| Exploratory Landscape Analysis (ELA) |
black-box |
1 |
continuous |
unconstrained or box-constrained |
https://doi.org/10.1145/2001576.2001690 |
https://github.com/Reiyan/pflacco |
Exploratory Landscape Analysis (ELA) features |
| Cell Mapping Features |
black-box |
1 |
continuous |
unconstrained or box-constrained |
https://doi.org/10.1007/978-3-319-07494-8_9 |
https://github.com/Reiyan/pflacco |
Cell Mapping Techniques for Exploratory Landscape Analysis |
| Dispersion Features |
black-box |
1 |
continuous |
unconstrained or box-constrained |
https://doi.org/10.1145/1143997.1144085 |
https://github.com/Reiyan/pflacco |
The Dispersion Metric |
| Information Content-Based Features |
black-box |
1 |
continuous |
unconstrained or box-constrained |
https://doi.org/10.1109/TEVC.2014.2302006 |
https://github.com/Reiyan/pflacco |
Exploratory Landscape Analysis of Continuous Space Optimization Problems Using Information Content. Information Content of Fitness Sequences (ICoFiS). |
| Nearest Better Features |
black-box |
1 |
continuous |
unconstrained or box-constrained |
https://doi.org/10.1145/2739480.2754642 |
https://github.com/Reiyan/pflacco |
The Nearest-Better Features - also called Nearest-Better Clustering (NBC) Features. Features for detecting funnel structures. |
| Barrier Tree Features |
black-box |
1 |
continuous |
unconstrained or box-constrained |
https://doi.org/10.1007/978-3-030-25147-5_7 |
https://github.com/kerschke/flacco |
Following generalized cell mapping, barrier trees can be used to characterize the problem structure. |
| Principal Components Features |
black-box |
1 |
continuous |
unconstrained or box-constrained |
https://doi.org/10.1007/978-3-030-25147-5_7 |
https://github.com/Reiyan/pflacco |
Describe the variable scaling of continuous problems by applying a Principal Component Analysis. |
| Linear model features |
black-box |
1 |
continuous |
unconstrained or box-constrained |
https://doi.org/10.1007/978-3-030-25147-5_7 |
https://github.com/kerschke/flacco |
Following generalized cell mapping, barrier trees can be used to characterize the problem structure. |
| Multi-objective Combinatorial Problem Features |
black-box |
2+ |
binary/combinatorial |
unconstrained |
https://doi.org/10.1162/evco_a_00193 |
? |
Features describing Multi-objective Combinatorial Problems. |
| Local Optima Networks (LON) |
black-box |
1 |
combinatorial |
unconstrained |
https://doi.org/10.1007/978-3-642-41888-4_9 |
? |
Local Optima Networks (LON): A network-based model of combinatorial landscapes. |
| DynamoRep |
black-box |
1 |
continuous |
unconstrained |
https://doi.org/10.1162/evco_a_00370 |
? |
DynamoRep computes basic descriptive statistics such as min, max, mean, std over x and y values to capture algorithm-problem interaction in single-objective continuous optimization. |
| Opt2Vec |
black-box |
1 |
continuous |
unconstrained |
https://doi.org/10.1016/j.ins.2024.121134 |
? |
A continuous optimization problem representation based on algorithm behavior. |
| DoE2Vec |
black-box |
1 |
continuous |
unconstrained |
https://doi.org/10.1145/3583133.3590609 |
https://github.com/nikivanstein/doe2vec |
DoE2Vec: Deep-learning Based Features for Exploratory Landscape Analysis. Uses autoencoder (AE) based latent-space features. Does not require any feature engineering and is easily applicable to high-dimensional search spaces. |
| Best-so-far trajectories |
black-box |
1 |
continuous |
unconstrained |
https://doi.org/10.1007/978-3-031-56852-7_7 |
? |
Use raw optimisation (probing) trajectories containing the best performance values seen so far for each evaluation. |
| Current trajectories |
black-box |
1 |
continuous |
unconstrained |
https://doi.org/10.1007/978-3-031-56852-7_7 |
? |
Use raw optimisation (probing) trajectories containing the current performance values seen at each evaluation. |
| Time series features using TSFRESH |
black-box |
1 |
continuous |
unconstrained |
https://doi.org/10.1145/3449639.3459399 |
? |
Compute time series features using TSFRESH. The authors did this for internal CMA-ES variables, but this might also be applied to, e.g., performance trajectories. |
| Deep learning-based features |
black-box |
1 |
continuous |
unconstrained |
https://doi.org/10.1145/3512290.3528834 |
? |
Represents the initially sampled points as point clouds to 2D images for use with deep-learning models. |
| Deep-ELA |
black-box |
1, 2+ |
continuous |
unconstrained |
https://doi.org/10.1162/evco_a_00372 |
https://github.com/mvseiler/deep_ela |
Deep-ELA: Deep Exploratory Landscape Analysis with Self-Supervised Pretrained Transformers for Single-Objective and Multiobjective Continuous Optimization Problems. |
| Decomposition-Based Multi-objective Landscape Features |
black-box |
2+ |
continuous |
unconstrained |
https://doi.org/10.1007/978-3-030-72904-2_3 |
? |
A set of landscape features for multi-objective combinatorial optimization, by decomposing the original multi-objective problem into a set of single-objective sub-problems. |
| SOO search tree |
black-box |
1 |
continuous |
unconstrained |
https://doi.org/10.1145/3299904.3340308 |
? |
Features on the basis of the search tree constructed by the so-called SOO global optimizer. |
| Scalarization-based features |
black-box |
2+ |
continuous |
unconstrained |
https://doi.org/10.1145/3712256.3726378 |
? |
Scalarization-based ELA (S-ELA) for multi-objective continuous optimization using objective scalarization methods: decomposition and non-dominated sorting. |
| Landscape Features for Multi-objective Interpolated Continuous Optimisation Problems |
black-box |
2+ |
continuous |
unconstrained |
https://doi.org/10.1145/3449639.3459353 |
? |
Landscape Features for Multi-objective Interpolated Continuous Optimisation Problems aimed at measuring aspects of: global properties, multimodality, evolvability, and ruggedness. Uses a different sampling method to use features originally designed for discrete problems for the continuous case. |
| Fitness distance correlation (FDC) |
white-box, grey-box |
1 |
continuous, combinatorial |
unconstrained |
Jones and Forrest 1995 - Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms |
? |
Correlation between performance values and the distance to the global optimum. I.e., the global optimum must be known to compute this feature. |
| Evolvability metrics |
black-box |
1 |
continuous, combinatorial |
unconstrained |
https://doi.org/10.1162/106365602317301754 |
? |
Evolvability statistics of the fitness landscape surrounding sampled solutionas, to assess the ruggedness and neutrality of a landscape. |
| Bag of local landscape patterns (BoLLP) |
black-box |
1 |
continuous, combinatorial |
unconstrained |
https://doi.org/10.1007/s00500-016-2091-4 |
? |
Uses the fitness patterns of local candidate solutions. |
| Bag of evolvability (BoEvo) |
black-box |
1 |
continuous, combinatorial |
unconstrained |
https://doi.org/10.1007/s00500-016-2091-4 |
? |
Uses the evolvability of candidate solutions as local landscape feature. |