# Discrete Mother Tree Optimization and Swarm Intelligence for Constraint Satisfaction Problems

### Wael Korani, Malek Mouhoub

#### 2022

#### Abstract

The Constraint Satisfaction Problem (CSP) is a powerful framework for a wide variety of combinatorial problems. The CSP is known to be NP-complete, and many algorithms have been developed to tackle this challenge in practice. These algorithms include the backtracking technique, improved with constraint propagation and variable ordering heuristics. Despite its success, backtracking still suffers from its exponential time cost, especially for large to solve problems. Metaheuristics, including local search and nature-inspired methods, can be an alternative that trades running time for the quality of the solution. Indeed, these techniques do not guarantee to return a complete solution, nor can they prove the inconsistency of the problem. They are, however time-efficient, thanks to their polynomial running time. In particular, nature-inspired techniques can be very effective if designed with a good exploitation/exploration balance during the search. To solve CSPs, we propose two discrete variants of two known nature-inspired algorithms. The first one is an adaptation of the Mother Tree Optimization (MTO). In contrast, the second is an extension of the Particle Swarm Optimization (PSO) with a new operator that we propose. Both variants rely on a heuristic that gathers information about constraints violations during the search. The latter will then be used to update candidate solutions, following a given topology for MTO, and position/velocity equations for PSO. To assess the performance of both methods, we conducted several comparative experiments, considering other known systematic methods and metaheuristics. The results demonstrate the effectiveness of both methods.

Download#### Paper Citation

#### in Harvard Style

Korani W. and Mouhoub M. (2022). **Discrete Mother Tree Optimization and Swarm Intelligence for Constraint Satisfaction Problems**. In *Proceedings of the 14th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART,* ISBN 978-989-758-547-0, pages 234-241. DOI: 10.5220/0010803100003116

#### in Bibtex Style

@conference{icaart22,

author={Wael Korani and Malek Mouhoub},

title={Discrete Mother Tree Optimization and Swarm Intelligence for Constraint Satisfaction Problems},

booktitle={Proceedings of the 14th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART,},

year={2022},

pages={234-241},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010803100003116},

isbn={978-989-758-547-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 14th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART,

TI - Discrete Mother Tree Optimization and Swarm Intelligence for Constraint Satisfaction Problems

SN - 978-989-758-547-0

AU - Korani W.

AU - Mouhoub M.

PY - 2022

SP - 234

EP - 241

DO - 10.5220/0010803100003116