# Population Economic Transfer Function Model Based on Genetic Tabu Search Algorithm

Authors: Qian Wang
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

Aiming at the problem that the evaluation effect of the traditional analysis model of population economic transfer is not good, a population economic transfer function model based on the genetic tabu search algorithm is proposed. Firstly, the defects of the genetic algorithm are analyzed, and the tabu search algorithm is integrated into the genetic tabu search algorithm to obtain the genetic tabu search algorithm, which avoids the problems of premature convergence and low search efficiency. Secondly, the population migration algorithm is designed. On this basis, the design process of the population economic transfer function model is determined. Finally, the effectiveness of the model is verified by comparative experiments. The experimental results show that when the population area is 50 km2 and 500 km2, the evaluation accuracy of the proposed method is 99% and 97%, respectively, which can avoid falling into a local maximum advantage to a certain extent.


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## Body

## 1. Introduction

Generally speaking, population movement refers to all movements of the population in space or geographical position, including population movement and migration. Population migration is the movement of people in the living environment, and it is a kind of population behavior with some spontaneity and relatively poor migration regularity [1–3]. Population migration is the movement of people across specific geographical boundaries to change their permanent residence, which is usually a population behavior with the nature of selection. What are the main drivers of migration? Some migrate because they are pushed out of their places of origin, while others are pulled elsewhere. Evil or repressive laws and heavy tax, bad weather, alien social environment, even forced, all of which have been caused and still cause migration flows, the migration flow without a can and by the majority of your hopes on the amount they are better in material migration caused by the desire to flow compared [4, 5]. Ravenstein’s view shows that material and economic factors are the main factors that often play a role in population migration, the population center of gravity shifts along with the economy [6, 7]. In other words, people tend to move to more favorable areas with high economic development levels and more job opportunities [8, 9]. For example, Wang Guixin studied the effects of regional economic development levels and differences on interprovincial population migration and its characteristics in the second half of the 1980s. This study uses per capita national income as the index of regional economic development level. According to the per capita national income of each province in 1990, the economic development level of each province is divided into the following six levels: less than 900 yuan, 900∼1000 yuan, 1000∼1200 yuan, 1200∼1500 yuan, 1500∼2000 yuan, and more than 2000 yuan. One of the conclusions of the study is that nearly 70% of the net emigration population is distributed in the lower income areas of 900∼1000 yuan, while more than 94% of the net emigration population is distributed in the higher income areas of more than 1500 yuan. This shows that the population migration since the reform of China’s economic system has obvious basic characteristics of the flow of people to the rich.Research shows that relatives and friends (family ties, human relations), media advertising, the labor market, and farmers’ market are the main sources of information [10–12]. These media collect information about the economic situation of preferential areas, such as income and employment opportunities, and disseminate it to potential migrants. Under the guidance and pull of information, population migration occurs [13–15]. If the relative surplus population continues to increase, population pressure will increase and population density will increase too. Areas with high economic development levels will also see the spread of population outward, usually to undeveloped areas with low population density or to areas where it is relatively easy to make a living [16–18].In recent 30 years, a series of new global optimization search algorithms have appeared. These algorithms are mainly established by simulating the evolution process of a population with some optimization characteristics in the natural domain [19–22]. The typical ones are the genetic algorithm, simulated annealing algorithm, and ant colony algorithm. A genetic algorithm is used to simulate the population genetic evolutionary process of organisms’ chromosomes. A simulated annealing algorithm simulates the system in the process of solid annealing atomic groups toward the ground state of the lowest energy process; ant colony algorithm is simulated by the individual information exchange and cooperation between finders of nests to the food source of the shortest path. These algorithms successfully solve many complex optimization problems [23, 24]. The construction method of the algorithm shows that the simulation of the population evolution process with some optimization characteristics is an effective way to establish the global optimization search algorithm [25, 26]. The existing research work pays more attention to the selection of simulation prototypes in the field of nature and pays little attention to the research and excavation in other fields [27–29]. In view of this situation, this paper has carried out some work in this field, focusing on finding the group evolution process with certain optimization characteristics in the research objects of social fields or social science, and then establishing the global optimization search algorithm that simulates the operation mechanism of this process [30–33]. After a period of exploration, the process of population economic migration has been found in the research objects of demography and its related branches, and a more in-depth study has been conducted on it. This article and subsequent articles will introduce the preliminary research results in this field.Against the above background, this paper proposes a population economic transfer function model based on the genetic tabu search algorithm. The tabu search algorithm is integrated into the genetic tabu search algorithm to avoid the problems of premature convergence and low search efficiency, and the genetic tabu search algorithm is obtained. Based on this, the population migration algorithm is designed and the design process of the population economic transfer function model is determined.


