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.
In this study, a hybrid approach that employs Hopfield neural network and a genetic algorithm in
doing k-SAT problems was proposed. The Hopfield neural network was used to minimise logical
inconsistency in interpreting logic clauses or programme. Hybrid optimisation made use of the global
convergence advantage of the genetic algorithm to deal with learning complexity in the Hopfield
network. The simulation incorporated with genetic algorithm and exhaustive search method with different
k-Satisfiability (k-SAT) problems, namely, the Horn-Satisfiability (HORN-SAT), 2-Satisfiability (2-SAT)
and 3-Satisfiability (3-SAT) will be developed by using Microsoft Visual C++ 2010 Express Software.
The performance of both searching techniques was evaluated based on global minima ratio, hamming
distance and computation time. Simulated results suggested that the genetic algorithm outperformed
exhaustive search in doing k-SAT logic programming in the Hopfield network.
Swarm intelligence is a research area that models the population of swarm that is able to self-organise effectively. Honey bees that gather around their hive with a distinctive behaviour is another example of swarm intelligence. In fact, the artificial bee colony (ABC) algorithm is a swarm-based meta-heuristic algorithm introduced by Karaboga in order to optimise numerical problems. 2SAT can be treated as a constrained optimisation problem which represents any problem by using clauses containing 2 literals each. Most of the current researchers represent their problem by using 2SAT. Meanwhile, the Hopfield neural network incorporated with the ABC has been utilised to perform randomised 2SAT. Hence, the aim of this study is to investigate the performance of the solutions produced by HNN2SAT-ABC and compared it with the traditional HNN2SAT-ES. The comparison of both algorithms has been examined by using Microsoft Visual Studio 2013 C++ Express Software. The detailed comparison on the performance of the ABC and ES in performing 2SAT is discussed based on global minima ratio, hamming distance, CPU time and fitness landscape. The results obtained from the computer simulation depict the beneficial features of ABC compared to ES. Moreover, the findings have led to a significant implication on the choice of determining an alternative method to perform 2SAT.
Since its debut in 2009, League of Legends (LoL) has been on a rise in becoming an extremely favoured multiplayer online battle arena (MOBA) game. This paper presented a logic mining technique to model the results (Win / Lose) of the LoL games played in 3 regions, namely South Korea, North America and Europe. In this research, a method named k satisfiability based reverse analysis method (kSATRA) was brought forward to obtain the logical relationship among the gameplays and objectives in the game. The logical rule obtained from the LoL games was used to categorize the results of future games. kSATRA made use of the advantages of Hopfield Neural Network and k Satisfiability representation. The data set used in this study included the data of all 10 teams from each region, which composed of all games from Spring Season 2018. The effectiveness of kSATRA in obtaining logical rule in LoL games was tested based on root mean square error (RMSE), mean absolute error (MAE), mean absolute percentage error (MAPE) and CPU time. Results acquired from the computer simulation showed the robustness of kSATRA in exhibiting the performance of the LoL teams.
Clonal selection algorithm and discrete Hopfield neural network are extensively employed for solving higher-order optimization problems ranging from the constraint satisfaction problem to complex pattern recognition. The modified clonal selection algorithm is a comprehensive and less iterative immune-inspired searching algorithm, utilized to search for the correct combination of instances for Very large-scale integrated (VLSI) circuit structure. In this research, the VLSI circuit framework consists of Boolean 3-Satisfiability instances with the different complexities and number of transistors are considered. Hence, a hybrid modified clonal selection algorithm with discrete Hopfield neural network is well developed to optimize the configuration of VLSI circuits with different number of electronic components such as transistors as the instances. Therefore, the performance of the developed hybrid model was assessed experimentally with the standard models, HNNVLSI-3SATES and HNNVLSI-3SATGA in term of circuit accuracy, sensitivity, robustness and runtime to complete the verification process. The results have demonstrated the developed model, HNNVLSI-3SATCSA produced a minimum error (consistently approaching 0), better accuracy (more than 80%) and faster computational time (less than 125 seconds) against changes in the complexity in term of the number of transistors. Furthermore, the developed hybrid model is able to minimize the computational burden and configurational noises for the variant of VLSI circuits.
