# Nature-Inspired Algorithms for Solving Weighted Constraint Satisfaction Problems

### Mehdi Bidar, Malek Mouhoub

#### 2023

#### Abstract

Several applications such as timetabling, scheduling and resource allocation, can be represented as a Constraint Satisfaction Problem (CSP). Solving a CSP consists in finding a complete assignment of values to variables satisfying all the constraints. In many real-life scenarios (including over-constrained problems), some constraints (called soft constraints) can be violated according to some penalty function. In this regard, the Weighted CSP (WCSP) can be used as an extension of the CSP where each constraint comes with a cost function. Solving a WCSP consists in finding an optimal solution minimizing the total costs related to all constraints. Searching for an optimal solution to a WCSP is usually dealt with classical complete methods like backtracking and bucket elimination techniques. However, since WCSPs are NP-hard, complete methods will require exponential time cost. Therefore, approximation methods such as metaheuristics are appropriate alternatives as they are capable of providing a good compromise between the quality of the solution and the corresponding running time. We study the applicability of several nature-inspired techniques including; Particle Swarm Optimization (PSO), Firefly, Genetic Algorithms (GAs), Artificial Bee Colony (ABC), Mushroom Reproduction Optimization (MRO), Harmony Search (HS) and Focus Group (FG). While these methods do not guarantee the optimality of the solution returned, they are in general successful in returning a good solution in a desirable time cost. This statement has been demonstrated through the experimental results we conducted on randomly generated WCSP instances following the known RB model. The latter has been adopted as it has the ability to produce hard-to-solve random problem instances. The obtained results are promising and show the potential of the considered nature-inspired techniques.

Download#### Paper Citation

#### in Harvard Style

Bidar M. and Mouhoub M. (2023). **Nature-Inspired Algorithms for Solving Weighted Constraint Satisfaction Problems**. In *Proceedings of the 15th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART,* ISBN 978-989-758-623-1, pages 63-72. DOI: 10.5220/0011614900003393

#### in Bibtex Style

@conference{icaart23,

author={Mehdi Bidar and Malek Mouhoub},

title={Nature-Inspired Algorithms for Solving Weighted Constraint Satisfaction Problems},

booktitle={Proceedings of the 15th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART,},

year={2023},

pages={63-72},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0011614900003393},

isbn={978-989-758-623-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 15th International Conference on Agents and Artificial Intelligence - Volume 3: ICAART,

TI - Nature-Inspired Algorithms for Solving Weighted Constraint Satisfaction Problems

SN - 978-989-758-623-1

AU - Bidar M.

AU - Mouhoub M.

PY - 2023

SP - 63

EP - 72

DO - 10.5220/0011614900003393