## 2. Design of Genetic Tabu Search Algorithm Flow

In order to solve the problems of easy premature convergence and low search efficiency in the later stages of the evolution of traditional genetic algorithms, a tabu search algorithm was introduced to obtain a hybrid genetic tabu search algorithm, and the individuals generated by the tabu search algorithm were optimized and mutation operations to generate a new generation of populations to improve the computational performance of the algorithm.


### 2.1. Genetic Algorithm Defects

A large number of previous research documents have proved that genetic algorithm is an excellent optimization algorithm, but also pointed out that the traditional genetic algorithm has the following two serious defects:(1)
Premature convergence is easy. The traditional genetic algorithm is prone to premature convergence for two reasons: first, in the process of optimization, an evolutionary group can produce a few individual fitness function value that is much better than other individuals, after a few iterations, the offspring of the previous outstanding individuals will occupy almost the whole of the group, and therefore, evolution will convergence in advance; Secondly, in the process of traditional genetic algorithm optimization, the competition between individuals only exists in the offspring, while there is no competition between the offspring and the parent, which will lead to the loss of excellent individuals in the parent generation.(2)
Search efficiency is low in the late evolutionary period. When the traditional genetic algorithm evolves to the vicinity of the optimal solution or has been iterated many times, it is easy to skip the optimal solution because of the large coverage of its crossover operation, resulting in a sharp decrease in the search efficiency in the latter period. And the crossover operation also has a fatal weakness, that is, it is easy to destroy the already searched optimal solution, thus affecting the later search efficiency.


### 2.2. Tabu Search Algorithm Fusion

The tabu search algorithm is an extension of the traditional local search algorithm, which is a simulation of the human logical thinking process. Compared with traditional local search algorithms, its unique feature is the introduction of a memory function. The tabu algorithm uses a tabu table to record the traversed local optimal solutions, and in the next search, it uses the information in the tabu table to avoid or selectively deal with these solutions, so as to avoid falling into local optimal and ensure that different effective ways are searched. From the above analysis, it can be concluded that the tabu search algorithm can effectively avoid the already searched local optimal solution, thus improving the search efficiency, avoiding the algorithm oscillating near the local optimal solution and better converging to the global optimal solution. The general tabu search process is relatively simple, and its basic process is shown in Figure1.Figure 1
Basic flow of tabu search algorithm.According to Figure1, the following solving steps can be obtained:Step 1: We generate an initial feasible solution, set it as the current solution and the best solution so far, set the parameters of the tabu search algorithm, and empty the tabu table;Step 2: We judge whether the termination condition is met. If so, the algorithm will stop and output the current solution and the optimal solution. If not, go to Step 3.Step 3: The neighborhood is defined according to a neighborhood structure definition method, and the neighborhood structure is used to generate the neighborhood solution set of the current solution, and the objective function is used to evaluate the fitness of each solution set.Step 4: We analyze the neighborhood solution set. If there is a solution set that is better than the best solution so far, amnesty is given to the best solution, and the best solution is set as the new best solution so far; if there is no, the non-tabu best solution in the current solution set is set as the current solution.Step 5: We update the current taboos table and go to Step 2.