Maximum k Satisfiability logical rule (MAX-kSAT) is a language that bridges real life application to neural network optimization. MAX-kSAT is an interesting paradigm because the outcome of this logical rule is always negative/false. Hopfield Neural Network (HNN) is a type of neural network that finds the solution based on energy minimization. Interesting intelligent behavior has been observed when the logical rule is embedded in HNN. Increasing the storage capacity during the learning phase of HNN has been a challenging problem for most neural network researchers. Development of Metaheuristics algorithms has been crucial in optimizing the learning phase of Neural Network. The most celebrated metaheuristics model is Genetic Algorithm (GA). GA consists of several important operators that emphasize on solution improvement. Although GA has been reported to optimize logic programming in HNN, the learning complexity increases as the number of clauses increases. GA is more likely to be trapped in suboptimal fitness as the number of clauses increases. In this paper, metaheuristic algorithm namely Artificial Bee Colony (ABC) were proposed in learning MAX-kSAT programming. ABC is swarm-based metaheuristics that capitalized the capability of Employed Bee, Onlooker Bee, and Scout Bee. To this end, all the learning models were tested in a new restricted learning environment. Experimental results obtained from the computer simulation demonstrate the effectiveness of ABC in modelling MAX-kSAT.
Artificial neural networks (ANNs) are actively utilized by researchers due to their extensive capability during the training process of the networks. The intricate training stages of many ANNs provide a powerful mechanism in solving various optimization or classification tasks. The integration of an ANN with a robust training algorithm is the supreme model to outperform the existing framework. Therefore, this work presented the inclusion of three satisfiability Boolean logic in the Hopfield neural network (HNN) with a sturdy evolutionary algorithm inspired by the Imperialist Competitive Algorithm (ICA). In general, ICA stands out from other metaheuristics as it is inspired by the policy of extending the power and rule of a government/country beyond its own borders. Existing models that incorporate standalone HNN are projected as non-versatile frameworks as it fundamentally employs random search in its training stage. The main purpose of this work was to conduct a comprehensive comparison of the proposed model by using two real data sets with an elementary HNN with exhaustive search (ES) versus a HNN with a standard evolutionary algorithm, namely- the genetic algorithm (GA). The performance evaluation of the proposed model was analyzed by computing plausible errors, such as root mean square error (RMSE), mean absolute error (MAE), global minima ratio (Rm), computational time (CT) and accuracy (Q). The computational simulations were carried out by operating the different numbers of neurons in order to validate the efficiency of the proposed model in the training stage. Based on the simulations,
the proposed model was found to execute the best performance in terms of attaining small
errors and efficient computational time compared to other existing models.
Analyzing commodity prices contributes greatly to traders, economists and analysts in
ascertaining the most feasible investment strategies. Limited knowledge about the price
trend of the commodities indeed will affect the economy because commodities like palm
oil and gold contribute a huge source of income to Malaysia. Therefore, it is important to
know the optimal price trend of the commodities before making any investments. Hence,
this paper presents a logic mining technique to study the price trend of palm oil with other
commodities. This technique employs 2-Satisfiability based Reverse Analysis Method
(2-SATRA) consolidated with 2-Satisfiability logic in Discrete Hopfield Neural Network
(DHNN2-SAT). All attributes in the data set are represented as a neuron in DHNN which
will be programmed based on a 2-SAT logical rule. By utilizing 2-SATRA in DHNN2-SAT,
the induced logic is generated from the commodity price data set that explains the trend
of commodities price. Following that, the performance evaluation metric; error analysis
and accuracy will be calculated based on the induced logic. In this case, the experimental
result has shown that the best-induced logic identifies which trend will lead to an increase
in the palm oil price with the highest accuracy rate.