### Abstract

The Particle Swarm Optimization (PSO) algorithm is a flexible heuristic optimizer that can be used for solving cardinality constrained binary optimization problems. In such problems, only K elements of the N-dimensional solution vector can be non-zero. The typical solution is to use a mapping function to enforce the cardinality constraint on the trial PSO solution. In this paper, we show that when K is small compared to N, the use of the mapped solution in the velocity vector tends to lead to early stagnation. As a solution, we recommend to use the untransformed solution as a direction in the velocity vector. We use numerical experiments to document the gains in performance when K is small compared to N.

Original language | English |
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Journal | Optimization Letters |

DOIs | |

Publication status | Accepted/In press - 2019 |

### Fingerprint

### Keywords

- Binary particle swarm optimization
- Cardinality mapping
- Portfolio optimization

### Cite this

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**The effect of velocity sparsity on the performance of cardinality constrained particle swarm optimization.** / Boudt, Kris; Wan, Chunlin.

Research output: Contribution to Journal › Article › Academic › peer-review

TY - JOUR

T1 - The effect of velocity sparsity on the performance of cardinality constrained particle swarm optimization

AU - Boudt, Kris

AU - Wan, Chunlin

PY - 2019

Y1 - 2019

N2 - The Particle Swarm Optimization (PSO) algorithm is a flexible heuristic optimizer that can be used for solving cardinality constrained binary optimization problems. In such problems, only K elements of the N-dimensional solution vector can be non-zero. The typical solution is to use a mapping function to enforce the cardinality constraint on the trial PSO solution. In this paper, we show that when K is small compared to N, the use of the mapped solution in the velocity vector tends to lead to early stagnation. As a solution, we recommend to use the untransformed solution as a direction in the velocity vector. We use numerical experiments to document the gains in performance when K is small compared to N.

AB - The Particle Swarm Optimization (PSO) algorithm is a flexible heuristic optimizer that can be used for solving cardinality constrained binary optimization problems. In such problems, only K elements of the N-dimensional solution vector can be non-zero. The typical solution is to use a mapping function to enforce the cardinality constraint on the trial PSO solution. In this paper, we show that when K is small compared to N, the use of the mapped solution in the velocity vector tends to lead to early stagnation. As a solution, we recommend to use the untransformed solution as a direction in the velocity vector. We use numerical experiments to document the gains in performance when K is small compared to N.

KW - Binary particle swarm optimization

KW - Cardinality mapping

KW - Portfolio optimization

UR - http://www.scopus.com/inward/record.url?scp=85061637885&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061637885&partnerID=8YFLogxK

U2 - 10.1007/s11590-019-01398-w

DO - 10.1007/s11590-019-01398-w

M3 - Article

JO - Optimization Letters

JF - Optimization Letters

SN - 1862-4472

ER -