Intuitionistic Fuzzy Set Similarity Degree Based on Modified Genetic Algorithm for Solving Heterogenous Multi-dimension Targeted Poverty Alleviation Data Scheduling Problem on Scalable Systems

Targeted poverty alleviation is a proposed concept in comparison with extensive poverty alleviation. It mainly aims at the poverty situation of different rural areas and farmers in China and adopts scientific and reasonable methods to carry out targeted assistance policies. It executes accurate management for the targeted poverty alleviation. This way for poverty alleviation is more precise. In the research of heterogenous multi-dimension targeted poverty alleviation data scheduling, the multi-dimension processing is very important. In this paper, we propose an intuitionistic fuzzy set similarity degree based on modified genetic algorithm for solving heterogenous multi-dimension targeted poverty alleviation data scheduling problem. In the proposed algorithm, the reference solution and Pareto solution are mapped to the reference solution intuitive fuzzy set and Pareto solution intuitive fuzzy set respectively. The intuitionistic fuzzy similarity between two sets is calculated to judge the quality of Pareto solution. The similarity value of intuitionistic fuzzy sets is used to guide the evolution of multi--dimension genetic algorithm. The results show that the proposed algorithm can effectively solve the problem of heterogenous multi-dimension targeted poverty alleviation data scheduling, especially, in large scale problems.


Introduction
Rural poverty has always been an important factor hindering China rural economic development. It is an important task for China rural poverty alleviation and development work to help the poor people in rural areas get rid of poverty smoothly. But poverty control work is still very difficult to carry out, which has brought great pressure to the party and the government. This is because poverty alleviation data scheduling is not timely and data cannot be shared in real time, which affects the accuracy of poverty alleviation work.
Data scheduling problems cover a wide range including single machine scheduling problem, resource scheduling problem, poverty alleviation job scheduling problem and open data scheduling problem [1]. About 25% of the production and manufacturing systems can be simplified to data scheduling problem. Therefore, the multi-dimension targeted poverty alleviation data scheduling problem (MTPA) is one of the most widely studied production scheduling problems. For the single-dimension targeted poverty alleviation data scheduling problem, Wang [2] proposed an evolutionary search algorithm based on multiple agents. Zheng [3] used the improved basic quantum evolutionary algorithm to solve the problem. Lin [4] proposed a hybrid-discrete biogeography based optimization (HDBBO) algorithm to solve the problem. Liu [5] proposed a hybrid discrete artificial bee colony algorithm. Lu [6] proposed a hybrid multi-objective backtracking search algorithm to solve the multiple targets flow-shop scheduling problem. Li [7] proposed a multi-population and multiobjective genetic algorithm based on decomposition method. At present, for multi-dimension targeted poverty alleviation data scheduling, one or two optimization objectives are mostly considered. Considering more than three dimensions targeted poverty alleviation data scheduling problems is less because of the complexity of targeted poverty alleviation data scheduling problem [8,9]. On the other hand, with the increase of the target dimension, the proportion of the nondominant solution increases rapidly when the commonly used multi-dimension targeted poverty alleviation data scheduling algorithm is adopted. It is difficult to distinguish the better solution with the dominance relation as the fitness value resulting in the high-dimensional multi-objective (target number). Multi-dimension targeted poverty alleviation data scheduling is extremely challenging, but with the increasingly fierce competition among enterprises, decision makers need to consider a variety of factors when selecting scheduling schemes, such as completion time, delay cost, idle time, cost, inventory, etc,. Therefore, it is particularly important to study the high-dimensional multiobjective data scheduling problem.
Genetic algorithms (GA) are derived from computer simulations of biological systems [10]. Compared with other algorithms, genetic algorithm has the unique characteristics of universality, adaptability, expansibility and implicit parallelism, and has great advantages in solving the approximate optimal solution of complex multi-dimension targeted poverty alleviation data scheduling problems. After years of research and experiments, it is proved that the genetic algorithm is feasible and effective in solving the heterogenous multi-dimension targeted poverty alleviation data scheduling problem.
Intuitionistic fuzzy set is a generalization of fuzzy set theory, which considers membership degree, nonmembership degree and hesitation degree at the same time. Many scholars have studied the measurement analysis of fuzzy set and applied it to various fields. Nguyen [11] proposed a similarity/dissimilarity measurement method for intuitionistic fuzzy sets and applied it to pattern recognition. Ananthi [12] proposed a thresholding method based on interval intuitionistic fuzzy sets and applied it to image segmentation. Lee [13] put forward a kind of intuitionistic fuzzy genetic algorithm solving weapon target assignment problem. Wang kaijun combined intuitionistic fuzzy set and grey model in fuzzy mathematics to design a fault prediction method. At present, the application of intuitionistic fuzzy sets similar to the research of shop scheduling is few.
MTPA is a simplified model for many practical production scheduling problems. Therefore, this paper combines intuition fuzzy similarity method with modified genetic algorithm and proposes a SIFSMGA algorithm, which is applied to multi-dimension targeted poverty alleviation data scheduling problem. The similarity of intuitionistic fuzzy set is used to explore the effective information between Pareto solution and each target, effectively eliminating the influence of magnitude and dimension of target, solving the problem of information loss [14]. The main contributions are as follows. The similarity of intuitionistic fuzzy sets is used as the fitness of the evolutionary algorithm to guide the evolution of the algorithm. Pareto solution is mapped to intuitionistic fuzzy set by membership function, non-membership function and intuitionistic index. It calculates the similarity between Pareto solution intuitionistic fuzzy set and reference solution intuitionistic fuzzy set. The advantage of Pareto solution is judged by the similarity size. Simulation experiments are conducted on 6 CEC standard test sets and 10 multidimension targeted poverty alleviation data scheduling test cases. The superiority of SIFSMGA algorithm is verified, and it can effectively solve the multi-dimension targeted poverty alleviation data scheduling problem, especially in solving large-scale problems.

