A New Artificial Immune System for Solving the Maximum Satisfiability Problem

Layeb, Abdesslem; Deneche, Abdel Hakim; Meshoul, Souham

doi:10.1007/978-3-642-13025-0_15

Cited by 14 publications

(22 citation statements)

References 11 publications

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“…Given a Boolean formula P in conjunctive normal form (CNF) with n clauses containing variable each and positive integer g where g ≤ n. MAX-kSAT can be defined implicitly as a pair (λ, θ) where λ is the set of all possible solution {1, -1} n and θ is a mapping of λ → T which denotes the score of the assignments (Layeb et al 2010). T is scored based on true clauses (Satisfied clause).…”

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).…”

Section: Introductionmentioning

confidence: 99%

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

Kasihmuddin¹,

Mansor²,

Sathasivam³

2018

JSM

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Section: Restricted Maximum K-satisfiabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Kasihmuddin¹,

Mansor²,

Sathasivam³

2018

JSM

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show abstract

“…Given a Boolean formula P in conjunctive normal form (CNF) with n clauses containing k number of variables per clause and positive integer g where g n ≤ . MAXkSAT can be defined implicitly as a pair of ( ) , λ θ [10] where λ is the set of all possible solution { } 1, 1 n − bit string and θ is a mapping λ ξ → which denotes the score of the assignments. ξ is scored based on correct clauses.…”

Section: B Restricted Maximum K-satisfiabilitymentioning

confidence: 99%

“…The AIS algorithm has been applied to wide range problems such as global optimization [6], pattern recognition [7], multiple sequence alignment [8] and shop scheduling conundrum [9]. The related work by Layeb et al [10] has demonstrated the robustness of the artificial immune system in tackling the general maximum satisfiability problem. Hence, 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.…”

mentioning

confidence: 99%

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

Mansor¹,

Kasihmuddin²,

Sathasivam³

2017

IJIMAI

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-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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“…In our experiment, we have used only the satisfiable benchmarks because we want to evaluate the performances of our approach to find the exact solutions for yes-instances. We have compared our algorithm against three popular stochastic local search methods: Walksat, Novelty [36] and an Iterated Robust Tabu Search IROTS [37]; and two memetic algorithms: Clonsat [38] which is based on Clonal selection algorithm and walksat and QGASAT [32]. The purpose of the last comparison is to show the impact of local search on quantum genetic optimization in order to solve the MAX 3-SAT problem.…”

Section: Implementation and Evaluationmentioning

confidence: 99%

A Hybrid Quantum Genetic Algorithm and Local Search based DPLL for Max 3-SAT Problems

Layeb¹,

Saïdouni²

2014

Appl. Math. Inf. Sci.

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Abstract:In this paper, we present a new framework for combining complete and incomplete methods in order to deal with the Max Sat problem. The objective is to find the best assignment for a set of Boolean variables, which gives the maximum of verified clauses in a Boolean formula. Unfortunately, this problem has been shown to be NP-hard (non-deterministic polynomial-time hard) if the number of variables per clause is greater than 3. The proposed approach is based on quantum inspired genetic principles and the well known exact algorithm DPLL. The underlying idea is to harness the optimization capabilities of quantum genetic algorithm to achieve good quality solutions for Max SAT problem. A new local search based on DPLL algorithm has been embodied in the quantum genetic algorithm leading to an efficient hybrid framework which achieves better balance between diversification and intensification search. The obtained results are very encouraging and show the feasibility and effectiveness of the proposed hybrid approach.

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A New Artificial Immune System for Solving the Maximum Satisfiability Problem

Cited by 14 publications

References 11 publications

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

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

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

A Hybrid Quantum Genetic Algorithm and Local Search based DPLL for Max 3-SAT Problems

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