### 2.3. Process Design of Hybrid Genetic Tabu Search Algorithm

The genetic algorithm (GA) and the tabu search algorithm (TSA) are two widely used meta-heuristic algorithms for solving population economic transfer problems. They are based on natural heuristics and have complementary characteristics in performance. A genetic algorithm is a kind of group parallel search. Its global search ability is good, but the local search ability is poor and prone to precocity. The tabu search algorithm is a serial search, which moves from one solution to another in each iteration. Its local search ability is strong, but the global search ability is poor, and it is easy to fall into the local optimal solution. Therefore, by organically combining the advantages of genetic algorithm and tabu search algorithm, a hybrid genetic tabu search algorithm with strong global search ability and strong local search ability can be obtained.Because the genetic algorithm only needs to adjust several parameters of the population rather than for a single solution, this paper adopts a hybrid algorithm that integrates the genetic algorithm into the tabu search algorithm. Figure2 shows the mixed structure diagram of the genetic algorithm and the tabu search method in the genetic tabu search algorithm. Specifically, the multiple new individuals generated by crossover and mutation operations in the genetic algorithm are regarded as the neighborhood VXn of the current solution of Xn in the tabu search method, and then each individual in the neighborhood VXn is traversed. The genetic tabu search algorithm in this paper can select multiple solutions from the neighborhood VXn and then use the tabu table of the genetic tabu search algorithm to screen these solutions. These operations reflect the collective parallel search performance of the genetic algorithm.Figure 2
Hybrid genetic tabu search algorithm.Solution flow of hybrid genetic tabu search algorithm is as follows:Step 1: Initialization generatesN feasible solutions, where N is the population size;Step 2: We evaluate the fitness value of each individual in the populationStep 3:We judge whether the population meets the termination condition. If so, the optimal solution will be output. Otherwise go to Step 4; Step 4: select a selection strategy to select the next generation population;Step 4: We perform crossover operation according to crossover probabilityPc to generate two new individuals;Step 5: We perform mutation operation according to mutation probabilityPm to generate two new individuals;Step 6: We use tabu search algorithm to optimize the generated new individuals;Step 8:
We generate a new generation population and return to step 3.The specific flow chart is shown in Figure3.Figure 3
Flow chart of mixed genetic tabu search algorithm.As shown in Figure3, the hybrid genetic tabu search algorithm achieves the optimization of individuals generated by the tabu search algorithm and generates a new generation of the population through selection strategy, crossover operation, and mutation operation.


## 2.1. Genetic Algorithm Defects

A large number of previous research documents have proved that genetic algorithm is an excellent optimization algorithm, but also pointed out that the traditional genetic algorithm has the following two serious defects:(1)
Premature convergence is easy. The traditional genetic algorithm is prone to premature convergence for two reasons: first, in the process of optimization, an evolutionary group can produce a few individual fitness function value that is much better than other individuals, after a few iterations, the offspring of the previous outstanding individuals will occupy almost the whole of the group, and therefore, evolution will convergence in advance; Secondly, in the process of traditional genetic algorithm optimization, the competition between individuals only exists in the offspring, while there is no competition between the offspring and the parent, which will lead to the loss of excellent individuals in the parent generation.(2)
Search efficiency is low in the late evolutionary period. When the traditional genetic algorithm evolves to the vicinity of the optimal solution or has been iterated many times, it is easy to skip the optimal solution because of the large coverage of its crossover operation, resulting in a sharp decrease in the search efficiency in the latter period. And the crossover operation also has a fatal weakness, that is, it is easy to destroy the already searched optimal solution, thus affecting the later search efficiency.


## 2.2. Tabu Search Algorithm Fusion

The tabu search algorithm is an extension of the traditional local search algorithm, which is a simulation of the human logical thinking process. Compared with traditional local search algorithms, its unique feature is the introduction of a memory function. The tabu algorithm uses a tabu table to record the traversed local optimal solutions, and in the next search, it uses the information in the tabu table to avoid or selectively deal with these solutions, so as to avoid falling into local optimal and ensure that different effective ways are searched. From the above analysis, it can be concluded that the tabu search algorithm can effectively avoid the already searched local optimal solution, thus improving the search efficiency, avoiding the algorithm oscillating near the local optimal solution and better converging to the global optimal solution. The general tabu search process is relatively simple, and its basic process is shown in Figure1.Figure 1
Basic flow of tabu search algorithm.According to Figure1, the following solving steps can be obtained:Step 1: We generate an initial feasible solution, set it as the current solution and the best solution so far, set the parameters of the tabu search algorithm, and empty the tabu table;Step 2: We judge whether the termination condition is met. If so, the algorithm will stop and output the current solution and the optimal solution. If not, go to Step 3.Step 3: The neighborhood is defined according to a neighborhood structure definition method, and the neighborhood structure is used to generate the neighborhood solution set of the current solution, and the objective function is used to evaluate the fitness of each solution set.Step 4: We analyze the neighborhood solution set. If there is a solution set that is better than the best solution so far, amnesty is given to the best solution, and the best solution is set as the new best solution so far; if there is no, the non-tabu best solution in the current solution set is set as the current solution.Step 5: We update the current taboos table and go to Step 2.


