# Metaheuristics for (Variable-Size) Mixed Optimization Problems: A Unified Taxonomy and Survey

arXiv: https://arxiv.org/abs/2401.03880 · HTML: https://mlsanity.com/paper/2401.03880/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 215 references that are in the map.
- First posted on arXiv 8 Jan 2024.

## Builds on (most cited first, 5 of 5)

- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [An Easy-to-use Real-world Multi-objective Optimization Problem Suite](https://mlsanity.com/paper/2009.12867/) (2020)
- [A Survey for Solving Mixed Integer Programming via Machine Learning](https://mlsanity.com/paper/2203.02878/) (2022)
- [Mixed-Integer Optimization with Constraint Learning](https://mlsanity.com/paper/2111.04469/) (2021)
- [Random-Key Cuckoo Search for the Travelling Salesman Problem](https://mlsanity.com/paper/1607.04324/) (2016)

## Built on by (most cited first, 3 of 3)

- [Modeling Hierarchical Spaces: A Review and Unified Framework for Surrogate-Based Architecture Design](https://mlsanity.com/paper/2506.22621/) (2025)
- [Neuromorphic-based metaheuristics: A new generation of low power, low latency and small footprint optimization algorithms](https://mlsanity.com/paper/2505.16362/) (2025)
- [A Firefly Algorithm for Mixed-Variable Optimization Based on Hybrid Distance Modeling](https://mlsanity.com/paper/2603.26792/) (2026)

## Abstract (arXiv)

Many real world optimization problems are formulated as mixed-variable optimization problems (MVOPs) which involve both continuous and discrete variables. MVOPs including dimensional variables are characterized by a variable-size search space. Depending on the values of dimensional variables, the number and type of the variables of the problem can vary dynamically. MVOPs and variable-size MVOPs (VMVOPs) are difficult to solve and raise a number of scientific challenges in the design of metaheuristics. Standard metaheuristics have been first designed to address continuous or discrete optimization problems, and are not able to tackle (V)MVOPs in an efficient way. The development of metaheuristics for solving such problems has attracted the attention of many researchers and is increasingly popular. However, to our knowledge there is no well established taxonomy and comprehensive survey for handling this important family of optimization problems. This paper presents a unified taxonomy for metaheuristic solutions for solving (V)MVOPs in an attempt to provide a common terminology and classification mechanisms. It provides a general mathematical formulation and concepts of (V)MVOPs, and identifies the various solving methodologies than can be applied in metaheuristics. The advantages, the weaknesses and the limitations of the presented methodologies are discussed. The proposed taxonomy also allows to identify some open research issues which needs further in-depth investigations.