Abstract
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.
Highlights
The astonishing power of the biological systems has been a core impetus for the researcher to enhance and create a computational paradigm [1]
The k-SAT problem can be defined as a problem to determine the satisfiability of a particular Boolean formula containing k literals per clause [36]. k-SAT is generally expressed in terms of k – conjunctive normal form (CNF) (Conjunctive Normal Form) or Krom formula [37]. k-SAT has been a special NP problem that represents various optimization problems such as circuit and pattern recognition
We only focused on clonal selection that will be implemented in our binary artificial immune system (AIS)
Summary
The astonishing power of the biological systems has been a core impetus for the researcher to enhance and create a computational paradigm [1]. We will improve the work by taking the advantage of clonal selection power in artificial intelligence together with the Hopfield network to solve maximum k-satisfiability problem. The main motivation of this paper is to compare the effectiveness of the searching techniques incorporated with the Hopfield neural network in solving MAX-kSAT problem. The main work of this paper is to propose a hybrid computational model by incorporating artificial immune system (AIS) and Hopfield neural network (HNN-MAXkSATAIS) in solving maximum k-satisfiability (MAX-kSAT) problem. The novelty can be found in the proposed hybrid technique since most of the researchers are only focusing on the standalone Hopfield neural network or metaheuristic to solve any maximum k-satisfiability problem. As the number of clauses increases, finding satisfying assignment will be terribly complex
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