## 2.3. Process Design of Hybrid Genetic Tabu Search Algorithm

The genetic algorithm (GA) and the tabu search algorithm (TSA) are two widely used meta-heuristic algorithms for solving population economic transfer problems. They are based on natural heuristics and have complementary characteristics in performance. A genetic algorithm is a kind of group parallel search. Its global search ability is good, but the local search ability is poor and prone to precocity. The tabu search algorithm is a serial search, which moves from one solution to another in each iteration. Its local search ability is strong, but the global search ability is poor, and it is easy to fall into the local optimal solution. Therefore, by organically combining the advantages of genetic algorithm and tabu search algorithm, a hybrid genetic tabu search algorithm with strong global search ability and strong local search ability can be obtained.Because the genetic algorithm only needs to adjust several parameters of the population rather than for a single solution, this paper adopts a hybrid algorithm that integrates the genetic algorithm into the tabu search algorithm. Figure2 shows the mixed structure diagram of the genetic algorithm and the tabu search method in the genetic tabu search algorithm. Specifically, the multiple new individuals generated by crossover and mutation operations in the genetic algorithm are regarded as the neighborhood VXn of the current solution of Xn in the tabu search method, and then each individual in the neighborhood VXn is traversed. The genetic tabu search algorithm in this paper can select multiple solutions from the neighborhood VXn and then use the tabu table of the genetic tabu search algorithm to screen these solutions. These operations reflect the collective parallel search performance of the genetic algorithm.Figure 2
Hybrid genetic tabu search algorithm.Solution flow of hybrid genetic tabu search algorithm is as follows:Step 1: Initialization generatesN feasible solutions, where N is the population size;Step 2: We evaluate the fitness value of each individual in the populationStep 3:We judge whether the population meets the termination condition. If so, the optimal solution will be output. Otherwise go to Step 4; Step 4: select a selection strategy to select the next generation population;Step 4: We perform crossover operation according to crossover probabilityPc to generate two new individuals;Step 5: We perform mutation operation according to mutation probabilityPm to generate two new individuals;Step 6: We use tabu search algorithm to optimize the generated new individuals;Step 8:
We generate a new generation population and return to step 3.The specific flow chart is shown in Figure3.Figure 3
Flow chart of mixed genetic tabu search algorithm.As shown in Figure3, the hybrid genetic tabu search algorithm achieves the optimization of individuals generated by the tabu search algorithm and generates a new generation of the population through selection strategy, crossover operation, and mutation operation.


## 3. Population Economic Transfer Function Model Based on Genetic Tabu Search

### 3.1. Population Migration Algorithm Construction

In the following part, combining with the function global optimization problem, we study how to establish a new global optimization search algorithm, namely PMA, by simulating the population economic transfer mechanism. The current study is aimed at forms such as(1)maxfx,s.t.x∈S.For unconstrained function optimization problems, the problem (1), f:S⟶R1 is a real valued mapping:(2)x∈Rn,S=∏i=1nai,bi,where S is the search space and ai<bi, and it is assumed that problem (1) always has a solution, that is, the global optimal value f∗ exists and the global optimal set M is nonempty.Function optimization is to find the optimal solution in the search space, and population economic transfer is to find preferential areas in the regional space. There are similarities between the two. Table1 shows the analogy relationship between some elements of the two.Table 1
Comparison of function optimization factors and population economic transfer.
Function optimization elementsFactors of population economic transferxPopulation locationfxEconomic factors such as income or attractiveness of population locationSMobile surface space of populationThe bestThe highest income point or the most attractive pointOptimal valueThe highest income or attractionAscent/climbMove to preferential areasBreak away from local optimumPopulation pressure leads to relocation from preferential areasIt should be noted that the economic transfer of population is a complex process, which does not completely correspond to the global optimization of function. Therefore, the principle of establishing a global optimization search algorithm by simulating the population economic transfer mechanism is to extract the useful elements in the process of population economic transfer, rather than copy them completely. The simulation implementation of each link is discussed below. Population flow is carried out in each residential area, which originally refers to the space specified on the Earth’s surface. When it is extended to the space specified in PMA, the population flow is simulated in each residential area. If it is divided directly by administrative region or longitude and latitude line, then with the increase in the dimension of the optimization problem, the problem of dimension disaster will appear.In the search spaceS, N points x1,x2,…,xN are randomly generated. For each point xi and the predetermined area:(3)δixi,δi∈Rn;δji>0;i=1,2,…,N;j=1,2,…,n.∏j=1nxji−δji,xji+δji.Considering the poor regularity of the population flow, the population flow is treated as random. In addition, in order to make the search opportunities in the region equal, the population flow is further treated as a uniform random change. In the simulation, several points can be randomly generated in each region, and then these points can be randomly changed. A simpler equivalent method can also be used to deal with the population flow. That is to say, multiple random changes of a point are equivalent to one random change of multiple points. In this way, only one random change point in each region can make a predetermined number of uniform random changes.Preferential areas attract people from other areas. For simplicity, the process of population economic transfer is simplified, that is, all people and their economy migrate to preferential areas. In the simulation,N points are randomly generated in the preferential area to replace the points in other areas. The preferential area is redrawn with the point where the current maximum fx value is located as the center. The maximum fx value is used to measure the attraction of the preferential zone, and each fx value is used to represent the population income of each point. After the population moves into the preferential zone, there are n points in the preferential zone. Every time the N points complete a random change, it is necessary to find out the point with the highest income, and redefine the zone with it as the center. This is to simulate the shift of the population center of gravity with the shift of the economic center of gravity. When the preferential area shrinks to a certain extent, that is, when the population pressure increases to a certain extent, the population will spread outward, and the population will move out of the preferential area and spread to the undeveloped area with low population density. In the search space, N points are randomly generated and the area is redivided. Finally, the simulation of preferential area information media is given. The media such as relatives and friends, media advertising, and the labor market are abstracted as the best recording unit. In the algorithm, the best recording unit records the current maximum value of fx and the corresponding point x, which provides the basis for determining the preferential area.


