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

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

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

The restricted Maximum k-Satisfiability MAX- kSAT 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

Evolutionary techniques in a constraint satisfaction problem: Puzzle Eternity II

Proceeding of: IEEE Congress on Evolutionary Computation (CEC 2009), May 18-21 (Monday - Thursday), 2009, Trondheim, Norway.This work evaluates three evolutionary algorithms in a constraint satisfaction problem. Specifically, the problem is the Eternity II, a edge-matching puzzle with 256 unique square tiles that have to be placed on a square board of 16 times 16 cells. The aim is not to completely solve the problem but satisfy as many constraints as possible. The three evolutionary algorithms are: genetic algorithm, an own implementation of a technique based on immune system concepts and a multiobjective evolutionary algorithm developed from the genetic algorithm. In addition to comparing the results obtained by applying these evolutionary algorithms, they also will be compared with an exhaustive search algorithm (backtracking) and random search. For the evolutionary algorithms two different fitness functions will be used, the first one as the score of the puzzle and the second one as a combination of the multiobjective algorithm objectives. We also used two ways to create the initial population, one randomly and the other with some domain information.This work was supported in part by the University Carlos III of Madrid under grant PIF UC3M01-0809 and by the Ministry of Science and Innovation under project TRA2007- 67374-C02-02

Quantum Algorithm for Variant Maximum Satisfiability

In this paper, we proposed a novel quantum algorithm for the maximum satisfiability problem. Satisfiability (SAT) is to find the set of assignment values of input variables for the given Boolean function that evaluates this function as TRUE or prove that such satisfying values do not exist. For a POS SAT problem, we proposed a novel quantum algorithm for the maximum satisfiability (MAX-SAT), which returns the maximum number of OR terms that are satisfied for the SAT-unsatisfiable function, providing us with information on how far the given Boolean function is from the SAT satisfaction. We used Grover’s algorithm with a new block called quantum counter in the oracle circuit. The proposed circuit can be adapted for various forms of satisfiability expressions and several satisfiability-like problems. Using the quantum counter and mirrors for SAT terms reduces the need for ancilla qubits and realizes a large Toffoli gate that is then not needed. Our circuit reduces the number of ancilla qubits for the terms T of the Boolean function from T of ancilla qubits to ≈⌈log2⁡T⌉+1. We analyzed and compared the quantum cost of the traditional oracle design with our design which gives a low quantum cost

Enhanced Hopfield Neural Networks With Artificial Immune System Algorithm For Satisfiability Logic Programming

The emergence of 3-Satisfiability (3-SAT) problem has produced a prolific number of works devoted to the field of logic and data mining. In this study, a new hybrid method in doing logic programming by incorporating 3-SAT logical rules as a computational tool will be presented. Hence, a robust intelligence system that integrates the Hopfield neural network and metaheuristic paradigm is constructed to extract the data set hidden knowledge in the form of 3-Satisfiability logical rule. A hybrid network called HNN-3SATAIS is proposed by assimilating the Hopfield neural network with the enhanced artificial immune system (AIS) algorithm as a training tool in doing 3-Satisfiability logic programming

Satisfiability Logic Analysis Via Radial Basis Function Neural Network with Artificial Bee Colony Algorithm

Radial Basis Function Neural Network (RBFNN) is a variant of artificial neural network (ANN) paradigm, utilized in a plethora of fields of studies such as engineering, technology and science. 2 Satisfiability (2SAT) programming has been coined as a prominent logical rule that defines the identity of RBFNN. In this research, a swarm-based searching algorithm namely, the Artificial Bee Colony (ABC) will be introduced to facilitate the training of RBFNN. Worth mentioning that ABC is a new population-based metaheuristics algorithm inspired by the intelligent comportment of the honey bee hives. The optimization pattern in ABC was found fruitful in RBFNN since ABC reduces the complexity of the RBFNN in optimizing important parameters. The effectiveness of ABC in RBFNN has been examined in terms of various performance evaluations. Therefore, the simulation has proved that the ABC complied efficiently in tandem with the Radial Basis Neural Network with 2SAT according to various evaluations such as the Root Mean Square Error (RMSE), Sum of Squares Error (SSE), Mean Absolute Percentage Error (MAPE), and CPU Time. Overall, the experimental results have demonstrated the capability of ABC in enhancing the learning phase of RBFNN-2SAT as compared to the Genetic Algorithm (GA), Differential Evolution (DE) algorithm and Particle Swarm Optimization (PSO) algorithm