TDMBBO: a novel three-dimensional migration model of biogeography-based optimization (case study: facility planning and benchmark problems)

The ability to respond quickly to emergency patients depends on the distribution of ambulance stations. Therefore, the location of these stations is an important issue in urban planning. Health center location-allocation is considered as an NP-hard problem. Due to the long computation time, exact methods will not be effective in solving these problems. On the contrary, many meta-heuristic algorithms have been introduced as promising solutions in various engineering applications. But, it is realized that adaptation of the exploration and exploitation for solving complex optimization problems are challenging tasks. To cope with these challenges, a novel three-dimensional migration model of biogeography-based optimization (TDMBBO) has been introduced to optimize the constrained linear p-median problem. In TDMBBO, nonlinear migration rates based on quadratic, cubic, sinusoidal, and hyperbolic tangent functions have been proposed. In most of the previous migration models, one function for the migration rate has been used. The main disadvantage of these models is that emigration and immigration rates follow a single mathematical function. In the proposed model, for the migration rates of each habitat, a special mathematical model is considered that can apply the appropriate migration rate. The behavior of TDMBBO has been examined on two allocation datasets, IEEE CEC benchmark problems, three random datasets, and two real-world optimization problems. To evaluate the performance of TDMBBO, 31 competitive and state-of-the-art meta-heuristics and five BBO algorithms with different migration models (previous studies) have been used. In allocation datasets, geographic information system has been used to select candidate sites. Parametric and nonparametric tests have also been used to evaluate the performance of algorithms. Overall, TDMBBO yields far better results in many aspects than the other algorithms. The TDMBBO results show a high potential for a location-allocation problems. In IEEE CEC problems, TDMBBO showed rapid convergence compared to other algorithms. The results show the TDMBBO's superiority and this algorithm's capability in solving real-world optimization problems. In the end, some open problems related to TDMBBO are highlighted encouraging future research in this area.