### 3.2. Design Process of the Population Economic Transfer Function Model

In the algorithm, people and their places are represented by points.(4)xi=x1i,…,xni.We denote thei-th point, xi∈Rn, xji we denote the j-th component of the i-th point.(5)δiδi,…,δji,δi∈Rn,δji is the j-th component of δi, δji>0; i=1,2,…,N,j=1,2,…,n, N is population size.Step 1.
WegenerateN points x1,x2,…,xN evenly and randomly in the search space. For each i, let the center centeri±xi of the i-th region determine the upper and lower boundaries of the i-th region, centeri±δi, where(6)δji=bj−aj2N,i=1,2,…,N,j=1,2,…,n.
The above-given method ofδji makes each δi equal, so the superscript of δi is cancelled in the following steps:Step 2.
The income / attractionfxi of each point is calculated.Step 3.
The optimal record value and the optimal record point according to the calculated value obtained in step2 is intialized.Step 4.
The population flow is carried out in each area.(7)xi=2δrand∗+centeri−δ,where rand∗ is a random number function.(8)xji=ajxji<ajxji=bjxji>bj..Step 5.
The income / attractionfxi of each point is calculated.Step 6.
The best value and the best point is recorded.Step 7.
If the number of population movementsL is less than the preset number, we go to step 4.Step 8.
Population economic transfer: we take the most attractive point (i.e., the best record point) as the center, determine the preferential area according to the size of each component ofδ. in this area, evenly and randomly generate N points to replace the original points.Step 9.
The income / attractionfxi of each point is calculated.Step 10.
The best value and the best point is recorded.Step 11.
The preferential area is reduced:(9)δ=1−Δ.(Δ is contraction coefficient, 0 < Δ < 1).Step 12.
We then carry out population flow in the preferential area and the population changes with the economic center of gravity: take the most attractive point (i.e. the best record point) as the center, determine the preferential area according to the size of each component ofδ. Evenly and randomly generate N points in the area to replace the original points.Step 13.
The income / attractionfxi of each point is calculated.Step 14.
The best value and the best point is recorded.Step 15.
Ifmaxj>α (α is the population pressure parameter, the preset positive small amount), we go to step 11.Step 16.
The results are reported.Step 17.
Population diffusion: we evenly and randomly generateN points x1,x2,…,xN in the search space to replace the original points. We determine the population flow area according to the method in step 1.Step 18.
The income / attractionfxi of each point is calculated.Step 19.
The best value and the best point is recorded.Step 20.
The number of iterations ism plus 1. If the number of iterations is less than the specified number, we go to step 4.Step 21.
We thenend the process.
PMA mainly simulates the mechanism of population transfer with the economic center of gravity and disperses with the increase of population pressure. The former promotes the algorithm to select better region search, while the latter can avoid falling into local optimum to a certain extent, so the search process presents the characteristics of alternating centralized search and decentralized search. This reflects the characteristics of the contradictory movement of population and economy in the process of population migration.


