A new approach to solve the of maximum constraint satisfaction problem (original) (raw)
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A New Method to Solve the Constraint Satisfaction Problem Using the Hopfield Neural Network
The constraint satisfaction problem is constituted by several condition formulas, which makes it difficult to be solved. In this paper, using the Hopfield neural network, a new method is pro posed to solve the constraint satisfaction problem by simplifying its condition formula. In this method, all restriction conditions of a constraint satisfaction problem are divided into two restrictions: restriction I and restriction II. In processing step, restriction II is satisfied by setting its value to be 0 and the value of restriction I is always made on the decreasing direction. The optimum so- lution could be obtained when the values of energy, restriction I and restriction II become 0 at the same time. To verify the valid ity of the proposed method, we apply it to two typical constraint satisfaction problems: N-queens problem and four-coloring prob lem. The simulation results show that the optimum solution can be obtained in high speed and high convergence rate. Moreover, compared ...
A wide variety of combinatorial problems can be viewed as Weighted Constraint Satisfaction Problems (WCSPs). All resolution methods have an exponential time complexity for big instances. Moreover, they combine several techniques, use a wide variety of concepts and notations that are difficult to understand and implement. In this paper, we model this problem in terms of an original 0-1 quadratic programming subject to linear constraints. This model is validated by the proposed and demonstrated theorem. View its performance, we use the Hopfield neural network to solve the obtained model basing on original energy function. To validate our model, we solve several instances of benchmarking WCSP. Our approach has the same memory complexity as the HNN and the same time complexity as Euler-Cauchy method. In this regard, our approach recognizes the optimal solution of the said instances.
Maximal constraint satisfaction problems solved by continuous hopfield networks
2013
In this paper, we propose a new approach to solve the maximal constraint satisfaction problems (Max-CSP) using the continuous Hopfield network. This approach is divided into two steps: the first step involves modeling the maximal constraint satisfaction problem as 0-1 quadratic programming subject to linear constraints (QP). The second step concerns applying the continuous Hopfield network (CHN) to solve the QP problem. Therefore, the generalized energy function associated with the CHN and an appropriate parametersetting procedure about Max-CSP problems are given in detail. Finally, the proposed algorithm and some computational experiments solving the Max-CSP are shown. Key-Words: Maximal constraint satisfaction problems, quadratic 0-1 programming, continuous Hopfield network, energy function
Bachelor Thesis - Variants of Simulated Annealing For Solving Constraint Satisfaction Problems
Constraint Satisfaction Problem (CSP) is widely known within the field of optimization and artificial intelligence (AI) research. It is used to represent various optimization problems. In academic circles the concept is often represented by the N-queens problem, graph colouring and so on. Representations in the industry are examples such as scene analysis and interpretation, planning, scheduling and allocation of resources [12]. Various methods have been researched in order to solve these problems in a reliable and time effective manner. In this project the purpose is to solve the CSP with well known metaheuristics such as the popular simulated annealing (SA). In addition, two variants of this method are proposed as well. The first variant is based on introducing the weight mechanism in order to escape from local minima. The other variant is a multilevel SA. The approach is based on reducing the size of the problem using a coarsening scheme until the size of the problem reaches a predefined threshold, thereafter, a random solution is computed at the lowest level and an improvement is carried out on the different levels in reverse order.
In recent decays, soft computing techniques such as genetic algorithm (GA) and artificial neural networks (ANN) are increasingly employed in a diverse area of applications. As optimization tools, genetic algorithm and Hopfield net are successfully applied in constrained optimization problems. In this study suitability of Multi-Layered Perceptron (MLP) for a constrained optimization problem; namely economic dispatch problem, is investigated and a comparison is carried out between GA, Hopfield and MLP. As a case study, the performance of the MLP techniques in economic dispatch problem is compared to the results given in literature. For economic dispatch problem, the MLP approach is compared with an improved Hopfield NN approach (IHN) [1], a fuzzy logic controlled genetic algorithm (FLCGA) [2], an advance engineered-conditioning genetic approach (AECGA) [3] and an advance Hopfield NN approach (AHNN) . Results show that although MLP neural network is inherently not suitable for optimization task when compared to GA and Hopfield, the performance of MLP neural network may be highly improved in order to obtain comparable results to that of GA and Hopfield neural networks.