Optimally Enhancement Rural Development Support Using Hybrid Multy Object Optimization (MOO) and Clustering Methodologies: A Case South Sulawesi - Indonesia

The European Union has discussed a framework for sustainable rural development from 2021 to 2027, related to the growing importance of rural areas. The multiplicity of resources and their positive benefits can be influential factors for sustainable rural development [1]. With regard to the implementation of the European Union's framework, all levels of government can work together to develop rural areas.

The author's concern in this study is the prolonged delivery of the latest information about the status of villages. In addition, there has been no information source explaining the stages of implementing equitable development through village assistance programs. One research paper stated that data collection on village potential was carried out by the Central Bureau of Statistics of South Sulawesi Province every three times in 10 years but did not explain which areas had high or low village potential [2]. Village potential refers to resources or assets owned by a village that can be utilized to advance the village and improve community welfare, covering social, economic, and regional facilities and infrastructure [3].

Subsequent research stated that the Ministry of Rural and Transmigration had not provided the latest data regarding the updating of village data in Yogyakarta city up to 2022. As a result, the classification results displayed still use data from 2016, although several studies reported that some village statuses had changed [4].

The low participation of the community and village institutions in planning, implementing, and controlling village development activities, as well as the preservation of development results, has led to many natural potentials in the village remaining managed traditionally. This is due to the inability to master technology, relatively low community education, and the tendency of villagers to accept conditions as they are. Generally, the development of rural areas has not been implemented due to internal factors originating from the village, such as the lack of initiative and knowledge from the village community, and external factors originating from the government in socializing and providing assistance to rural communities [5].

Implementation of the set strategy takes about 3 to 4 months, starting with collecting information about the living conditions of the community, and then clustering villages based on the Community Standard of Living Index (CSLI), especially in villages in the Province of South Sulawesi. In this study, the Multi-Object Optimization (MOO) method is used to determine priority scales and weighting of multi-criteria to form an instrument sequence that can objectively accommodate information from the public. Research has stated that the multi-objective optimization approach can be applied in a management context to optimize solutions in complex situations and multi-criteria [6]. The clustering approach can be applied to optimize solutions in complex and multi-criteria situations. Clustering is done to group the sub-cluster centers obtained and extract the final clusters from the dataset using criteria [7].

In general, the structure of this research framework is as follows: First, the process of implementing the MOO method is carried out through establishing criteria, validating, verifying, evaluating, and weighting. Second, building Village Input is done by changing the criteria into a questionnaire instrument. Third, building a Cluster Community Standard of Living Index (CSLI). The remaining parts of this study are organized as follows: Section 2 contains the literature review. Section 3 presents the methodology. Section 4 discusses the results and discussion. Finally, conclusions are provided in Section 5.

3.1 Research design

The theoretical contribution of research design is that research can be better evaluated in terms of understanding, theory building, theory development, and theory testing [25]. The research design refers to the plan or strategy that researchers use to guide investigation and answer research questions. The theoretical contribution of research design lies in the fact that can help this research to systematically and rigorously test theories to get generate new knowledge.

The research design can contribute to developing new methods or techniques for collecting and analyzing data. By developing innovative research designs and methods, this research can contribute to the overall advancement of the field and enable others to build the research. Overall, the theoretical contribution of research design lies in its ability to help researchers generate new knowledge and advance existing theories through rigorous and systematic. The research design is used to gather relevant data and techniques to facilitate the smooth scaling of various research operations so as to produce maximum information, it also provides the researcher with structure for planning to answer research questions or testing of hypotheses [26]. Figure 1 illustrates the research design in this research.

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Figure 1. Research design

Based on the illustration shown in Figure 1 that each stage will be explained particularly in order to obtain a deep understanding.

Table 1. List of criteria

3.2 Identification of criteria

A research stated that the foundation of any successful survey-based research is that the questions asked can be used to accurately describe the practices, conditions, experiences, personal characteristics, or opinions of the respondents [27]. Therefore, interviews were conducted with sources including local governments, experts in the field of regional development planning, and village heads to collect information as an initial stage in building a questionnaire. Asking questions is an essential component of the learning experience, which is structurally embedded in critical thinking [25]. The questionnaire format is based on 38 criteria arranged as guidelines in this study. The criteria for this research is shown in Table 1.

All criteria were obtained through an interview process with experts from representatives of academics, government, researchers and village officials totalling 16 experts.