## 3.1. Population Migration Algorithm Construction

In the following part, combining with the function global optimization problem, we study how to establish a new global optimization search algorithm, namely PMA, by simulating the population economic transfer mechanism. The current study is aimed at forms such as(1)maxfx,s.t.x∈S.For unconstrained function optimization problems, the problem (1), f:S⟶R1 is a real valued mapping:(2)x∈Rn,S=∏i=1nai,bi,where S is the search space and ai<bi, and it is assumed that problem (1) always has a solution, that is, the global optimal value f∗ exists and the global optimal set M is nonempty.Function optimization is to find the optimal solution in the search space, and population economic transfer is to find preferential areas in the regional space. There are similarities between the two. Table1 shows the analogy relationship between some elements of the two.Table 1
Comparison of function optimization factors and population economic transfer.
Function optimization elementsFactors of population economic transferxPopulation locationfxEconomic factors such as income or attractiveness of population locationSMobile surface space of populationThe bestThe highest income point or the most attractive pointOptimal valueThe highest income or attractionAscent/climbMove to preferential areasBreak away from local optimumPopulation pressure leads to relocation from preferential areasIt should be noted that the economic transfer of population is a complex process, which does not completely correspond to the global optimization of function. Therefore, the principle of establishing a global optimization search algorithm by simulating the population economic transfer mechanism is to extract the useful elements in the process of population economic transfer, rather than copy them completely. The simulation implementation of each link is discussed below. Population flow is carried out in each residential area, which originally refers to the space specified on the Earth’s surface. When it is extended to the space specified in PMA, the population flow is simulated in each residential area. If it is divided directly by administrative region or longitude and latitude line, then with the increase in the dimension of the optimization problem, the problem of dimension disaster will appear.In the search spaceS, N points x1,x2,…,xN are randomly generated. For each point xi and the predetermined area:(3)δixi,δi∈Rn;δji>0;i=1,2,…,N;j=1,2,…,n.∏j=1nxji−δji,xji+δji.Considering the poor regularity of the population flow, the population flow is treated as random. In addition, in order to make the search opportunities in the region equal, the population flow is further treated as a uniform random change. In the simulation, several points can be randomly generated in each region, and then these points can be randomly changed. A simpler equivalent method can also be used to deal with the population flow. That is to say, multiple random changes of a point are equivalent to one random change of multiple points. In this way, only one random change point in each region can make a predetermined number of uniform random changes.Preferential areas attract people from other areas. For simplicity, the process of population economic transfer is simplified, that is, all people and their economy migrate to preferential areas. In the simulation,N points are randomly generated in the preferential area to replace the points in other areas. The preferential area is redrawn with the point where the current maximum fx value is located as the center. The maximum fx value is used to measure the attraction of the preferential zone, and each fx value is used to represent the population income of each point. After the population moves into the preferential zone, there are n points in the preferential zone. Every time the N points complete a random change, it is necessary to find out the point with the highest income, and redefine the zone with it as the center. This is to simulate the shift of the population center of gravity with the shift of the economic center of gravity. When the preferential area shrinks to a certain extent, that is, when the population pressure increases to a certain extent, the population will spread outward, and the population will move out of the preferential area and spread to the undeveloped area with low population density. In the search space, N points are randomly generated and the area is redivided. Finally, the simulation of preferential area information media is given. The media such as relatives and friends, media advertising, and the labor market are abstracted as the best recording unit. In the algorithm, the best recording unit records the current maximum value of fx and the corresponding point x, which provides the basis for determining the preferential area.


