Complex nonlinear optimization problems are involved in optimal spatial search, such as location allocation problems that occur in multidimensional geographic space. Such search problems are generally difficult to solve by using traditional methods. The bat algorithm (BA) is an effective method for solving optimization problems. However, the solution of the standard BA is easily trapped at one of its local optimum values. The main cause of premature convergence is the loss of diversity in the population. The niche technique is an effective method to maintain the population diversity, to enhance the exploration of the new search domains, and to avoid premature convergence. In this paper, a geographic information system- (GIS-) based niche hybrid bat algorithm (NHBA) is proposed for solving the optimal spatial search. The NHBA is able to avoid the premature convergence and obtain the global optimal values. The GIS technique provides robust support for processing a substantial amount of geographical data. A case in Fangcun District, Guangzhou City, China, is used to test the NHBA. The comparative experiments illustrate that the BA, GA, FA, PSO, and NHBA algorithms outperform the brute-force algorithm in terms of computational efficiency, and the optimal solutions are more easily obtained with NHBA than with BA, GA, FA, and PSO. Moreover, the precision of NHBA is higher and the convergence of NHBA is faster than those of the other algorithms under the same conditions.
Binary Spring Search Algorithm for Solving Various Optimization Problems