Mathematical model
The MTPA problem can be regarded as a job shop scheduling problem. Therefore, the description of MTPA problem is as follows: n workpieces are processed on m machines. The processing path of each workpiece is the same, and the processing order of the workpiece on all machines is the same. The processing time of one workpiece on one machine is fixed. The same workpiece cannot be processed on different machines at the same time, and multiple workpieces cannot be processed on one machine at the same time. The goal is to study and determine the optimal processing sequence of all the workpiece so as to achieve the optimal set of performance indicators. Where, the set of After receiving the order from the retailer, the manufacturer needs to process n workpieces and transport them to the retailer after processing. Subjected to the retailer's delivery date and its own inventory capacity, the manufacturer must complete all work within a reasonable time. The completion of the work ahead of time or delay will have a negative impact on the economic benefits of the Intuitionistic Fuzzy Set Similarity Degree Based on Modified Genetic Algorithm for Solving Heterogenous Multi-dimension Targeted Poverty Alleviation Data Scheduling Problem 3 enterprise. The workpieces need to be stored before they can be transported. If the workpiece is completed in advance, there will be inventory costs; If the workpiece is completed after the delivery date, there will be delay cost. Inventory cost and delay cost are proportional to time. After the work is finished, it will be transported to the retailer in batches. The maximum volume of shipments is fixed and the same. When the number of finished workpieces reaches the maximum traffic, they will be transported. And the transporting time of each batch is the completion time of the last workpiece. If the last batch of workpieces is less than the maximum shipment, the last batch of workpieces will still be transported as a batch. The problem can be described by the following notations. ) (x f k is the function value of the k-th objective function.  In enterprises, different departments have different expectations for shop floor scheduling decisions based on their own interests. For example, the production workshop wants to improve production efficiency, the sales department wants to be able to deliver goods on time, and the manufacturing department wants to reduce costs as much as possible. Therefore, the following meaningful and conflicting optimization goals are set in this paper. The purpose of shortening the maximum completion time is to improve the production efficiency of the enterprise. The purpose of reducing the maximum delay time is to improve customer satisfaction. Reducing the delay cost and inventory cost is to improve the economic efficiency of enterprises. The optimized objective function is as follows: The completion time (i.e., the maximum completion time) of the last workpiece on the last machine is: Because of the delay in completion of each workpiece, the manufacturer will be charged (i.e., the maximum delay time) is: The inventory cost (i.e., the total inventory cost) of each workpiece before transportation is: A certain delay cost (i.e., total delay cost) may be incurred for all the delayed workpieces, namely and objective function are subject to the following constraints: 11 11 Formula (9) describes the transport capacity of all transports. The mathematical model of the multi-objective replacement flow shop scheduling problem is as follows:

