meta-heuristic algorithms

Efficiency of Gravitational Search Algorithm on Land Multi-Objectives Allocation in optimal selection of Agricultural Land use in Birjand Basin The background of spatial sustainable land planning is based on the position and establishment suitability of the land use activities and the interaction of judgments should be rooted in the three main elements of sustainable development, namely economic, social, and environmental. To the best of our knowledge, over the past 20 years, many significant the developments have been invented in the field of artificial intelligence techniques and 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. The Birjand basin with 3435km2 area located in longitude from 88º, 41´ to 59º,44´ E and attitude 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 compared to Evolutionary Algorithms (EA) and no need for memory in comparison with other collective intelligence algorithms has created a new research field for researchers. Therefore, in the present study, by considering the advantages of GSA, its capability in optimizing the multi-objective land suitability problems was used.
The objective functions of optimization model
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 as the preservation of natural features and environmental structures by maximizing the green lands, which 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, 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 of shape index (SHAPE_MN), mean of plot area (PARA_MN), proximity index (PROX_MN) and cohesion of spot (COHESION) using FRAGSTATS software. All objectives and constraints of optimization model were mapped. Therefore, amount of agriculture use suitability 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 ease of change from land covers to agricultural use was mapped (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 of agricultural suitability in MOLA had better performance, but in terms of SD, GSA showed better performance. Besides, analyzing all landscape measures demonstrated the efficiency and relative advantage of GSA compared to MOLA.
Discussion and In the present research, optimal allocation of agricultural use was carried out using GSA. Besides, in order to measure the efficiency, its results were compared with those of MOLA. The results showed higher allocated spot for agriculture in MOLA as a disadvantage and higher suitability average was an advantage. On the other hand, since in the GSA, the number of allocated spots was less than MOLA, their suitability was not that much high. 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 to MOLA. Finally, it can result that the GSA have higher capacity in solving problems with complex and large space in short time and higher objectives and constraints.  

Bank branches location-allocation problem belongs to NP-Hard problems which can be possibly solved only in exponential time by the increase in the number of banks and the large number of customers; especially when the location model includes various datasets, several objectives and constraints. As a consequent, we need to use heuristic methods to solve this type of problems. Also, since majority of data and analyses applied in the location-allocation problems are spatial; GIScience’s abilities should be employed beside optimization methods.
Nowadays, to perform particular financial tasks bank customers often need to be present at their bank. For the sake of its customers, a bank should increase its branches in the city to attract more customers in the race with competing banks. However, establishing new branches is too expensive and banks prefer to carry out an optimal location finding procedure. Such procedures should consider many criteria and objectives including spatial data of customers, new and existing bank branches as well as level of attraction of banks –in the real-life. Customers often select a bank that is closer to them, has better services or financial records and also consider other human or physical factors. Hence, planning to increase the number of customers for a new branch of a bank considering spatial criteria and various other objectives appear necessary.

This paper determines the location of bank branches. Finding an optimum location of branches depends on many factors and these problems are known as NP-hard problems. Despite being approximate methods, meta-heuristic algorithms seem suitable tools for solving NP-hard problems. In this paper, Grey Wolf Optimizer (GWO), Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Cultural Algorithms (CA) and Invasive Weed Optimization (IWO) are applied for finding the best location of bank branches. From marketing point of view, the aim is to attract more customers while the number of attracted persons to a new branch should be acceptable. The new methods have capability to find the optimum location of new branches. The location of a new branch should be as far away as possible from branches of the same bank. The other condition is that the total number of customers for the new branch should not be less than a specified number, while the new branch should not attract customers of old branches of the same bank more than a threshold. To fulfill this propose a part of the Tabriz city was selected for implementation.
The assumptions for the defined problem can be expressed as the following statements: a)We consider four different banks (Melli, Mellat, Sepah and Meher) in our study area.
b)Population density (of people over 15 years of age) is available at the building block level.
c)Banks have infinite capacity for accepting customers.
d)Each customer refers to only one bank.
e)New bank branches should have maximum distance from branches of the same bank, so that; it attracts minimum number of customers from branches of the same bank.
According to the above-mentioned assumptions, mathematical model of the function for optimization is as follows: Maximizes the distance between newly established branch and other existing branches of the same bank.
Constraint1: Not less likely to attract new customers to the bank established a certain extent.
Constraint2: Other branches of the same bank customers not less so after the creation of a new bank branch.
To assess the accuracy of the algorithms in the problem, suggests, in this study, repeatability and convergence of the algorithm is used. The results from the convergence of the algorithms used in this study, 100 iteration, is provided. For comparison, the cost for the logarithmic axis is provided. The axis can be said that IWA algorithm has better convergence than the other four algorithms. The convergence of the algorithm optimization methods, PSO and GW are next in priority. The answer and the cost of repeated 5 times 50 algorithm implementation of this algorithm is compared. It also answers the PSO algorithm and GW are next in priority. It should be noted that the number of adjustable parameters optimization algorithm optimization method IWA far more than the PSO and GW.
Finally, to evaluate quality and accuracy of the algorithms, several iterations are performed. The results of statistical and final tests indicate that the accuracy and convergence speed of Invasive Weed Optimization are more than other Algorithms in finding optimal location of bank branches.