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

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

Discrete hopfield neural network in restricted maximum k-satisfiability logic programming

Maximum k-Satisfiability (MAX-kSAT) consists of the most consistent interpretation that generate the maximum number of satisfied clauses. MAX-kSAT is an important logic representation in logic programming since not all combinatorial problem is satisfiable in nature. This paper presents Hopfield Neural Network based on MAX-kSAT logical rule. Learning of Hopfield Neural Network will be integrated with Wan Abdullah method and Sathasivam relaxation method to obtain the correct final state of the neurons. The computer simulation shows that MAX-kSAT can be embedded optimally in Hopfield Neural Network

Maximum 2-satisfiability in radial basis function neural network

Maximum k-Satisfiability (MAX-kSAT) is the logic to determine the maximum number of satisfied clauses. Correctly, this logic plays a prominent role in numerous applications as a combinatorial optimization logic. MAX2SAT is a case of MAX-kSAT and is written in Conjunctive Normal Form (CNF) with two variables in each clause. This paper presents a new paradigm in using MAX2SAT by implementing in Radial Basis Function Neural Network (RBFNN). Hence, we restrict the analysis to MAX2SAT clauses. We utilize Dev C++ as the platform of training and testing our proposed algorithm. In this study, the effectiveness of RBFNN-MAX2SAT can be estimated by evaluating the proposed models with testing data sets. The results obtained are analysed using the ratio of satisfied clause (RSC), the root means square error (RMSE), and CPU time. The simulated results suggest that the proposed algorithm is effective in doing MAX2SAT logic programming by analysing the performance by obtaining lower Root Mean Square Error, high ratio of satisfied clauses and lesser CPU time

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

Major 3 Satisfiability logic in Discrete Hopfield Neural Network integrated with multi-objective Election Algorithm

Discrete Hopfield Neural Network is widely used in solving various optimization problems and logic mining. Boolean algebras are used to govern the Discrete Hopfield Neural Network to produce final neuron states that possess a global minimum energy solution. Non-systematic satisfiability logic is popular due to the flexibility that it provides to the logical structure compared to systematic satisfiability. Hence, this study proposed a non-systematic majority logic named Major 3 Satisfiability logic that will be embedded in the Discrete Hopfield Neural Network. The model will be integrated with an evolutionary algorithm which is the multi-objective Election Algorithm in the training phase to increase the optimality of the learning process of the model. Higher content addressable memory is proposed rather than one to extend the measure of this work capability. The model will be compared with different order logical combinations $k = \mathrm{3, 2}$, $k = \mathrm{3, 2}, 1$ and $k = \mathrm{3, 1}$. The performance of those logical combinations will be measured by Mean Absolute Error, Global Minimum Energy, Total Neuron Variation, Jaccard Similarity Index and Gower and Legendre Similarity Index. The results show that $k = \mathrm{3, 2}$ has the best overall performance due to its advantage of having the highest chances for the clauses to be satisfied and the absence of the first-order logic. Since it is also a non-systematic logical structure, it gains the highest diversity value during the learning phase

K satisfiability programming by using estimation of distribution algorithm in Hopfield neural network

Hopfield Neural Network (HNN) is a sort of neural network that is strongly dependent to energy minimization of solution. Although HNN managed to solve various optimization problem, the output of HNN suffered from a lack of interpretability and variation. This has severely limited the practical usability of HNN in doing logic programming. Inspired by random neuron perturbation, Estimation of Distribution Algorithm (EDA) has been proposed to explore various optimal neuron state. EDAs employs a probabilistic model to sample the neuron state in order to move toward the various optimal location of global minimum energy. In this paper, a new Mutation Hopfield Neural Network (MHNN) will be proposed to do k Satisfiability programming. Based on the experimental result, the proposed MHNN has outperformed conventional HNN in various performance metric

Novel logic mining incorporating log linear approach

Mining the best logical rule from the data is a challenging task because not all attribute of the dataset will contribute towards the optimal logical representation. Even if the correct attributes were selected, wrong logical connection in the logical formula will lead to suboptimal logical representation of the datasets. These two factors must be carefully considered in creating more robust logic mining method. In this paper, we proposed a novel logic mining by introducing log-linear analysis to select the best attributes which formulate the logical rule that will be embedded into the energy-based ANN named Discrete Hopfield Neural Network (DHNN). In log-linear phase, the test of the association for each attributes will be carried out where the attributes that have a significant level less than α will be selected before proceeding to the logic mining phase. By using DHNN, the selected attributes via log-linear will be learned and retrieved the optimal induced logic with classification ability. The proposed hybrid model has been tested using various real-life datasets and was compared with several established logic mining methods. Based on the findings, several winning points for the proposed model where the proposed model dominates 3 metrics out of 5 in the average rank. The metrics that achieve the highest average rank are Accuracy (1.800), Precision (3.500), and Mathews Correlation Coefficient (2.700). In accordance with the experimental result obtained, the proposed model has achieved optimal performance with a statistically significant p-value. Hence, these findings lead to an advancement of the existing logic mining via the statistical method

Energy based logic mining analysis with hopfield neural network for recruitment evaluation

An effective recruitment evaluation plays an important role in the success of companies, industries and institutions. In order to obtain insight on the relationship between factors contributing to systematic recruitment, the artificial neural network and logic mining approach can be adopted as a data extraction model. In this work, an energy based k satisfiability reverse analysis incorporating a Hopfield neural network is proposed to extract the relationship between the factors in an electronic (E) recruitment data set. The attributes of E recruitment data set are represented in the form of k satisfiability logical representation. We proposed the logical representation to 2-satisfiability and 3-satisfiability representation, which are regarded as a systematic logical representation. The E recruitment data set is obtained from an insurance agency in Malaysia, with the aim of extracting the relationship of dominant attributes that contribute to positive recruitment among the potential candidates. Thus, our approach is evaluated according to correctness, robustness and accuracy of the induced logic obtained, corresponding to the E recruitment data. According to the experimental simulations with different number of neurons, the findings indicated the effectiveness and robustness of energy based k satisfiability reverse analysis with Hopfield neural network in extracting the dominant attributes toward positive recruitment in the insurance agency in Malaysia

Logic Mining Approach: Shoppers’ Purchasing Data Extraction via Evolutionary Algorithm

Online shopping is a multi-billion-dollar industry worldwide. However, several challenges related to purchase intention can impact the sales of e-commerce. For example, e-commerce platforms are unable to identify which factors contribute to the high sales of a product. Besides, online sellers have difficulty finding products that align with customers’ preferences. Therefore, this work will utilize an artificial neural network to provide knowledge extraction for the online shopping industry or e-commerce platforms that might improve their sales and services. There are limited attempts to propose knowledge extraction with neural network models in the online shopping field, especially research revolving around online shoppers’ purchasing intentions. In this study, 2-satisfiability logic was used to represent the shopping attribute and a special recurrent artificial neural network named Hopfield neural network was employed. In reducing the learning complexity, a genetic algorithm was implemented to optimize the logical rule throughout the learning phase in performing a 2-satisfiability-based reverse analysis method, implemented during the learning phase as this method was compared. The performance of the genetic algorithm with 2-satisfiability-based reverse analysis was measured according to the selected performance evaluation metrics. The simulation suggested that the proposed model outperformed the existing model in doing logic mining for the online shoppers dataset