SR) using genetic programming (GP) can generate a diverse set of candidate models that balance accuracy and complexity, particularly when configured with multi-objective optimisation, which produces a Pareto front of non-dominated solutions. However, selecting a single model from this population remains challenging, especially when relying only on training data. This study evaluates the effectiveness of model selection criteria in SR, which include Mean Squared Error (MSE), Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Description Length (DL), and PySR Score Metric (PSM). These criteria are evaluated using their training scores on 20 real-world regression datasets from the PMLB collection using PySR. We calculate the Spearman rank correlation coefficient ( ρ ) between each metric and test MSE to evaluate how well the metric ranks generalisable models. The results show that no single metric performs reliably across all datasets. Metrics that focus mainly on accuracy often lead to overfitting, while simplicity-based metrics can underfit. PSM aims to balance accuracy and complexity, but its performance is inconsistent, sometimes helpful, but often unstable across datasets. This study provides practical insights into the behaviour of model selection metrics in SR and offers guidance for selecting models that generalise well without overfitting.
Feature selection is indispensable for reducing dimensionality and improving performance and interpretability in high-dimensional domains such as gene expression analysis. Traditional binary adaptations of the Grey Wolf Optimizer (BGWO) often suffer from premature convergence and tend to select feature subsets containing high redundancy when relying on simple single-objective fitness functions. To overcome these limitations, we introduce the Adaptive Redundancy-aware Binary Grey Wolf Optimizer (AR-BGWO), a novel single-objective metaheuristic specifically tailored for binary feature selection. AR-BGWO incorporates two principal innovations: a non-linear, stagnation-responsive adaptation of the exploration-exploitation parameter a , which enables more effective navigation of the search space, and an implicit redundancy penalty within the fitness function that discourages highly correlated feature selections, thereby promoting both accuracy and conciseness without resorting to multi-objective formulations. Experimental analyses indicate that AR-BGWO consistently identifies smaller, less redundant feature sets while achieving higher or comparable classification accuracy relative to standard BGWO and other state-of-the-art methods.
This paper proposes a genetic programming (GP) algorithm for symbolic regression (SR), called the behavioral cloning guided genetic programming (BCGP) algorithm. The goal is to improve the effectiveness of crossover by preserving the relationship between parent operators and subtrees through imitating the behavior of subtree crossover during evolution. Specifically, BCGP investigates the application of a multilayer perceptron to capture features based on the parent operators and the subtrees. Across the benchmark problems from the SR benchmark and the Feyman SR database, BCGP gains the lowest count of maximum average MAEs and lowest average ranks, and statistically significantly outperforms ellynGP, and GP-GOMEA on 31 and 9 benchmark problems, respectively, out of a total of 43.
