---
title: "Constraint Satisfaction as Global Optimization"
authors:
  - "Pedro Meseguer"
  - "Javier Larrosa"
doi: ""
url: "https://ijcai.org/proceedings/1995/76"
pdf: "https://ijcai.org/proceedings/1995/0076.pdf"
venue: "Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence"
year: 1995
pages: "579-584"
track: "Constraint Satisfaction"
keywords:
---

# Constraint Satisfaction as Global Optimization

Pedro Meseguer, Javier Larrosa

*Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence*, pages 579-584.

## Abstract

We present a optimization formulation for discrete binary CSP, based on the construction of a continuous function A(P) whose global maximum represents the best possible solution for that problem. By the best possible solution we mean either (i) a solution of the problem, if it is solvable, or (ii) a partial solution violating a minimal number of constraints, if the problem is unsolvable. This approach is based on relaxation labeling techniques used to enforce consistency in image interpretation. We have used a projected gradient ascent algorithm to maximize A(P) on the n-queens problem obtaining good results but with a high computational cost. To elude this problem, we have developed a heuristic for variable and value selection inspired in the direction in which A(P) is maximized. We have tested this heuristic with forward checking on several classes of CSP.