# Soft Directional Substitutable based Decompositions for MOVCSP

### Maher Helaoui, Wady Naanaa

#### Abstract

To better model several artificial intelligence and combinatorial problems, classical Constraint Satisfaction Problems (CSP) have been extended by considering soft constraints in addition to crisp ones. This gave rise to a Valued Constraint Satisfaction Problems (VCSP). Several real-world artificial intelligence and combinatorial problems require more than one single objective function. In order to present a more appropriate formulation for these real-world problems, a generalization of the VCSP framework called Multi-Objective Valued Constraint Satisfaction Problems (MOVCSP) has been proposed. This paper addresses combinatorial optimization problems that can be expressed as MOVCSP. Despite the NP-hardness of general MOVCSP, we can present tractable versions by forcing the allowable valuation functions to have specific mathematical properties. This is the case for MOVCSP whose dual is a binary MOVCSP with crisp binary valuation functions only and with a weak form of Neighbourhood Substitutable Valuation Functions called Directional Substitutable Valuation Functions.

Download#### Paper Citation

#### in Harvard Style

Helaoui M. and Naanaa W. (2021). **Soft Directional Substitutable based Decompositions for MOVCSP**.In *Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,* ISBN 978-989-758-485-5, pages 218-225. DOI: 10.5220/0010271802180225

#### in Bibtex Style

@conference{icores21,

author={Maher Helaoui and Wady Naanaa},

title={Soft Directional Substitutable based Decompositions for MOVCSP},

booktitle={Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,},

year={2021},

pages={218-225},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0010271802180225},

isbn={978-989-758-485-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 10th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

TI - Soft Directional Substitutable based Decompositions for MOVCSP

SN - 978-989-758-485-5

AU - Helaoui M.

AU - Naanaa W.

PY - 2021

SP - 218

EP - 225

DO - 10.5220/0010271802180225