Efficiency of Gravitational Search Algorithm on Land Multi-Objectives Allocation in Optimal Selection of Agricultural Land Use in Birjand Basin

Introduction
The background of spatial sustainable land planning is based on the proper position and establishment of the land use activities and their interaction. The suitability should be rooted in three main elements of sustainable development including economic, social, and environmental aspects. To the best of our knowledge, over the past 20 years, significant developments have been invented in the field of artificial intelligence techniques and the tools that can be used to solve many practical geographic problems. The present research aims to introduce a new and effective searching method in order to solve complex, multiple, and non-obvious problems existing in the evolution of land suitability using optimization algorithms.
Materials and methods
The Birjand basin with 3435 km² is located in longitude from 88º, 41´ to 59º,44´ E and lattitude from 32º, 44´ to 33º, 8´ N in the northern part of Bagheran mountains.
Employing GSA
This algorithm is designed to simulate the laws of gravity and Newton's motion in a discrete-time environment in search space. The positive features of GSA, including fast convergence, non-stop in local optimizations and computational volume reduction are compared to Evolutionary Algorithms (EA). By the way, there is no need for memory in comparison with other collective intelligence algorithms as a new research field created for researchers. Therefore, in the present study, given the advantages of GSA, its capability was used in optimizing the multi-objective land suitability problems.
The objective functions of optimization model are including:
1- Maximize the environmental suitability: Compatibility of land for objective use based on physical, environmental and infrastructure factors requires the mapping of effective factors and their integration.
2- Minimize the Land-use conversion: it results in a decrease in social capital costs and increase in economic benefit of society.
3- Maximize the ecological suitability: it means the preservation of natural features and environmental structures by maximizing the green lands. This can be evaluated using the Ecosystem Service Values (ESV).
4- Maximize the stability of landscapes: in concepts of landscape, compressed forms close to the circle have more stability than shredded structures. This goal is achieved by maximizing compression function.
5- Maximizing the compression function: In the present study, in order to create an integrated and compact surface a circle form was used around the image gravity centers. Besides, the noise and single cells were removed using the image-processing algorithm.
Optimization model constraints
Setting constraint functions were applied in optimization model by considering the flood-protected areas, the areas with a slope over than 70%, amount of demand for agricultural areas, placing a user per pixel, and the total area of the region.
Measuring the efficiency of GSA
In order to evaluate the efficiency of GSA, its results were compared with those of MOLA. At the end, three following approaches were used to compare and measure the efficiency of the algorithm. 
First approach: visual evaluation and studying the coherence of allocated spots
Second approach: the use of statistical parameter such as mean and standard deviation of agricultural use suitability.
Third approach: Calculating and analyzing the landscape measures such as a number of plots (NP), plot density (PD), mean shape index (SHAPE_{_}MN), mean plot area (PARA_MN), proximity index (PROX_MN), and cohesion of spot (COHESION) using FRAGSTATS software.
Results and discussion
All objectives and constraints of optimization model were mapped. Therefore, suitability of agriculture use was applied using ANP Fuzzy technique of weight, fuzzier, and constraints (Fig. 1).
 
Fig. 1. Agriculture use suitability using ANP fuzzy and WLC
In Birjand basin, the change was mapped from land covers to agricultural use (Fig. 2).
 
 
Fig. 2. the ease of change from land covers to agricultural use
The results from maximizing the ecological suitability were modeled using the difference between the present and future ESV (Fig. 3).
 
 
Fig. 3. the difference between the present and future ESV
After fitting all considered objectives and constraints by GSA, the allocation of agricultural use was provided (Fig. 4).
 
Fig. 4. Allocated agricultural use through GSA
Relative efficiency of GSA
The results of GSA were compared with those of MOLA. The results of allocating agricultural use by MOLA were presented in Fig. 5.
 
Fig. 5. Allocated agricultural use through MOLA
According to the comparison of statistical parameters, mean agricultural suitability in MOLA had better performance. However, in terms of SD, GSA showed better performance. Besides, analysis of all landscape measures demonstrated the efficiency and relative advantage of GSA compared with MOLA.
Conclusion
In the present research, optimal allocation of agricultural use was carried out using GSA.I In order to measure the efficiency, its results was compared with those of MOLA. The results revealed higher allocated spot for agriculture in MOLA as a disadvantage and higher suitability average as an advantage. On the other hand, since in the GSA, the number of allocated spots was less than MOLA, their suitability was not much higher. The GSA showed the maximum sum of suitability with less spot on the map, which depended on the amount of demand. Therefore, it was a great advantage for GSA. Moreover, analyzing the landscape measures demonstrated the efficiency and priority of GSA compared with MOLA. Finally, it can show that the GSA have higher capacity in solving problems with complex and large space in short time and higher objectives and constraints.