Benchmark suite submitted to the GECCO BenchDesign 2026 competition (BenchDesign track). Contains 25 black-box optimisation functions designed to maximise algorithm discriminability, measured by Friedman IQR across five solvers: CMA-ES, Differential Evolution (DE),Particle Swarm Optimisation (PSO), L-BFGS-B, and COBYLA.

Functions were generated from a symbolic DSL that composes mathematical operators 
(quadratic, sinusoidal, exponential, rotation) into structured optimisation landscapes, evaluated at dimension 10 with a budget of 5000 function evaluations and 5 independent runs per algorithm.

Achieved Friedman IQR: 2.16 – 3.12 (stochastic metric; range over two independent 
evaluation runs using the official GECCO BenchDesign 2026 protocol).

This work is associated with the GECCO 2026 BenchDesign competition, hosted at the 
Genetic and Evolutionary Computation Conference (GECCO 2026) [1]. The benchmark design task and evaluation protocol are described in the IOHprofiler BenchDesign track [2],
with the official evaluator and baseline implementations available at [3].

[1] GECCO 2026 BenchDesign Competition. https://gecco-2026.sigevo.org/Competition?itemId=8257
[2] IOHprofiler BenchDesign Track. https://iohprofiler.github.io/competitions/benchdesign
[3] D. Vermetten, BenchDesign (GitHub repository). https://github.com/Dvermetten/BenchDesign

Summary

The Andean Condor Algorithm (ACA) [1] is a flexible metaheuristic method that has been adapted for the purpose of solving BBOB Many-Affine type problems provided by the IOHprofiler environment [2].

Objectives

- Solve Many-Affine BBOB Functions using the Andean Condor algorithm.

Experiment Result

- The best solution is extracted once the budget or iterations are reached. For this specific experiment [3][4], the average AOCC is calculated.

• 2D Experiment: Average AOCC 0.47256677552358844
• 5D Experiment: Average AOCC 0.3198143138317148

- The hardware used was a Lenovo computer (ThinkPad T14s Gen 4), with an AMD Ryzen 7 PRO 7840U w/ Radeon 780M Graphics, 32 GB RAM, running the Microsoft Windows 11 Pro Version 10.0.22631 Build 22631.

References

[1] Almonacid, B., & Soto, R. (2019). Andean Condor Algorithm for cell formation problems. Natural Computing, 18, 351-381. [https://doi.org/10.1007/s11047-018-9675-0].

[2] IOHprofiler [https://iohprofiler.github.io].

[3] GECCO 2024 Competition: Anytime Algorithms for Many-affine BBOB Functions [https://gecco-2024.sigevo.org/Competitions#id_Anytime Algorithms for Many-affine BBOB Functions].

[4] Anytime Algorithms for Many-affine BBOB Functions [https://iohprofiler.github.io/competitions/mabbob24].

Summary

This experiment focuses on applying the Andean Condor Algorithm (ACA)[1], a metaheuristic to compute the Star Discrepancy 𝐿∞ of a given set of points. The ACA metaheuristic has been adapted to solve Star Discrepancy problems and is employed to solve 30 different Star Discrepancy problems using the IOHprofiler environment [2] across instances ranging from 2 to 20 dimensions. It focuses on addressing numerical grey-box optimization problems [3][4] of the form max f(x) where x ∈ [1..n]^d, with experiment budgets set at 500 and 2500 evaluations. The ACA metaheuristic successfully solves the problems of the data set provided by the IOHprofiler environment [2].

Objectives

- Solve discrete Star Discrepancy problems using the Andean Condor algorithm.

Environment

- This dataset is configured for the grey-box, low-budget and high-budget categories with a budget of 500 and 2500 evaluations[4].

- The hardware used was a Lenovo computer (ThinkPad T14s Gen 4), with an AMD Ryzen 7 PRO 7840U w/ Radeon 780M Graphics, 32 GB RAM, running the Microsoft Windows 11 Pro Version 10.0.22631 Build 22631.

References

[1] Almonacid, B., & Soto, R. (2019). Andean Condor Algorithm for cell formation problems. Natural Computing, 18, 351-381. [https://doi.org/10.1007/s11047-018-9675-0].

[2] IOHprofiler [https://iohprofiler.github.io].

[3] GECCO 2024 Competition: Star Discrepancy Competition [https://gecco-2024.sigevo.org/Competitions#id_Star Discrepancy Competition @GECCO 2024].

[4] Star Discrepancy Computation [https://iohprofiler.github.io/competitions/stardiscr24].

Summary

The Progressive Sample Scaling (PSS) algorithm is a deterministic iterative method with the purpose of solving Many-Affine BBOB type problems provided by the IOHprofiler environment^[1]. The PSS algorithm operates in two stages: Sample and Scaling.

