-Artificial Immune System (AIS) algorithm is a novel and vibrant computational paradigm, enthused by the biological immune system. Over the last few years, the artificial immune system has been sprouting to solve numerous computational and combinatorial optimization problems. In this paper, we introduce the restricted MAX-kSAT as a constraint optimization problem that can be solved by a robust computational technique. Hence, we will implement the artificial immune system algorithm incorporated with the Hopfield neural network to solve the restricted MAX-kSAT problem. The proposed paradigm will be compared with the traditional method, Brute force search algorithm integrated with Hopfield neural network. The results demonstrate that the artificial immune system integrated with Hopfield network outperforms the conventional Hopfield network in solving restricted MAX-kSAT. All in all, the result has provided a concrete evidence of the effectiveness of our proposed paradigm to be applied in other constraint optimization problem. The work presented here has many profound implications for future studies to counter the variety of satisfiability problem.

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-The restricted Maximum k-Satisfiability MAXkSAT is an enhanced Boolean satisfiability counterpart that has attracted numerous amount of research. Genetic algorithm has been the prominent optimization heuristic algorithm to solve constraint optimization problem. The core motivation of this paper is to introduce Hopfield network incorporated with genetic algorithm in solving MAX-kSAT problem. Genetic algorithm will be integrated with Hopfield network as a single network. The proposed method will be compared with the conventional Hopfield network. The results demonstrate that Hopfield network with genetic algorithm outperforms conventional Hopfield networks. Furthermore, the outcome had provided a solid evidence of the robustness of our proposed algorithms to be used in other satisfiability problem.