On the efficiency of the binary flower pollination algorithm: Application on the antenna positioning problem

The Flower Pollination Algorithm (FPA) is a recently proposed continuous metaheuristic that was claimed to give promising results. However, its potential in binary problems has been vaguely investigated. The use of mapping techniques to adapt metaheuristics to handle binary optimisation problems is a widely-used approach, but these techniques are still fuzzy and misunderstood, since no work thoroughly studied them for a given problem or algorithm. This paper conducts a consistent and systematic study to assess the efficiency of the FPA and the common mapping techniques. This is done through proposing four Binary variants of the FPA (BFPA) that have been got by applying the principal mapping techniques existing in the literature. As benchmark problem; an NP-hard binary one in advanced cellular networks, the Antenna Positioning Problem (APP), is used. In order to assess the scalability, efficiency and robustness of the proposed BFPAs, the experiments have been carried out on realistic, synthetic and random data with different dimensions, and several statistical tests have been carried. Two of the top-ranked algorithms designed to solve the APP; the Population-Based Incremental Learning (PBIL) and the Differential Evolution algorithm (DE), are taken as a comparison basis. The results showed that the normalisation and angle modulation are the best mapping techniques. The experiments also showed that the BFPAs have some shortcomings but, they could outperform the PBIL in 4 out of 13 instances and the DE in 6 out of 13 instances and no statistical difference was found in the remaining instances. Besides, the BFPAs outperformed or gave competitive technical results compared to the PBIL and DE in all problem instances.