Multi-objective optimization of spatial sampling using a new hybrid AMOSA_NSGA-II algorithm

While many studies of spatial sampling have focused on optimizing only one objective, in many real-life problems, more than one objective is required to be simultaneously optimized. Hence, using multi-objective optimization techniques in spatial sampling is considerably increasing. In this paper, two bi-objective optimization problems of soil sampling are investigated. The variance of the sample mean and the mean total error are the first objective function of the first and second spatial optimization problems, respectively. Furthermore, in both Problems, the total distance travelled between sample points is considered as the second objective function. To deal with these spatial optimization problems, a new hybrid algorithm of the archived multi-objective simulated annealing algorithm and the non-dominated sorting genetic algorithm-II is developed and compared with well-known four multi-objective optimization algorithms, including the non-dominated sorting genetic algorithm-II, the multi-objective particle swarm optimization algorithm, the multi-objective grey wolf optimizer algorithm, and the archived multi-objective simulated annealing algorithm. Indeed, the performance of the algorithms is assessed and compared using four performance metrics, i.e. spacing metric, mean ideal distance, diversification metric, and spread of non-dominance solution. The parameters of the algorithms are set by the Taguchi method. Moreover, the performance of the algorithms is ranked using a hybrid multi-attribute decision-making process called the AHP-TOPSIS method. The results show that the proposed hybrid algorithm provides a Pareto frontier that dominates the frontiers resulting from other algorithms and has satisfactory diversity.