Binary Bat Algorithm: On The Efficiency of Mapping Functions When Handling Binary Problems Using Continuous-variable-based Metaheuristics

Global optimisation plays a critical role in today's scientific and industrial fields. Optimisation problems are either continuous or combinatorial depending on the nature of the parameters to optimise. In the class of combinatorial problems, we find a sub-category which is the binary optimisation problems. Due to the complex nature of optimisation problems, exhaustive search-based methods are no longer a good choice. So, metaheuristics are more and more being opted in order to solve such problems. Some of them were designed originally to handle binary problems, whereas others need an adaptation to acquire this capacity. One of the principal adaptation schema is the use of a mapping function to decode real-valued solutions into binary-valued ones. The Antenna Positioning Problem (APP) is an NP-hard binary optimisation problem in cellular phone networks (2G, EDGE, GPRS, 3G, 3G(+), LTE, 4G). In this paper, the efficiency of the principal mapping functions existing in the literature is investigated through the proposition of five binary variants of one of the most recent metaheuristic called the Bat Algorithm (BA). The proposed binary variants are evaluated on the APP, and have been tested on a set of well-known benchmarks and given promising results.