The original DE algorithm, conceived in the 1990s, operates with a fixed population size. A population of candidate solutions, each encoding a possible answer to the optimization problem, is iteratively improved through mutation, crossover, and selection. This fixed-size design is elegant and easy to implement, but decades of research have shown that it is rarely the most efficient choice. Early in a search, a large population promotes exploration, allowing the algorithm to survey many regions of the solution space and avoid premature convergence on poor solutions. Later, once promising regions have been identified, a smaller population concentrates computational effort on refining the best candidates. Modern DE variants therefore adopt advanced strategies for reducing the population size during evolution, trading breadth for depth as the run progresses.

The Maribor team’s review is remarkable in its scope: the researchers analyzed 204 studies on population size reduction methods, providing both a structured overview of the field and an original experimental analysis. The methods they surveyed fall broadly into two families. Linear population size reduction (LPSR) shrinks the population at a constant rate from its initial size down to a small minimum, typically a handful of individuals, by the end of the run. Non-linear population size reduction (NLPSR) methods, by contrast, use non-uniform schedules, adaptive rules, or problem-dependent mechanisms to decide when and how quickly to remove individuals. The distinction sounds technical, but it captures a genuine design tension: should the population contract steadily and predictably, or should its size respond dynamically to the state of the search itself?

To move beyond a literature survey, the authors conducted a rigorous comparative analysis. They selected representative reduction methods and integrated each of them into jSO, a state-of-the-art DE variant that has performed strongly in international optimization competitions. This controlled design is important, because it isolates the effect of the population size strategy from other algorithmic choices. By plugging different reduction mechanisms into the same underlying algorithm, the researchers could attribute differences in performance to the reduction strategy alone rather than to a tangle of interacting components. The resulting experiments compared fifteen methods across a demanding test environment.

The benchmark of choice was the CEC 2024 suite, a collection of numerical optimization functions maintained for the IEEE Congress on Evolutionary Computation. These functions are deliberately crafted to stress different aspects of an optimizer: unimodal functions test the ability to converge quickly on a single basin, multimodal functions scatter many local optima to trap premature convergence, hybrid functions combine different landscape characteristics within a single problem, and composition functions blend several sub-functions into landscapes of daunting complexity. The team ran the experiments at problem dimensions of 10, 30, 50, and 100 variables, since the dimensionality of a problem profoundly changes how an optimizer behaves. High-dimensional problems, in particular, are notoriously difficult because the search space grows exponentially with the number of variables.

The statistical analysis relied on the Friedman test, a non-parametric method for ranking multiple algorithms across many problems. Applied to the fifteen methods, the test delivered a striking result: on 100-dimensional problems, ten non-linear population size reduction methods were ranked higher than the linear reduction method. This suggests that as problems grow more complex, the flexibility of non-linear schedules pays off, allowing the population to contract in ways that better match the evolving structure of the search. The per-function-family analysis reinforced this picture while adding nuance. Different reduction methods excelled on different function families and at different dimensions, with methods such as APDSDE, CS-DE, HARD-DE, DPSHADE, dynNP-DE, AGDE-MPP, and NLPSR variants each topping the rankings in specific configurations.

Crucially, however, the study found no single population size adjustment strategy that consistently dominates across all problem dimensions and function families. This is a recurring theme in evolutionary computation research, and the review confirms it with unusual thoroughness. A method that thrives on multimodal landscapes at moderate dimensionality may falter on composition functions at 100 dimensions. The practical implication for practitioners is clear: the choice of population size strategy should be treated as a problem-dependent design decision, informed by the characteristics of the optimization task at hand, rather than as a one-size-fits-all setting.

Benchmarks alone can be criticized as artificial, so the team also tested the methods on two real-world optimization problems. Here the results were notable: a non-linear population size reduction method achieved the top rank on both real-world problems. Real-world engineering problems often feature irregular landscapes, constraints, and noisy evaluations that synthetic benchmarks only approximate, so this result provides encouraging evidence that the insights from the CEC 2024 experiments carry over to practical applications. For engineers using DE to calibrate models, design components, or optimize industrial processes, the message is that modern non-linear reduction strategies deserve serious consideration.

Why does population size reduction work so well in the first place? The underlying logic involves both search dynamics and computational economics. Each generation, the algorithm evaluates every individual in the population, so the population size directly determines how many function evaluations are consumed per generation. A bloated population late in a run wastes evaluations on near-duplicate candidates that contribute little new information. Conversely, shrinking too aggressively early on can collapse diversity before the algorithm has mapped the landscape, causing it to converge on a local optimum. The art of a good reduction strategy lies in timing: preserving enough diversity long enough to explore, then concentrating resources precisely when refinement matters most. Non-linear schedules attempt to encode this timing more intelligently than a straight line can.

The review arrives at a moment when AI-based optimization is enjoying renewed attention, with scientists, engineers, and practitioners increasingly expected to be fluent in evolutionary computing techniques. By cataloguing 204 studies, subjecting fifteen representative methods to controlled experiments on a modern benchmark suite and real-world problems, and publishing the work open access under a Creative Commons licence, the Maribor group has produced both a reference work and a practical guide. The detailed appendices, including per-dimension performance tables and Friedman rank figures for every function family, give researchers the granular evidence needed to select and design reduction mechanisms. As optimization problems in science and industry continue to grow in scale and complexity, the study’s central lesson stands out: in differential evolution, how you shrink the swarm can matter as much as how you search with it.

Subject of Research: Population size reduction methods in the differential evolution optimization algorithm

Article Title: Population size reduction methods in differential evolution: a comprehensive review and experimental analysis

Article References: Brest, J., Popič, J., Pšeničnik, B., Bošković, B., & Sepesy Maučec, M. (2026). Population size reduction methods in differential evolution: a comprehensive review and experimental analysis. Artificial Intelligence Review. https://doi.org/10.1007/s10462-026-11712-5

Image Credits: AI Generated

DOI: 10.1007/s10462-026-11712-5

Keywords: differential evolution, evolutionary computation, numerical optimization, population size reduction, linear population size reduction, non-linear population size reduction, CEC 2024 benchmark, Friedman test, jSO algorithm, artificial intelligence, real-world optimization, University of Maribor