An improved genetic algorithm based on similarity of intuitionistic fuzzy sets
We adopt the similarity of intuitionistic fuzzy sets as the fitness of evolutionary algorithms to guide the evolutionary algorithm. Through the membership functions, the nonmembership functions and intuitionistic index, it maps the Pareto solution and reference solution to form the Pareto solution intuitionistic fuzzy sets and reference solution intuitionistic fuzzy sets. Calculate the similarity between two intuitionistic fuzzy sets, in a similar size to judge the merits of the Pareto solutions. The similarity between two intuitionistic fuzzy sets is calculated to judge the quality of Pareto solution.

Definition of intuitionistic fuzzy sets
Intuitionistic Fuzzy Set (IFS) is an extension of the fuzzy set theory to deal with uncertain incomplete information. It uses the membership degree, non-membership degree and hesitation (intuitionistic index) to describe information to evaluate the relationship between comparison fuzzy sets. The intuitionistic fuzzy set is defined as: If X is a given finite field of element x , then an intuitionistic fuzzy set A on X is, In order to measure the hesitation degree of x for A, in each intuitionistic fuzzy subset of x , we put forward intuitionistic fuzzy set A becomes the ordinary fuzzy set.
If the totality of intuitionistic fuzzy sets defined on X is represented by IFS(X), then an intuitive fuzzy set A∈IFS(X), respectively represent the degree of supporting, opposing and neutral evidence of the intuitionistic fuzzy set A.

Set up intuitionistic fuzzy sets
When applying the of intuitionistic fuzzy sets similarity to multi-objective optimization, it is necessary to establish a relation between the multi-objective solution and the intuitionistic fuzzy sets. For this reason, this paper proposes a two-step mapping of multi-objective solution intuitionistic fuzzy set. Each sub-objective is optimized with q order single objective, and the maximum value of q order single objective optimization is selected as the upper bound of the sub-objective theory domain, and the λ times average value of the optimal value of the q order single objective optimization is selected as the lower bound of the subobjective theory domain.
In the formula, Step 2. The set of each sub-target intuitionistic fuzzy subset is mapped to a multi-objective intuitionistic fuzzy set. According to equations (14) and (15), the intuitionistic fuzzy subset of the i-th sub-target of the j-th solution is calculated. Define the mapping H2 as: Where j f i A is the intuitionistic fuzzy subset of the i-th objective of the j-th multi-objective solution.
To sum up, in order to establish the relationship between multi-objective solutions and intuitionistic fuzzy sets, H1 and H2 map are needed. By mapping H1, the j-th solution is calculated for each sub-target in intuitionistic fuzzy subset.
In the multi-objective optimization problem, there is often a contradiction between each target. Generally, there is no ideal solution to make each target reach its own optimal value. Therefore, in the target space, this paper conducts q single-target optimizations for each target, and takes the average value of q single-target optimal values as the point, which will be as the reference solution of the multi-objective problem. In order to solve the similarity between intuitionistic fuzzy sets, the reference solution and Pareto solution should be mapped into intuitionistic fuzzy sets first.

