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We describe a new approach to solve the problem to find the maximum independent set in a given Graph, known also as Max-Stable set problem (MSSP). In this paper, we show how Max-Stable problem can be reformulated into a linear problem under quadratic constraints, and then we resolve the QP result by a hybrid approach based Continuous Hopfeild Neural Network (CHN) and Local Search. In a manner that the solution given by the CHN will be the starting point of the local search. The new approach showed a good performance than the original one which executes a suite of CHN runs, at each execution a new leaner constraint is added into the resolved model. To prove the efficiency of our approach, we present some computational experiments of solving random generated problem and typical MSSP instances of real life problem.

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A 74-year-old male presented with bilateral invalidating claudication. A bilateral percutaneous transluminal angioplasty (PTA) with stenting of both superficial femoral arteries was performed but complicated by an urosepsis with Escherichia coli and a septic phlebitis at the site of an intravenous line. The phlebitis was complicated by a local abcedation for which incision and drainage were performed. One month after discharge he was readmitted at our hospital with septic fever and positive hemocultures for Escherichia coli. Positron emission tomography-computed tomographic scan (PET/CT-scan) showed a mycotic aneurysm of the thoracic aorta. Because no cryopreserved donor aorta was available and the aneurysm size rapidly increased, an open in situ repair was performed with a Dacron silver prosthesis soaked in rifampicin. His recovery was further complicated by a perforated toxic megacolon for which a subtotal colectomy was performed. Further recovery was uncomplicated and 10 months after the aortic repair patient is still free from infection.

Our approach CHN-MNC, based Continuous Hopfield neural network and Min-Conflict heuristic), have proved that is more efficient than using CHN alone to solve Constraints Satisfaction Problem (CSP). In This paper we study the performance of CHN-MNC by comparing it robustness with two evolutionary algorithms. We choose a Genetic Algorithm and Swarm optimisation to performers this study. Some numerical experiments are done over a variety of problems to verify the efficiency and fast convergence of our approach. abstract needs to summarize the content of the paper.