Evolutionary Algorithms in Chaotic Systems

Evolutionary algorithms are population-based optimisation techniques inspired by natural selection and genetic variation. Traditionally driven by pseudo-random number generators, these methods introduce stochasticity into operators such as mutation and crossover. Recent advances explore the replacement or augmentation of random mechanisms with deterministic chaos. Chaotic systems, characterised by sensitivity to initial conditions, mixing properties and dense periodic orbits, can generate sequences with quasi-random behaviour. Incorporating such sequences into evolutionary frameworks has been shown to enhance exploration of the search space, maintain population diversity and avoid premature convergence. Chaotic maps—most notably the logistic, tent, Gaussian and Hénon maps—have been employed to initialise populations, adapt control parameters dynamically and guide mutation steps. The deterministic yet unpredictable nature of chaos offers reproducibility alongside enhanced ergodicity, which translates into more robust global search capabilities and improved local exploitation when combined with hierarchical learning or interactive schemes. Applications range from engineering design and machine-learning parameter tuning to diagnostics in medical imaging and the generation of complex evolutionary art. The integration of chaos into metaheuristics underscores a shift towards hybrid deterministic-stochastic paradigms that marry theoretical rigour with practical effectiveness across complex optimisation landscapes.

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One recent study conducted a systematic experimental analysis of ten evolutionary algorithms, replacing standard pseudo-random number generators with sequences derived from the logistic map. The authors demonstrated that chaos-driven variants achieve superior convergence rates and solution quality on benchmark functions, highlighting the role of deterministic ergodicity in enhancing search dynamics and prompting new theoretical questions about chaos-based mutation schemes.

An earlier foundational work introduced a general framework for chaotic evolution, comparing logistic, tent, Gaussian and Hénon maps within differential evolution algorithms. The investigation revealed that the statistical distribution properties of each chaotic map significantly influence optimisation performance. The same study proposed an interactive chaotic evolution algorithm, wherein human-in-the-loop fitness evaluation replaces conventional objective functions, illustrating the potential for hybrid interactive systems to improve solution diversity and adaptability.

More recently, a Hierarchical Learning-Enhanced Chaotic Crayfish Optimisation Algorithm (HLCCOA) was developed to bolster the generalisation ability of extreme learning machines in breast cancer diagnosis. This approach uses chaotic sequences for population initialisation, leverages ergodicity to boost diversity, and incorporates a multi-layer learning mechanism that balances global exploration with fine-tuned local exploitation. Benchmark tests against standard crayfish optimisation and other heuristics demonstrated marked improvements in accuracy, sensitivity and specificity, underscoring the practical robustness of chaos-inspired metaheuristics in real-world classification tasks.

Evolutionary Algorithms in Chaotic Systems publication trend

The graph below shows the total number of articles in evolutionary algorithms in chaotic systems across all publications each year (not limited to Nature Index journals).

Technical terms

Evolutionary algorithm: A computational method that mimics biological evolution by iteratively selecting, recombining and mutating candidate solutions.

Chaotic system: A deterministic dynamical system exhibiting sensitive dependence on initial conditions, topological mixing and dense periodic orbits, producing complex quasi-random sequences.

Logistic map: A simple one-dimensional chaotic map defined by xₙ₊₁ = r xₙ (1 – xₙ), often used to generate chaotic sequences for optimisation.

Ergodicity: The property of a system whereby its trajectories eventually explore all available states in the phase space according to a well-defined invariant distribution.

Global search and local exploitation: Dual phases of optimisation, where global search broadly explores the solution space to avoid local optima, and local exploitation refines promising regions for precise convergence.

References

1. Impact of chaotic dynamics on the performance of metaheuristic optimization algorithms: An experimental analysis. Information Sciences (2022).
2. From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization. The Scientific World JOURNAL (2015).
3. Hierarchical Learning-Enhanced Chaotic Crayfish Optimization Algorithm: Improving Extreme Learning Machine Diagnostics in Breast Cancer. Mathematics (2024).
4. Pixel-Based Approach for Generating Original and Imitating Evolutionary Art. Electronics (2020).