1) Reference solution mapping
Genetic algorithm is used to optimize sub-objective i , and the average value of q target values after q optimizations is taken to form the multi-objective reference solution

2) Pareto solution mapping
After each iteration of multi-objective genetic algorithm, the current Pareto optimal frontier )) ( , ), x Through the above two-step mapping, j Y is mapped to Pareto to solve the intuitionistic fuzzy set ) , , , is the i-th sub-object function value of the jth Pareto solution.

Similarity measure between intuitionistic fuzzy sets
In order to calculate the similarity between Pareto solution and reference solution, it is necessary to measure the similarity of intuitionistic fuzzy set after mapping. Reference [15] put forward an intuitionistic fuzzy sets measurement method according to the geometric interpretation of IFS. This paper proposes a distance measurement formula between multi-objective intuitionistic fuzzy sets as (18): N is the number of solutions. The ρ value considers the indecision state, which contains similarity and dissimilarity. In the absence of any other prior information, it is reasonable to consider that similarity and dissimilarity are equal to each other, so ρ =0.5. The similarity between intuitionistic fuzzy sets with multi-objective is calculated according to the distance measurement.
It can be seen from equation (18) and (19)  In order to solve the high dimensional multi-objective optimization problem of displacement flow shop scheduling, this paper combines the intuitionistic fuzzy sets similarity with GA to solve this problem. According to the description of the displacement flow shop scheduling problem, the machining path of the workpiece is the same as the machining order of the workpiece on all machines [16][17][18][19]. Therefore, this paper adopts the integer to encode the scheduling process, and each chromosome is corresponding to an arrangement of n workpieces. For represents the workpiece number.
Occurrence frequency of each i is 1, so that each position component of chromosome corresponds to an workpiece number. Continuous transformation of GA algorithm from real numbers to discrete processes is realized by ROV(Rank Order Value).
The specific steps of the proposed algorithm are as follows: Step 1. Population initialization.
Initializing the parameters, NP genes gen j X are randomly generated to form the initial parent population, where gen is the evolution number of the current population. Creating an initial external file.
Step 2. Establishing an intuitionistic fuzzy set of reference solutions.
It solves the optimization problem by formula (1) Step 4. Calculating the similarity between the intuitionistic fuzzy sets.
The similarity )) 0 ( ), ( ( IFS j IFS S between ) ( j IFS gen and IFS(0) of each gene gen j X in gen-th population is calculated according to equation (19), which will be regarded as the fitness value of GA algorithm to guide the algorithm evolution.
Step 5. Selection, crossover and mutation operations. The binary championship method is used to select the best genes. A new gene (Pareto solution) is generated by partial mapping crossover (PMX) and SWAP mutation (SWAP), and a new sub-population is formed.
Step 6. Maintaining and updating external files.
Merging the sub-population and external files. Calculating their crowding distance, keeping Pareto solutions with large crowding distance, deleting Pareto solutions with small crowding distance and trimming them to obtain updated external files.
Step 7. Judging the termination condition. Judging whether the fitness value of the group does not change continuously for a certain time or whether it meets the maximum iteration number. If No, gen=gen+1, return to Step 3. Otherwise, stop.

Experiment and analysis
In order to verify the superiority of the proposed algorithm and the feasibility, effectiveness of solving the multi-dimension targeted poverty alleviation data scheduling problem, six latest CEC standard test sets and ten targeted poverty alleviation test examples with different sizes are selected for experiment testing in this paper. We also compare our method with MDWW [20], ECOTD [21], HGA [22].