In the Sample stage, the algorithm generates a combination of equidistant points within the problem's boundaries, where each point corresponds to a variable array with a fixed dimension size. Subsequently, the points are evaluated, a fitness array is generated, and the best fitness value is recorded. The number of points to generate combinations is specified by the user, if an array of points is provided, these points are evaluated, and the one with the highest fitness is selected.

In the Scaling stage, the number of points around the best point identified in the Sample stage is increased, the best point is chosen, the search is refined progressively around it. This process is repeated until the budget is exhausted. Optionally, there is a factor value that can increase or decrease the number of points during execution in the Scaling stage.

Once the budget or iterations are exhausted, the best solution is extracted. For this specific experiment^[2][3], the average AOCC is calculated.

Objectives

• Solve Many-Affine BBOB Functions using a Deterministic Algorithm.

Limitations

• This algorithm is designed for Many-Affine BBOB problems of 2 and 5 dimensions.

Experiment Result

• 2D Experiment: Average AOCC 0.5911357090193021
• 5D Experiment: Average AOCC 0.4861510330030686

Environment

• The notebooks are configured for 2 and 5 dimensions.
• The hardware used was a Lenovo computer (ThinkPad T14s Gen 4), with an AMD Ryzen 7 PRO 7840U w/ Radeon 780M Graphics, 32 GB RAM, running the Microsoft Windows 11 Pro Version 10.0.22631 Build 22631.

References

[1] IOHprofiler https://iohprofiler.github.io.

[2] GECCO 2024 Competition: Anytime Algorithms for Many-affine BBOB Functions https://gecco-2024.sigevo.org/Competitions#id_Anytime Algorithms for Many-affine BBOB Functions.

[3] Anytime Algorithms for Many-affine BBOB Functions https://iohprofiler.github.io/competitions/mabbob24.

Summary

This experiment focuses on the application of AutoMH, a framework for the automatic generation of evolutionary algorithms, to address the problem of calculating the Star Discrepancy 𝐿∞ of a given set of points. The AutoMH with the use of reinforcement learning has searched in the episodes for an algorithm that satisfactorily solves problems 39, 49, and 59 of the data set provided by the IOHprofiler environment [1]. Once the episodes are finished, the algorithm that has had the best performance is extracted, this algorithm will be called AutoMH-SD. The AutoMH-SD algorithm will be the one that solves 30 different Star Discrepancy problems using the IOHprofiler environment in instances from 2 to 20 dimensions [2]. The AutoMH-SD algorithm will focus on solving the problems of numerical black box optimization approaches operating on [0,1), with low budget of 500 and high budget of 2500.

1. https://iohprofiler.github.io IOHprofiler.

2. https://iohprofiler.github.io/competitions/stardiscr GECCO 2023 Competition on Star Discrepancy Computation.

Objectives

Obtain through the AutoMH framework an algorithm with a low number of intensification and exploration instructions to solve the Star Discrepancy problem.

Environment

This notebook is configured for a high budget of 2500.

The hardware used was a MacBook Pro computer (Retina, 13-inch, Late 2013), with an Intel Core i5 2,4 GHz, 4 GB RAM 1600 MHz DDR3, running the OSx Catalina version 10.15.7.

References

[1] Almonacid, B. (2022). AutoMH: Automatically Create Evolutionary Metaheuristic Algorithms Using Reinforcement Learning. Entropy, 24(7), 957. https://doi.org/10.3390/e24070957

Dataset for Towards an Automatic Optimisation Model Generator Assisted
with Generative Pre-trained Transformer

Preprint: https://doi.org/10.48550/arXiv.2305.05811

Abstract:  This article presents a framework for generating optimisation models using a pre-trained generative transformer. The framework involves specifying the features that the optimisation model should have and using a language model to generate an initial version of the model. The model is then tested and validated, and if it contains build errors, an automatic edition process is triggered. An experiment was performed using MiniZinc as the target language and two GPT-3.5 language models for generation and debugging. The results show that the use of language models for the generation of optimisation models is feasible, with some models satisfying the requested specifications, while others require further refinement. The study provides promising evidence for the use of language models in the modelling of optimisation problems and suggests avenues for future research.   

Dataset Experiment 2: Comparison with other Metaheuristic Algorithms

- Data Descriptor AutoMH

Results of the experiment performed when using the Andean Condor Algorithm in a continuous domain function.

Dataset for Cell Formation Problems (35 problems with three cells) in txt and json.

Provide the data set to be able to reproduce the experiment.

It provides the results as raw data of the experiment.

Dataset - Solving the Manufacturing Cell Design Problem using the Artificial Bee Colony.

Dataset - Selecting a Biodiversity Conservation Area with a Limited Budget Using the Binary African Buffalo Optimization Algorithm