Oppositional biogeography-based optimization

We propose a novel variation to biogeography-based optimization (BBO), which is an evolutionary algorithm (EA) developed for global optimization. The new algorithm employs opposition-based learning (OBL) alongside BBO's migration rates to create oppositional BBO (OBBO). Additionally, a new opposition method named quasi-reflection is introduced. Quasi-reflection is based on opposite numbers theory and we mathematically prove that it has the highest expected probability of being closer to the problem solution among all OBL methods. The oppositional algorithm is further revised by the addition of dynamic domain scaling and weighted reflection. Simulations have been performed to validate the performance of quasi-opposition as well as a mathematical analysis for a single-dimensional problem. Empirical results demonstrate that with the assistance of quasi-reflection, OBBO significantly outperforms BBO in terms of success rate and the number of fitness function evaluations required to find an optimal solution.