The quadratic assignment problem (QAP) is a well-known challenging combinational optimization problem that has received many researchers’ attention with varied real-world and industrial applications areas. Using the framework of basic artificial bee colony algorithm, frequently used crossover and mutation operators, and combined with an effective local search method, this paper proposes a simple but effective discrete artificial bee colony (DABC) algorithm for solving quadratic assignment problems (QAPs). Typical QAP benchmark instances are selected from QAPLIB in order to conduct the simulation experiment where common performance metrics are used to evaluate the algorithm. The paper also investigates the influence factors of the algorithm’s performance. The results show that the proposed algorithm is a quite effective and practical new approach for handling QAP problems.

An irregularity index $IR\left(\mathsf{\Gamma }\right)$ of a graph $\mathsf{\Gamma }$ is a nonnegative numeric quantity (i.e., $IR\left(\mathsf{\Gamma }\right)\ge 0$) such that $IR\left(\mathsf{\Gamma }\right)=0$ iff $\mathsf{\Gamma }$ is a regular graph. In this paper, we show that $IRC$ closely correlates with the normal boiling point $T_{bp}$ and the standard heat of formation $\Delta H_f^o$ of lower benzenoid hydrocarbons. The correlation models that fit the data efficiently for both $T_{bp}$ and $\Delta H_f^o$ are linear. We develop further mathematical properties of $IRC$ by calculating its exact expressions for the recently introduced transformation graphs as well as certain derived graphs, such as the total graph, semi-total point graph, subdivision graph, semi-total line graph, double, strong double, and extended double cover graphs. Some open problems are proposed for further research on the $IRC$ index of graphs.