Abstract
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.
Highlights
Literature ReviewOptimal spatial search is involved in combinatorial optimization problems such as location allocation. e genetic algorithm (GA), which searches over regions, was first proposed to identify a final, feasible, optimal, or near-optimal solution to a relaxed version of the redundancy allocation problem [18]
Introduction toniche hybrid bat algorithm (NHBA). e NHBA treats each solution as a bat searching in D-dimensional hyperspace
The aim of this study is to propose the niche hybrid bat algorithm (NHBA) to enhance the performance of BA on nonlinear optimization problems, avoid becoming trapped in a locally optimal value with the subsequent premature convergence problem of BA, and solve the complex problems of optimal spatial search more efficiently, precisely, and reliably
Summary
Optimal spatial search is involved in combinatorial optimization problems such as location allocation. e genetic algorithm (GA), which searches over regions, was first proposed to identify a final, feasible, optimal, or near-optimal solution to a relaxed version of the redundancy allocation problem [18]. Generate M bats from the initial population with random positions and velocities, and calculate the fitness value F(Bi) of each bat of the population based on the objective function in step 1. At each iteration of the algorithm, the loudness Ax(t) and Ay(t) and the pulse rates rxi(t) and ryi(t) are updated based on the equations (16)–(18) if the new solutions are improved. It means that these bats are moving toward the optimal solution. (5.6) Update the frequency, velocity, position, loudness, pulse rate, and fitness values of each bat because the values of the parameters change.
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