The fourth industrial revolution (IR 4.0) supports new solid waste management and effective routing system for collection and transport of solid wastes, especially in achieving Penang 2030 vision to become a pollution free smart city. This study will enhance Seberang Perai Municipal Council (MBSP) solid waste routing system in Prai industrial area by implementing Dijkstra and Travelling Salesman Problem (TSP) algorithms using Geographic Information System version 10.1. The route optimization study involved 24 companies in Phase I, Phase II, and Phase IV of Prai industrial area. The authority is currently using only one route to transfer the waste-to-waste transfer station. The Dijkstra algorithm can optimize alternative route 1 distance by 19.74% whereby alternative route 2 ended up with extra distance by 3.73% compared to existing single route used by MBSP. The forward Dijkstra algorithm involves single direction route with cleaning depot (source) as starting point and waste transfer station (destination) as ending point. TSP algorithm is having advantage with return direction route. The alternative route 1 evaluated through TSP algorithm gave shorter distance by 6.61% compared to existing route. Alternative route 1 evaluated through Dijkstra algorithm is potential to save fuel cost by 19.75%. Existing route carries 9.2% per year of transportation carbon emission level. The alternative route 1 assessed through Dijkstra and TSP algorithms reported lower carbon emission level at 7.4% per year and 8.6% per year, respectively. Findings of this study can help in improving MBSP’s routing system and realize Penang 2030 vision.

Recently, a variety of non-systematic satisfiability studies on Discrete Hopfield Neural Networks have been introduced to overcome a lack of interpretation. Although a flexible structure was established to assist in the generation of a wide range of spatial solutions that converge on global minima, the fundamental problem is that the existing logic completely ignores the probability dataset’s distribution and features, as well as the literal status distribution. Thus, this study considers a new type of non-systematic logic termed S-type Random k Satisfiability, which employs a creative layer of a Discrete Hopfield Neural Network, and which plays a significant role in the identification of the prevailing attribute likelihood of a binomial distribution dataset. The goal of the probability logic phase is to establish the logical structure and assign negative literals based on two given statistical parameters. The performance of the proposed logic structure was investigated using the comparison of a proposed metric to current state-of-the-art logical rules; consequently, was found that the models have a high value in two parameters that efficiently introduce a logical structure in the probability logic phase. Additionally, by implementing a Discrete Hopfield Neural Network, it has been observed that the cost function experiences a reduction. A new form of synaptic weight assessment via statistical methods was applied to investigate the effect of the two proposed parameters in the logic structure. Overall, the investigation demonstrated that controlling the two proposed parameters has a good effect on synaptic weight management and the generation of global minima solutions.

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Choosing the best attribute from a dataset is a crucial step in effective logic mining since it has the greatest impact on improving the performance of the induced logic. This can be achieved by removing any irrelevant attributes that could become a logical rule. Numerous strategies are available in the literature to address this issue. However, these approaches only consider low-order logical rules, which limit the logical connection in the clause. Even though some methods produce excellent performance metrics, incorporating optimal higher-order logical rules into logic mining is challenging due to the large number of attributes involved. Furthermore, suboptimal logical rules are trained on an ineffective discrete Hopfield neural network, which leads to suboptimal induced logic. In this paper, we propose higher-order logic mining incorporating a log-linear analysis during the pre-processing phase, the multi-unit 3-satisfiability-based reverse analysis with a log-linear approach. The proposed logic mining also integrates a multi-unit discrete Hopfield neural network to ensure that each 3-satisfiability logic is learned separately. In this context, our proposed logic mining employs three unique optimization layers to improve the final induced logic. Extensive experiments are conducted on 15 real-life datasets from various fields of study. The experimental results demonstrated that our proposed logic mining method outperforms state-of-the-art methods in terms of widely used performance metrics.