Journal of Theoretical and Applied Information Technology 20 th October 2013. Vol. 56 No.2 © 2005 - 2013 JATIT & LLS. All rights reserved . ISSN: 1992-8645 www.jatit.org E-ISSN: 1817-3195 362 CONTINUOUS HOPFIELD NETWORK AND QUADRATIC PROGRAMMING FOR SOLVING THE BINARY CONSTRAINT SATISFACTION PROBLEMS 1 KHALID HADDOUCH, 1* MOHAMED ETTAOUIL and 2 CHAKIR LOQMAN 1 UFR: Scientific Computing and Computer sciences, Engineering sciences, Faculty of Science and Technology, University Sidi Mohamed Ben Abdellah Box 2202, Fez, Morocco 2 Department of Computer Engineering, Moulay Ismail University, High School of technology, B. P. 3103, 50000, Toulal, Meknes, Morocco E-mail : 1 haddouchk@yahoo.fr , 1* mohamedettaouil@yahoo.fr , 2 chakirfst@yahoo.fr ABSTRACT Many important computational problems may be formulated as constraint satisfaction problems (CSP). In this paper, we propose a new approach to solve the binary CSP problems using the continuous Hopfield networks (CHN). This approach is divided into three steps: the first concerns reducing the size of the CSP problems using arc consistency technique AC3. The second step involves modeling the filtered constraint satisfaction problems as 0-1 quadratic programming subject to linear constraints. The last step concerns applying the continuous Hopfield networks to solve the obtained 0-1 optimization model. Therefore, the mapping procedure and an appropriate parameter setting procedure about CSP problems are given in detail. Finally, some computational experiments solving the CSP problems are shown. Keywords: Constraint Satisfaction Problems, Filtering Algorithms, Quadratic 0-1 Programming, Continuous Hopfield Networks, Energy Function. 1. INTRODUCTION A large number of problems in artificial intelligence and other areas of computer science can be viewed as special cases of the constraint satisfaction problems. Some examples include machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, aircraft conflict, etc. A constraint satisfaction problem is defined by a set of variables, a finite and discrete domain for each variable and a set of constraints. Each constraint restricts the combination of values that a set of variables may take simultaneously. Solving the CSP problem requires assigning a value for each variable from each domain in such a way that all constraints are satisfied. The task is to find one solution or all solutions. However, the CSP problems are NP-complete problems requiring a combination of heuristics and combinatorial search methods in order to be solved in a reasonable time[12]. A number of different approaches have been developed for solving the constraint satisfaction problems [10], [18], [19], [21]. Some of them use backtracking to directly search for possible solutions [5], others use consistency techniques to simplify the original problems [3], [4], [24], and some are a combination of these two techniques [2], [5], [13]. Moreover, we proposed different approaches to solve the constraint satisfaction problems. The first one consists of modeling a constraint satisfaction problem as 0-1 quadratic knapsack problem subject to quadratic constraint [6], [7]. The second one is a new model of the binary CSP problem as 0-1 quadratic programming which consists in minimizing the quadratic function subject to linear constraints[8]. The later model will be used in order to determine a generalized energy function for the binary constraint satisfaction problem. This step is the most important one for solving any binary CSP problem using continuous Hopfield networks. This neural network was introduced by Hopfield and Tank [13], [14] and it has been extensively studied, developed and has found many applications in many areas, such as pattern recognition, model identification, and optimization [11], [28]. Moreover, this neural network is applied to solve many problems such as traveling salesman problems [27], graph coloring problems [17], allocation problems [16], etc. It is important to note