Fast and robust parametric and functional learning with Hybrid Genetic Optimisation (HyGO)

TL;DR

HyGO tackles the challenge of efficient, unified optimisation for parametric and functional learning in high-dimensional engineering problems. It introduces a two-stage Hybrid Genetic Optimisation framework that couples global genetic search with a degeneracy-proof DSM local search, using binary GA and Linear Genetic Programming representations. The framework demonstrates faster convergence and enhanced robustness across Rosenbrock benchmarks, a damped Landau oscillator control task, and a high-dimensional Ahmed body drag-reduction problem, with the stepped HyGO variant achieving the largest drag reductions (> $20\%$). By delivering an open-source, modular tool, HyGO enables practical application to flow control, design optimisation, and automated policy synthesis in simulation-based engineering.

Abstract

The Hybrid Genetic Optimisation framework (HyGO) is introduced to meet the pressing need for efficient and unified optimisation frameworks that support both parametric and functional learning in complex engineering problems. Evolutionary algorithms are widely employed as derivative-free global optimisation methods but often suffer from slow convergence rates, especially during late-stage learning. HyGO integrates the global exploration capabilities of evolutionary algorithms with accelerated local search for robust solution refinement. The key enabler is a two-stage strategy that balances exploration and exploitation. For parametric problems, HyGO alternates between a genetic algorithm and targeted improvement through a degradation-proof Dowhill Simplex Method (DSM). For function optimisation tasks, HyGO rotates between genetic programming and DSM. Validation is performed on (a) parametric optimisation benchmarks, where HyGO demonstrates faster and more robust convergence than standard genetic algorithms, and (b) function optimisation tasks, including control of a damped Landau oscillator. Practical relevance is showcased through aerodynamic drag reduction of an Ahmed body via Reynolds-Averaged Navier-Stokes simulations, achieving consistently interpretable results and reductions exceeding 20% by controlled jet injection in the back of the body for flow reattachment and separation bubble reduction. Overall, HyGO emerges as a versatile hybrid optimisation framework suitable for a broad spectrum of engineering and scientific problems involving parametric and functional learning.

Figures (14)

• Figure 1: Hybrid Genetic Optimisation algorithm: exploration and exploitation scheme. (a) Schematic flowchart, highlighting its two-phase structure. In each generation $n$, exploration is performed by creating individuals $\bm{f}^n_i$ via genetic operations, which include elitism, crossover, mutation, and replication, selected through a tournament process; the resulting solutions are evaluated and sorted according to the cost function $J_i^n$. After exploration, exploitation is performed by applying DSM to refine the best candidates. The horizontal bars visually encode individual performance within the population, with brighter and shorter bars indicating lower (better) costs and darker, longer bars reflecting higher (poorer) solutions. (b) Conceptual map illustrating an example of an algorithmic sequence in a two-dimensional landscape, alternating between exploration and local exploitation. Coloured points indicate the origin of each solution: random initialisation, genetic operations (crossover, mutation), and simplex-based moves (reflection, expansion, contraction, shrinkage, centroid). Light-shaded regions correspond to low (optimal) cost areas, while dark regions denote high (suboptimal) cost; the arrows and markers trace how exploration enables the population to sample broadly, while exploitation directs progress toward local minima.
• Figure 2: Solution encoding and genetic operations for Genetic Algorithm (GA) and Linear Genetic Programming (LGP). (a1) Binary-encoded chromosomes for GA represent sets of parameters. (b1) Encoding of LGP individuals as instruction matrices acting on program registers (variables, constants, memory, and inputs). (a2, b2) Examples of genetic operations: (a2) In GA, crossover swaps chromosome segments between parents (highlighted), and mutation randomly flips selected bits. (b2) In LGP, crossover exchanges blocks of instructions between programs, and mutation replaces random instructions, enabling structural diversity in candidate solutions.
• Figure 3: Hyperplane degeneracy into a 1-dimensional hyperplane in a 2D parametric domain. Image (a) displays all the operations and the topology under normal conditions. Image (b) shows a degenerate scenario where the Simplex collapsed into a line and lost the ability to move in the normal direction.
• Figure 4: Example of HyGO performance on the optimisation of the Rosenbrock function in 2D: (a) cost evolution of the individuals through the generations. (b) Individuals' distribution in the parametric space in each of the five generations ($\#1-5$). The arrow in generation #5 shows the tendency of the DSM solution towards the global minimum of the Rosenbrock function at (1,1). Individuals are coloured by the type of operation that created each individual (see \ref{['fig:HYGO_Algorithm']}, black for random initialisation, red tones for the different genetic operations, and blue tones for the DSM operations).
• Figure 5: Convergence comparison of HyGO, GA, and CMA-ES algorithms on the Rosenbrock, Rastrigin, and Sphere benchmark functions in 2D (top row) and 25D (bottom row). Each panel shows the evolution of the cost function $J$ as a function of the number of iterations across 50 independent runs with randomised initial conditions. Solid lines denote the mean run, dashed lines indicate the median, and lighter trajectories display individual runs. This visualisation highlights both the average performance and variability of each algorithm under different dimensionalities, illustrating convergence rates and robustness in complex landscapes