Performance evaluation index
To verify the performance of the proposed algorithm. In this paper, three performance evaluation indexes are adopted: space distance (SP), general distance (GD) and C index. 1) Diversity index. Space distance (SP) is used to evaluate the distribution uniformity of solution set in the target space. The calculation formula is as follows: If the SP value is smaller, the solution set distribution is more uniform.
2) Convergence index. General distance (GD) is used to evaluate the convergence of the algorithm. The formula is as follows: Where i d is the Euclidean distance between the i-th nondominant solution and the reference solution. The smaller GD value is, the closer Pareto solution is to reference solution, and the better convergence is.
C index is used to measure the relative merits between two optimal solution sets A and B obtained by optimizing the same problem by two algorithms A and B. The calculation formula is as follows:

Results of CEC data set
The six MaF standard test functions selected from the CEC set have different characteristics. Their theoretical fronts have different shapes, which can reflect the complex properties of practical optimization problems. Therefore, the performance of the proposed evolutionary high-dimensional multi-objective optimization method to solve practical optimization problems can be tested. The average value of evaluation indexes with different algorithms is shown in Table 1.
In terms of SP, in MaF2, MaF5 and MaF10, the SP value of proposed method is lower than that of the other three algorithms. In MaF1 and MaF4, the SP value of proposed method is greater than HGA, but less than the other two algorithms. In MaF11, the SP value of proposed method is greater than MDWW and HGA but less than ECOTD. It shows that, on the whole, Pareto solution set distribution obtained by proposed method is better than other algorithms. For GD, in MaF1, MaF2, MaF4, MaF5 and MaF11, the GD value of proposed method is less than that of the other three algorithms. In MaF10, the GD value of proposed method is greater than HGA but less than that of the other two algorithms. It shows that Pareto solution obtained by proposed method is closer to the reference solution, and its convergence is better than other three methods.

Results of ten data test sets
The results are the average values after 10 iterations as shown in Table 2. In instance 2, proposed method has 4 targets that are better than MDWW and ECOTD, and 2 targets that are better than HGA. In instances 1,3,4,5,6,7,8,9,10, proposed method obtains the optimal multi-dimension solution better than the other three algorithms. This indicates that proposed multi-dimension optimization solution is superior to the three methods in solving the problem of multi-dimension replacement flow shop scheduling. According to Table 2, the intuitive fuzzy set similarity (S) of the 10 instances are all greater than 0.8. The Pareto optimal solution obtained by proposed method is similar to the reference solution.
In terms of SP, the SP value of proposed method is lower than that of the other three algorithms. The results show that the distribution uniformity of Pareto solution set obtained by proposed method is better than other algorithms. In terms of GD, the GD value of proposed method is lower than that of the other three algorithms, indicating that Pareto solution obtained by proposed method is closer to the reference solution and its convergence is optimal.
The coverage indexes results with different algorithms are shown in Table 3. It can be seen from the table that the optimization effect of the proposed method is obviously better than other methods. It is concluded that the proposed method is effective in solving multidimension targeted poverty alleviation data scheduling problems and more suitable for solving large-scale problems.

Conclusion
In this paper, we propose a new method based on the similarity of intuitionistic fuzzy sets to solve the highdimensional multi-dimension targeted poverty alleviation data scheduling problem. The reference solution and Pareto solution are mapped to the intuitionistic fuzzy set respectively. The similarity of Pareto solution intuitionistic fuzzy set and Pareto solution is calculated and used as the fitness value of the evolutionary algorithm. A genetic algorithm based on the similarity of intuitionistic fuzzy sets is established to solve the multidimension targeted poverty alleviation data scheduling problem of four targets. The simulation results show that the similarity of intuitionistic fuzzy sets can be effectively combined with the genetic algorithm, and the performance of the algorithm is better than that of the common multi-objective optimization algorithm. Moreover, a high-quality Pareto solution can be obtained in the multi-objective replacement flow shop scheduling problem, which is more suitable for solving large-scale problems. In this paper, the multi-dimension targeted poverty alleviation data scheduling problem is selected to solve the shop scheduling problem. In actual production, more complex situations may occur, such as zero idle flow shop scheduling, blocked flow shop scheduling, job shop scheduling, flexible job shop scheduling, dynamic scheduling, etc. The next step is to explore the above problems by improving the algorithm, and further expand the application scope of the algorithm proposed in this paper.