Algorithm Families Consistently Outperformed Rivals in Tests Spanning 14 Years

A thorough analysis of fifteen years of results from the IEEE CEC Single-Objective Optimisation competitions, spanning 2010 to 2024, reveals how changes in benchmark functions directly influenced the development of successful optimisation algorithms. Vojtěch Novák and colleagues at VSB, Technical University of Ostrava, alongside a collaboration between the Technical University of Munich, Indian Statistical Institute, and Università dell’Aquila, found that the introduction of dense rotation matrices in 2014 played a key role, favouring algorithms preserving rotational invariance, such as L-SHADE, and diminishing the performance of coordinate-dependent methods. The research sharply reveals a recent trend towards increasingly complex hybrid optimisers, and proposes that the adaptive capabilities honed by these algorithms in classical optimisation are also vital to the challenges of controlling variational quantum algorithms.

Tracing algorithmic lineages and the emergence of parameter non-separability in optimisation

Detailed dissection of each winning entry’s core mechanisms underpinned the analysis of algorithm performance, tracing their evolution across the fifteen-year competition period. The study constructed a detailed ‘family tree’ of optimisation techniques, identifying how successful strategies adapted to changing benchmark designs. Categorising algorithms by their primary search operators and adaptation strategies allowed for a comparative assessment of their strengths and weaknesses over time.

The team identified instances of parameter non-separability, where altering one variable unexpectedly impacts others, akin to a complex puzzle rather than a simple radio with independent controls. To understand algorithm development, the analysis focused on the fifteen-year history of the IEEE CEC Single Objective Optimisation competition, spanning from 2010 to 2024. The 2014 introduction of dense rotation matrices proved a key turning point, complicating benchmark functions and favouring algorithms preserving rotational invariance. This design choice specifically hindered coordinate-dependent methods such as Particle Swarm Optimisation and Genetic Algorithms, prompting a shift towards Differential Evolution variants like L-SHADE, and the evolution of these techniques was traced by categorising them by search operators and adaptation strategies to assess performance changes over time.

Rotation Matrices and the Rise of Rotationally Invariant Optimisation Algorithms

Results from fifteen years of IEEE CEC Single-Objective Optimisation competition, from 2010 to 2024, revealed a plummet in the success rate of coordinate-dependent algorithms, including Particle Swarm Optimisation and Genetic Algorithms, falling from consistent benchmark wins to less than 10% success after 2014. This dramatic decline followed the introduction of dense rotation matrices into benchmark functions, creating parameter non-separability, as algorithms previously navigated problems with independent variables effectively. The shift favoured rotationally invariant methods, most notably variants of Differential Evolution such as L-SHADE, which became dominant. By 2017, the field had entered a phase of hybridization, with algorithms like AGSK and IMODE structurally combining two distinct search logics to navigate increasingly complex benchmark fields.

After 2020, this trend intensified, with winning entries routinely incorporating mechanisms such as Eigenvector Crossover, designed to mimic covariance learning, and Success Rate based adaptation to refine exploitation. Societal Sharing, a technique encouraging exploration of diverse solutions, also became prevalent in these high-complexity optimizers. The analysis identified parallels between these modern benchmark functions and the challenging fields found in Variational Quantum Algorithms, suggesting CEC-evolved solvers may possess the adaptive capabilities needed for quantum control.

Benchmark evolution drives algorithmic adaptation in optimisation competitions

Optimisation algorithms, relentlessly refined through fifteen years of competition, now exhibit a surprising capacity for adaptability. This ability stems from responding to increasingly complex benchmark functions, rigorously designed to test their performance, but the very success of these algorithms raises a vital question. While the analysis demonstrates a correlation between benchmark complexity and the rise of hybrid optimisers, combining techniques like Eigenvector Crossover and Societal Sharing, it does not definitively prove that benchmarks caused this shift.

Acknowledging that correlation does not equal causation remains important, this fifteen-year record of optimisation competition results remains valuable. The analysis clearly demonstrates how benchmark design, specifically the introduction of dense rotation matrices in 2014, actively filtered out less effective algorithms such as Particle Swarm Optimisation and Genetic Algorithms. Identifying this shift provides valuable insight for designing future benchmarks and suggests these evolved solvers may possess the adaptability needed for tackling complex problems in emerging fields like quantum computing.

A fifteen-year analysis of optimisation competitions reveals how benchmark function design actively steers algorithmic development, moving beyond simple evaluation. The introduction of dense rotation matrices in 2014 created ‘parameter non-separability’, meaning changes to one variable unexpectedly impact others, fundamentally altering the competitive field. Algorithms like variants of Differential Evolution, which maintain performance irrespective of axis orientation, proved more durable when faced with scrambled problem spaces. Consequently, the field transitioned from diverse approaches to increasingly complex hybrid optimisers, combining techniques to improve performance.

The research demonstrated that optimisation algorithms evolved in response to increasingly complex benchmark functions over fifteen years of competition. This matters because it highlights how benchmark design actively shapes the development of these algorithms, favouring those, like L-SHADE variants of Differential Evolution, capable of handling parameter non-separability introduced by dense rotation matrices in 2014. The observed shift towards hybrid optimisers utilising methods such as Eigenvector Crossover suggests these solvers possess adaptive capabilities potentially useful for tackling challenging landscapes found in areas like variational quantum algorithm control. This understanding could inform the creation of new benchmarks and accelerate progress in quantum computing applications.