Maximum Exact Satisfiability: NP-completeness Proofs and Exact Algorithms

2017

IJIMAI

-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.

Section: B Restricted Maximum K-satisfiabilitymentioning

confidence: 99%

Robust Artificial Immune System in the Hopfield network for Maximum k-Satisfiability

Mansor¹,

Kasihmuddin²,

2017

IJIMAI

“…T is scored based on true clauses (Satisfied clause). Therefore, MAX-kSAT problem consists of defining the best bipolar/ binary assignments to the k variables per clause in P that simultaneously satisfies at least g of the n clauses (Madsen & Rossmanith 2004).…”

Section: Restricted Maximum K-satisfiabilitymentioning

confidence: 99%

“…Basically, MAX-kSAT is the notable counterpart of the Boolean satisfiability (SAT) optimization problem, represented in Conjunctive Normal Form (CNF) form (Layeb et al 2010). In theory, MAX-kSAT problem can be defined as the maximum number of satisfied clauses achieved by any optimum interpretation (Borchers & Furman 1998;Madsen & Rossmanith 2004). Berg and Järvisalo (2015) proposed the implementation of MAX-kSAT incorporated with the data mining and constrained clustering.…”

Section: Introductionmentioning

confidence: 99%

Discrete Hopfield Neural Network in Restricted Maximum k-Satisfiability Logic Programming

Kasihmuddin¹,

Mansor²,

2018

JSM

“…It was proven that MAX-kSAT is NP-complete problem for any 3 k ≥ . There are numerous classifications of the MAX-kSAT namely, weighted MAXSAT [42] and Partial MAXSAT [43]. However, restricted MAX-kSAT constrained optimization problem that can be included in maximization problem [39].…”

Section: B Restricted Maximum K-satisfiabilitymentioning

confidence: 99%

Genetic Algorithm for Restricted Maximum k-Satisfiability in the Hopfield Network

Kasihmuddin¹,

Mansor²,

2016

IJIMAI

-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.