A Novel Multi-Objective Hybrid Election Algorithm for Higher-Order Random Satisfiability in Discrete Hopfield Neural Network
Hybridized algorithms are commonly employed to improve the performance of any existing method. However, an optimal learning algorithm composed of evolutionary and swarm intelligence can radically improve the quality of the final neuron states and has not received creative attention yet. Considering...
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| Format: | Article |
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/12/1963 |
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| author | Syed Anayet Karim Mohd Shareduwan Mohd Kasihmuddin Saratha Sathasivam Mohd. Asyraf Mansor Siti Zulaikha Mohd Jamaludin Md Rabiol Amin |
| author_facet | Syed Anayet Karim Mohd Shareduwan Mohd Kasihmuddin Saratha Sathasivam Mohd. Asyraf Mansor Siti Zulaikha Mohd Jamaludin Md Rabiol Amin |
| author_sort | Syed Anayet Karim |
| collection | DOAJ |
| description | Hybridized algorithms are commonly employed to improve the performance of any existing method. However, an optimal learning algorithm composed of evolutionary and swarm intelligence can radically improve the quality of the final neuron states and has not received creative attention yet. Considering this issue, this paper presents a novel metaheuristics algorithm combined with several objectives—introduced as the Hybrid Election Algorithm (HEA)—with great results in solving optimization and combinatorial problems over a binary search space. The core and underpinning ideas of this proposed HEA are inspired by socio-political phenomena, consisting of creative and powerful mechanisms to achieve the optimal result. A non-systematic logical structure can find a better phenomenon in the study of logic programming. In this regard, a non-systematic structure known as Random <i>k</i> Satisfiability (RAN<i>k</i>SAT) with higher-order is hosted here to overcome the interpretability and dissimilarity compared to a systematic, logical structure in a Discrete Hopfield Neural Network (DHNN). The novelty of this study is to introduce a new multi-objective Hybrid Election Algorithm that achieves the highest fitness value and can boost the storage capacity of DHNN along with a diversified logical structure embedded with RAN<i>k</i>SAT representation. To attain such goals, the proposed algorithm tested four different types of algorithms, such as evolutionary types (Genetic Algorithm (GA)), swarm intelligence types (Artificial Bee Colony algorithm), population-based (traditional Election Algorithm (EA)) and the Exhaustive Search (ES) model. To check the performance of the proposed HEA model, several performance metrics, such as training–testing, energy, similarity analysis and statistical analysis, such as the Friedman test with convergence analysis, have been examined and analyzed. Based on the experimental and statistical results, the proposed HEA model outperformed all the mentioned four models in this research. |
| first_indexed | 2024-03-09T23:09:36Z |
| format | Article |
| id | doaj.art-342f7f4a607f422e8c921fde0e53b088 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T23:09:36Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-342f7f4a607f422e8c921fde0e53b0882023-11-23T17:47:26ZengMDPI AGMathematics2227-73902022-06-011012196310.3390/math10121963A Novel Multi-Objective Hybrid Election Algorithm for Higher-Order Random Satisfiability in Discrete Hopfield Neural NetworkSyed Anayet Karim0Mohd Shareduwan Mohd Kasihmuddin1Saratha Sathasivam2Mohd. Asyraf Mansor3Siti Zulaikha Mohd Jamaludin4Md Rabiol Amin5School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, MalaysiaSchool of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, MalaysiaSchool of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, MalaysiaSchool of Distance Education, Universiti Sains Malaysia, Penang 11800, MalaysiaSchool of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, MalaysiaDepartment of Computer Science and Engineering, CCN University of Science and Technology, Cumilla 3503, BangladeshHybridized algorithms are commonly employed to improve the performance of any existing method. However, an optimal learning algorithm composed of evolutionary and swarm intelligence can radically improve the quality of the final neuron states and has not received creative attention yet. Considering this issue, this paper presents a novel metaheuristics algorithm combined with several objectives—introduced as the Hybrid Election Algorithm (HEA)—with great results in solving optimization and combinatorial problems over a binary search space. The core and underpinning ideas of this proposed HEA are inspired by socio-political phenomena, consisting of creative and powerful mechanisms to achieve the optimal result. A non-systematic logical structure can find a better phenomenon in the study of logic programming. In this regard, a non-systematic structure known as Random <i>k</i> Satisfiability (RAN<i>k</i>SAT) with higher-order is hosted here to overcome the interpretability and dissimilarity compared to a systematic, logical structure in a Discrete Hopfield Neural Network (DHNN). The novelty of this study is to introduce a new multi-objective Hybrid Election Algorithm that achieves the highest fitness value and can boost the storage capacity of DHNN along with a diversified logical structure embedded with RAN<i>k</i>SAT representation. To attain such goals, the proposed algorithm tested four different types of algorithms, such as evolutionary types (Genetic Algorithm (GA)), swarm intelligence types (Artificial Bee Colony algorithm), population-based (traditional Election Algorithm (EA)) and the Exhaustive Search (ES) model. To check the performance of the proposed HEA model, several performance metrics, such as training–testing, energy, similarity analysis and statistical analysis, such as the Friedman test with convergence analysis, have been examined and analyzed. Based on the experimental and statistical results, the proposed HEA model outperformed all the mentioned four models in this research.https://www.mdpi.com/2227-7390/10/12/1963hybridized algorithmevolutionary algorithmhybrid election algorithmrandom <i>k</i> satisfiabilityelection algorithmDiscrete Hopfield Neural Network |
| spellingShingle | Syed Anayet Karim Mohd Shareduwan Mohd Kasihmuddin Saratha Sathasivam Mohd. Asyraf Mansor Siti Zulaikha Mohd Jamaludin Md Rabiol Amin A Novel Multi-Objective Hybrid Election Algorithm for Higher-Order Random Satisfiability in Discrete Hopfield Neural Network Mathematics hybridized algorithm evolutionary algorithm hybrid election algorithm random <i>k</i> satisfiability election algorithm Discrete Hopfield Neural Network |
| title | A Novel Multi-Objective Hybrid Election Algorithm for Higher-Order Random Satisfiability in Discrete Hopfield Neural Network |
| title_full | A Novel Multi-Objective Hybrid Election Algorithm for Higher-Order Random Satisfiability in Discrete Hopfield Neural Network |
| title_fullStr | A Novel Multi-Objective Hybrid Election Algorithm for Higher-Order Random Satisfiability in Discrete Hopfield Neural Network |
| title_full_unstemmed | A Novel Multi-Objective Hybrid Election Algorithm for Higher-Order Random Satisfiability in Discrete Hopfield Neural Network |
| title_short | A Novel Multi-Objective Hybrid Election Algorithm for Higher-Order Random Satisfiability in Discrete Hopfield Neural Network |
| title_sort | novel multi objective hybrid election algorithm for higher order random satisfiability in discrete hopfield neural network |
| topic | hybridized algorithm evolutionary algorithm hybrid election algorithm random <i>k</i> satisfiability election algorithm Discrete Hopfield Neural Network |
| url | https://www.mdpi.com/2227-7390/10/12/1963 |
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