# The importance of being constrained: dealing with infeasible solutions in Differential Evolution and beyond

arXiv: https://arxiv.org/abs/2203.03512 · HTML: https://mlsanity.com/paper/2203.03512/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 97 references that are in the map.
- First posted on arXiv 7 Mar 2022.

## Builds on (most cited first, 15 of 15)

- [COCO: A Platform for Comparing Continuous Optimizers in a Black-Box Setting](https://mlsanity.com/paper/1603.08785/) (2016)
- [IOHexperimenter: Benchmarking Platform for Iterative Optimization Heuristics](https://mlsanity.com/paper/2111.04077/) (2021)
- [Tuning as a Means of Assessing the Benefits of New Ideas in Interplay with Existing Algorithmic Modules](https://mlsanity.com/paper/2102.12905/) (2021)
- [Reproducibility in Evolutionary Computation](https://mlsanity.com/paper/2102.03380/) (2021)
- [Structural bias in population-based algorithms](https://mlsanity.com/paper/1408.5350/) (2014)
- [Differential Evolution with Reversible Linear Transformations](https://mlsanity.com/paper/2002.02869/) (2020)
- [Learning How to Optimize Black-Box Functions With Extreme Limits on the Number of Function Evaluations](https://mlsanity.com/paper/2103.10321/) (2021)
- [Infeasibility and structural bias in Differential Evolution](https://mlsanity.com/paper/1901.06153/) (2019)
- [Quantifying the Impact of Boundary Constraint Handling Methods on Differential Evolution](https://mlsanity.com/paper/2105.06757/) (2021)
- [Emergence of Structural Bias in Differential Evolution](https://mlsanity.com/paper/2105.04693/) (2021)
- [Feasibility Preserving Constraint-Handling Strategies for Real Parameter Evolutionary Optimization](https://mlsanity.com/paper/1504.04421/) (2015)
- [Differential evolution outside the box](https://mlsanity.com/paper/2004.10489/) (2020)
- [Is there Anisotropy in Structural Bias?](https://mlsanity.com/paper/2105.04480/) (2021)
- [An Enhanced Differential Evolution Algorithm Using a Novel Clustering-based Mutation Operator](https://mlsanity.com/paper/2109.09351/) (2021)
- [Benchmarking the Status of Default Pseudorandom Number Generators in Common Programming Languages](https://mlsanity.com/paper/2109.12997/) (2021)

## Built on by (most cited first, 1 of 1)

- [Explainable Benchmarking for Iterative Optimization Heuristics](https://mlsanity.com/paper/2401.17842/) (2024)

## Abstract (arXiv)

We argue that results produced by a heuristic optimisation algorithm cannot be considered reproducible unless the algorithm fully specifies what should be done with solutions generated outside the domain, even in the case of simple box constraints. Currently, in the field of heuristic optimisation, such specification is rarely mentioned or investigated due to the assumed triviality or insignificance of this question. Here, we demonstrate that, at least in algorithms based on Differential Evolution, this choice induces notably different behaviours - in terms of performance, disruptiveness and population diversity. This is shown theoretically (where possible) for standard Differential Evolution in the absence of selection pressure and experimentally for the standard and state-of-the-art Differential Evolution variants on special test function f0 and BBOB benchmarking suite, respectively. Moreover, we demonstrate that the importance of this choice quickly grows with problem's dimensionality. Different Evolution is not at all special in this regard - there is no reason to presume that other heuristic optimisers are not equally affected by the aforementioned algorithmic choice. Thus, we urge the field of heuristic optimisation to formalise and adopt the idea of a new algorithmic component in heuristic optimisers, which we call here a strategy of dealing with infeasible solutions. This component needs to be consistently (a) specified in algorithmic descriptions to guarantee reproducibility of results, (b) studied to better understand its impact on algorithm's performance in a wider sense and (c) included in the (automatic) algorithmic design. All of these should be done even for problems with box constraints.