## 3.2. Design Process of the Population Economic Transfer Function Model

In the algorithm, people and their places are represented by points.(4)xi=x1i,…,xni.We denote thei-th point, xi∈Rn, xji we denote the j-th component of the i-th point.(5)δiδi,…,δji,δi∈Rn,δji is the j-th component of δi, δji>0; i=1,2,…,N,j=1,2,…,n, N is population size.Step 1.
WegenerateN points x1,x2,…,xN evenly and randomly in the search space. For each i, let the center centeri±xi of the i-th region determine the upper and lower boundaries of the i-th region, centeri±δi, where(6)δji=bj−aj2N,i=1,2,…,N,j=1,2,…,n.
The above-given method ofδji makes each δi equal, so the superscript of δi is cancelled in the following steps:Step 2.
The income / attractionfxi of each point is calculated.Step 3.
The optimal record value and the optimal record point according to the calculated value obtained in step2 is intialized.Step 4.
The population flow is carried out in each area.(7)xi=2δrand∗+centeri−δ,where rand∗ is a random number function.(8)xji=ajxji<ajxji=bjxji>bj..Step 5.
The income / attractionfxi of each point is calculated.Step 6.
The best value and the best point is recorded.Step 7.
If the number of population movementsL is less than the preset number, we go to step 4.Step 8.
Population economic transfer: we take the most attractive point (i.e., the best record point) as the center, determine the preferential area according to the size of each component ofδ. in this area, evenly and randomly generate N points to replace the original points.Step 9.
The income / attractionfxi of each point is calculated.Step 10.
The best value and the best point is recorded.Step 11.
The preferential area is reduced:(9)δ=1−Δ.(Δ is contraction coefficient, 0 < Δ < 1).Step 12.
We then carry out population flow in the preferential area and the population changes with the economic center of gravity: take the most attractive point (i.e. the best record point) as the center, determine the preferential area according to the size of each component ofδ. Evenly and randomly generate N points in the area to replace the original points.Step 13.
The income / attractionfxi of each point is calculated.Step 14.
The best value and the best point is recorded.Step 15.
Ifmaxj>α (α is the population pressure parameter, the preset positive small amount), we go to step 11.Step 16.
The results are reported.Step 17.
Population diffusion: we evenly and randomly generateN points x1,x2,…,xN in the search space to replace the original points. We determine the population flow area according to the method in step 1.Step 18.
The income / attractionfxi of each point is calculated.Step 19.
The best value and the best point is recorded.Step 20.
The number of iterations ism plus 1. If the number of iterations is less than the specified number, we go to step 4.Step 21.
We thenend the process.
PMA mainly simulates the mechanism of population transfer with the economic center of gravity and disperses with the increase of population pressure. The former promotes the algorithm to select better region search, while the latter can avoid falling into local optimum to a certain extent, so the search process presents the characteristics of alternating centralized search and decentralized search. This reflects the characteristics of the contradictory movement of population and economy in the process of population migration.


## 4. Experiment

### 4.1. Experimental Methods

In order to verify the effectiveness of the population economic transfer function model, a simulation experiment is designed. The test environment is a Windows 10 system, including Intel Core i7, RAM16g and Windows iSCSI. This paper uses the population economic transfer function model based on improved density entropy, the population economic transfer function model based on the Markov model, the population economic transfer function model based on lasso variable selection, and the model in this paper to carry out the following experiments.


### 4.2. Evaluation Accuracy of Population Economic Transfer Function

In order to verify the evaluation effect of the population economic transfer function model, the improved density entropy model, the Markov model, the Lasso variable selection model, and the model in this paper are used to verify the evaluation accuracy of the population economic transfer function. The results are shown in Table2.Table 2
Evaluation accuracy of population economic transfer function under different models.
Area (km2)The accuracy of economic transfer function evaluation (%)Improved density entropy modelMarkov modelLasso variable selection modelModel of this paper506664819910076766598150867674952005764789625076586895300727369943507071739940059687897450677573965006674779855080728597600727874956507584649770071886393Mean value70.972.97396According to the analysis of Table1, the evaluation accuracy of the population economic transfer function model is different under different methods. When the area is 50 km2, the accuracy of the improved density entropy model is 66%, the Markov model is 64%, the lasso variable selection model is 81%, and the model in this paper is 99%. A comprehensive analysis of the data in the above table shows that this model can effectively improve the accuracy of the results of population economic transfer. This is because the model analyzes the defects of the genetic algorithm and designs a genetic tabu search algorithm on this basis, which improves the convergence of the algorithm, avoids falling into a local optimum, and improves the precision of the design model.


