Spatial area determination problem: Definition and solution method based on Memetic Algorithm

Abstract

Spatial area determination problem is defined herein as an optimization problem in which it is required to determine both the location and shape of a spatial area, given some constraints on the area (e.g., size) while maximizing or minimizing an objective function defined on spatial data (e.g., risk, cost, safety, security, etc.). The spatial area determination problem can be found in various domains such as hydrographic survey planning, conservation planning, military planning, etc., and it recently attracts research attention. Currently, there is no formal definition of the problem and the related solution methods are very limited. In this paper, first, the spatial area determination problem is defined and formulated, and then a solution method based on a Memetic Algorithm is developed to solve the problem. To deal with the constraints of the problem and to enhance the robustness of the traditional Memetic Algorithm, several innovations in the proposed Memetic Algorithm are introduced. Unlike the traditional Memetic Algorithm, the proposed Memetic Algorithm employs three crossover operators, two mutation operators, and a local search operator. In addition, the proposed Memetic Algorithm has a mechanism to automatically restart its search process if it gets stuck in the local optima. Moreover, parameters of the proposed Memetic Algorithm are systematically tuned by the Taguchi experimental design method to maximize its performance. The outperformance of the proposed Memetic Algorithm is validated through 18 test instances, 24 T-tests, and a Friedman test against four popular optimization algorithms, namely Simulated Annealing, Particle Swarm Optimization, Genetic Algorithm, and traditional Memetic Algorithm. The results indicate that, on average, the proposed Memetic Algorithm provided 36.5%, 43.3%, 20.4%, and 22.4% better solution, compared to Simulated Annealing, Particle Swarm Optimization, Genetic Algorithm, and the traditional Memetic Algorithm, respectively.