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.