### 4.3. Correction Effect of Population Economic Transfer Function

In order to verify the evaluation and correction effect of the population economic transfer function model, the improved density entropy model, Markov model, Lasso variable selection model, and the model in this paper are used to verify the correction accuracy of the population economic transfer function. The results are shown in Table3.Table 3
Correction accuracy of population economic transfer function under different models.
Area (km2)Correction accuracy of population economic transfer function (%)Improved density entropy modelMarkov modelLasso variable selection modelModel of this paper506854478910069574992150566363952003758429725045514598300623854963504239589240049466390450584851955005352369755055573399600576737966506263439870064694990Mean value55.554.447.894.6According to the analysis in Table3, when the area is 500km2, the correction accuracy of the population economic transfer function of the improved density entropy model is 53%, that of the Markov model is 52%, that of the lasso variable selection model is 36%, and that of the model in this paper is as high as 97%. When the area is 700 km2, the accuracy of the modified density entropy model is 64%, the Markov model is 69%, the Lasso variable selection model is 49%, and the accuracy of this model is as high as 90%. The model in this paper has a high correction effect on the population economic transfer function, which shows that the model can effectively improve the correction rate of the population economic transfer function. The results demonstrate the effectiveness of the genetic tabu search algorithm and can effectively improve the accuracy of the design model.


## 4.1. Experimental Methods

In order to verify the effectiveness of the population economic transfer function model, a simulation experiment is designed. The test environment is a Windows 10 system, including Intel Core i7, RAM16g and Windows iSCSI. This paper uses the population economic transfer function model based on improved density entropy, the population economic transfer function model based on the Markov model, the population economic transfer function model based on lasso variable selection, and the model in this paper to carry out the following experiments.


## 4.2. Evaluation Accuracy of Population Economic Transfer Function

In order to verify the evaluation effect of the population economic transfer function model, the improved density entropy model, the Markov model, the Lasso variable selection model, and the model in this paper are used to verify the evaluation accuracy of the population economic transfer function. The results are shown in Table2.Table 2
Evaluation accuracy of population economic transfer function under different models.
Area (km2)The accuracy of economic transfer function evaluation (%)Improved density entropy modelMarkov modelLasso variable selection modelModel of this paper506664819910076766598150867674952005764789625076586895300727369943507071739940059687897450677573965006674779855080728597600727874956507584649770071886393Mean value70.972.97396According to the analysis of Table1, the evaluation accuracy of the population economic transfer function model is different under different methods. When the area is 50 km2, the accuracy of the improved density entropy model is 66%, the Markov model is 64%, the lasso variable selection model is 81%, and the model in this paper is 99%. A comprehensive analysis of the data in the above table shows that this model can effectively improve the accuracy of the results of population economic transfer. This is because the model analyzes the defects of the genetic algorithm and designs a genetic tabu search algorithm on this basis, which improves the convergence of the algorithm, avoids falling into a local optimum, and improves the precision of the design model.


## 4.3. Correction Effect of Population Economic Transfer Function

In order to verify the evaluation and correction effect of the population economic transfer function model, the improved density entropy model, Markov model, Lasso variable selection model, and the model in this paper are used to verify the correction accuracy of the population economic transfer function. The results are shown in Table3.Table 3
Correction accuracy of population economic transfer function under different models.
Area (km2)Correction accuracy of population economic transfer function (%)Improved density entropy modelMarkov modelLasso variable selection modelModel of this paper506854478910069574992150566363952003758429725045514598300623854963504239589240049466390450584851955005352369755055573399600576737966506263439870064694990Mean value55.554.447.894.6According to the analysis in Table3, when the area is 500km2, the correction accuracy of the population economic transfer function of the improved density entropy model is 53%, that of the Markov model is 52%, that of the lasso variable selection model is 36%, and that of the model in this paper is as high as 97%. When the area is 700 km2, the accuracy of the modified density entropy model is 64%, the Markov model is 69%, the Lasso variable selection model is 49%, and the accuracy of this model is as high as 90%. The model in this paper has a high correction effect on the population economic transfer function, which shows that the model can effectively improve the correction rate of the population economic transfer function. The results demonstrate the effectiveness of the genetic tabu search algorithm and can effectively improve the accuracy of the design model.


## 5. Conclusion

This paper proposes a population economic transfer function model based on the genetic tabu search algorithm. The process of the genetic tabu search algorithm is designed; the design process of the population economic transfer function model is determined, and relevant comparative experiments are designed to verify the effectiveness of the model. The experimental results show that the proposed model can improve the accuracy of model evaluation and model correction rate, avoid falling into local optimum to a certain extent, and has good global optimization performance. The application of the population economic transfer function model can effectively improve the accuracy of the model.The research results on population migration are very rich, and it is necessary to further explore some useful mechanisms to enrich the existing algorithm. The next research will focus on population migration density to further improve the application of the proposed algorithm.



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*Source: 1356909-2022-09-19.xml*