Comparative study between a neural network, approach metaheuristic and exact method for solving Traveling salesman Problem

Rbihou, Safae; Haddouch, Khalid

doi:10.1109/icds53782.2021.9626724

Cited by 8 publications

(3 citation statements)

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“…Hopfield Neural Network (HNN) proposed by Hopfield and Tank in 1985 [3,16,36] have attracted the attention of researchers in the areas of optimization problems [18,19], especially NPcomplete problems, which have no satisfactory classical solution. In most HNN applications, it has been shown to have high performance and good results [32]. HNN is defined by a Lyapunov function for the dynamics of the activity.…”

Section: Introductionmentioning

confidence: 99%

“…Solving combinatorial optimization problems (COP) by CHN is efficient compared to other solution methods in terms of solution quality [32]. Solving COP by CHN requires the construction of an appropriate energetic function that implements penalty parameters.…”

Section: Introductionmentioning

confidence: 99%

“…Solving COP by CHN requires the construction of an appropriate energetic function that implements penalty parameters. The choice of the energy function parameters associated with the COP has a direct impact on the quality of the COP solutions by CHN and thus on the feasibility of the solutions [18,32].…”

Section: Introductionmentioning

confidence: 99%

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On Hyperparameters Optimization of the Continuous Hopfield Network via Genetic Algorithm

Safae,

Haddouch,

MOUTAOUAKIL

2023

Preprint

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Recurrent neural networks have proven to be effective in various domains due to their ability to remember key information during solution processes. The continuous Hopfield network is a recurrent neural network that can solve several complicated problems, including combinatorial optimization problems. The user of a continuous Hopfield network for solving combinatorial optimization problems must construct an energy function that combines the energy function and the constraints; this combination requires penalty hyper-parameters that have a direct impact on the quality of the solution and its feasibility. To ensure the convergence of the continuous Hopfield network and thus ensure the feasibility of the solutions to the combinatorial problems, we introduce a linear optimization model given by: the objective function represents the energy function of continuous Hopfield network, which controls the quality of the solution, and the constraints represent conditions on the parameters of the continuous Hopfield network penalty function extracted by the hyperplane procedure, which ensure the feasibility of the solutions. On the well-known NP-complete problem (task assignment problem, traveling salesman problem, weighted constraint satisfaction problem, max-stable problem, graph coloring problem, shortest path problem and portfolio selection problem) the genetic algorithm is used to solve the proposed model. The proposed method has shown its superiority over random methods for choosing continuous Hopfield network hyper-parameters: the solutions produced are all feasible, and the difference in accuracy between our method and random methods is 48.8%.

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