3.3 Verification of criteria

In this study, the validation process was carried out by evaluating the criteria used as input values using the Multy Objective Optimization (MOO) Fuzzy Delphi Method (FDM). As explained that Fuzzy Delphi provides a robust framework that can handle a lack of precision and clarity, as incomplete or inaccurate information is considered a problem in decision-making [28]. The flowchart of Fuzzy Delphi is shown in Figure 2.

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Figure 2. Flowchart of fuzzy delphi methodology

Based on Figure 2 is explained that the stages of the criteria evaluation process are carried out to determine the priority scale of criteria and weighting that was used in determining the village index and cluster. The process of comparing the performance of the MOO algorithm with each other is very necessary in order to guarantee the weight value of each criterion for the evaluation process [29]. The performance of the MOO algorithm is assessed based on the balance between convergence and diversity of non-dominated solutions which are measured using different evaluation criteria than quality performance indicators. The threshold value is calculated using the following formula.

$d(\bar{m}, \bar{n})=\sqrt{\frac{1}{3} *[(m 1+m 2+m 3)]}$                    (1)

As the data analysis is based on the triangular fuzzy number where it aims to get threshold value (d). The first condition to be followed is threshold value (d) must be less or equal to 0.2. Therefore, all experts are considered to have reached the agreement and made a consensus.

The aggregate calculation process is a fuzzy evaluation process to determine the value of the fuzzy score that obtain using the following formula:

$A_{M a x}=\frac{1}{3} *(M 1+M 2+M 3)$            (2)

Finally, stage is determining the position or ranking of each criteria as follows:

$\bar{A}=\left[\frac{\overline{A 1}}{\frac{\overline{A 2}}{A \ldots n}}\right] \quad A=1 . . m$               

The Delphi method allows research to act independently and adapt its dynamics to research objectives and make strategic decisions because an objective opinion of a group of specialists always is of higher quality than the opinion of one individual.

3.4 Validation of criteria

A fuzzy scale is a type of measurement scale that used in fuzzy logic, which is a mathematical approach to dealing with uncertain or unclear information using linguistic terms to describe the degree of membership of an object in a particular set. In this study, a validation process was carried out on the criteria through determining the approval weight and fuzzy scale, then all assessments by experts will be processed using the fuzzy delphi method to find out the total score against each criterion. Fuzzy scales are shown in Table 2.

Table 2. Fuzzy scale for validation of criteria

Table 2 shows guidelines and instructions to experts as a provision for the declaration and approval of each criteria. Based on the data in Table 2. On a traditional 0.2 to 1 scale, a score of 0.6 would represent the exact midpoint between low and high scores. However, on a fuzzy scale, the term Simply Agree can be used instead to describe the uncertainty or vagueness of a particular concept.

3.5 Weighting of criteria

In this Research the focus of the research is to determine the index value of the community standard of living index. After the criteria evaluation stage by the expert is completed. Respondents as representatives from each village will provide answers through instrument data as village input, and then the process of calculating the score for the village will be carried out according to the results of the answers from the respondents, the next step is to carry out a weighting process for all criteria using the Rank Reciprocal (RR) algorithm. The village score will be a measure of the CSLI value of a village and is also used as an input value in the self-organizing map algorithm as the initial stage of the clustering process. The process of weighting the criteria uses the Rank Reciprocal (RR) method to determine the magnitude of the weight values and works by emphasizing that the order of indexes has different importance values. The RR method is formulated as follows:

$W_j(\mathrm{RR})=\frac{1 / R_j}{\sum_{k=1}^n\left(1 / R_k\right)}$        (3)

Descriptions:

W_j    = Weighted value (criteria/subcriteria)

R_j      = Rank order value (criteria/subcriteria)

R_k     = Total number of goals(criteria/subcriteria).

For giving weighting to each criteria is done using Rank Reciprocal method. The flowchart is given in Figure 3.

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Figure 3. Flowchart rank reciprocal algorithm

Weighting in the Rank Reciprocal method gives a value to each criteria based on its ranking position. The score is then inverted and summed up for all relevant criteria, where the lower the total score generated, the better the ranking position of the criteria.

3.6 Clustering of community standard of living index

The clustering result is the grouping of villages based on the community standard of living score index in the high, medium and low-level categories. The standard of living index was combined with previous indicators so that each indicator can represent the actual conditions of the community in a village hence the decision-making process on the level of distribution of village development provides more objective information. In general, the stages of the process of determining the CSLI include:

1. Declaration of variable W_j, R_k, R_j, TS, TC, TP.

         R_k =Total goals(criteria/subcriteria)

         R_j = Rank order value (criteria/subcriteria)

         TC = Total of Community

         TP = Total of Patriarch.

2. W_j = Weight processing criteria/instrument.

3. Determine the total value generated from the answers to the community questionnaire for each village. Mathematically the formula used is as follows:

$\begin{aligned} & \text { TS } \quad=\text { Total of Scoring } \\ & (T S)=\frac{\sum \text { Criteria }(\mathrm{w}) * \text { Instrument }(\mathrm{w})}{\sum \text { Respondents }} \\ & \end{aligned}$            (4)

4. Initiation of output neuron output each y1, y3, ...yn.

5. Initial weight.

6. Finding the shortest distance from each output neuron to the input data using the Euclidian distance formula. Mathematically the formula used is as follows:

$D_j=\sum_{\mathrm{j}}\left(\mathrm{w}_{\mathrm{ji}}-\mathrm{x}_{\mathrm{j}}\right)$              (5)

7. Each weight w_ij is updated by neighbouring weights using the formula with the following equation:

$\mathrm{W}_{\mathrm{ij}}$ (new) $=\mathrm{W}_{\mathrm{ij}}($ old $)+\alpha\left(\mathrm{X}_{\mathrm{i}}-\mathrm{W}_{\mathrm{ij}}\right.$ (old) $)$            (6)

8. Update bias weight (error).

9. Repeat steps g to h until there is no weight update or it has reached a stop condition or error in the smallest

10. Save the convergent weight, Initiation cluster

11. Determine the total of clusters built

12. Determine the rank value (W)

13. Initialize the initial partition matrix

14. Calculating the centroid value using the formula:

                           $\mathrm{Vkj}=\frac{\Sigma_{\mathrm{i}=1}^{\mathrm{n}}\left((\mu \mathrm{ik})^{\mathrm{w}} * \mathrm{Xij}\right)}{\Sigma_{\mathrm{ij}}^{\mathrm{n}}(\mu \mathrm{ik})^{\mathrm{w}}}$               (7)

15. Calculating the value of membership degrees using the formula:

$\mathrm{Qj}=\sum_{\mathrm{k}=1}^{\mathrm{c}} \mu \mathrm{ik}$            (8)

16. Determine the cluster of selected

17. Save the data clusters.

In the early stages of the clustering process, initial weights are set randomly to initialize the weights or parameters so that more accurate patterns can be found in the data. The initial weight is shown in Table 3.

Table 3. Initiation weight

The process for clustering of villages is shown in the flowchart given in Figure 4.

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Figure 4. Flowchart clustering village

Figure 4 illustrates that the engineering process for indexing the community standard of living index consists of the data input process and the indexing process. In the data input process, criteria are set to guide the construction of a questionnaire, where each questionnaire has an answer that has a predetermined weight.

All questionnaires are stored on the server to access the public as responders. In the indexing process, the entire answer score from the respondent was calculated and then used as input in the scoring process and then set as the village score. After determining the score for each village, the following process combines the score, Total of the patriarch, and Total of residents to serve as input for the clustering process. Furthermore, from the clustering process, an index of the community standard of living index was generated, which is divided into three groups of categories, namely First, Excellent Level of CSLI, village with a high level of community welfare to create prosperity in life. Second, Average Level of CSLI, the village has a moderate level of community welfare, so it is seen that it still requires assistance from the government in several matters relating to improving community welfare. Third, Poor Level of CSLI, village with a low level of community welfare, so it is seen as in dire need of assistance from the government in all fields related to improving community welfare.

The conclusion of this study is that all elements and resources in each village can synergize in the implementation of equitable development. Through the use of Hybrid Multi-Object Optimization (MOO) and Clustering Methodologies, it is possible to determine the level of village development based on the CSLI. Furthermore, the information generated is more up-to-date and objective, so that it can be the basis for decision-making about village development priorities in the province of South Sulawesi. The innovation of this study is that the method used in the process of developing the Community Standard of Living Index for each village is a new knowledge that can be used as a solution to the problem of the lack of community participation and the delay in presenting information about development conditions in a village. The approach proposes in this study provides a perspective in which village development conditions can be measured through the community standard of living index. Constructing a different value index can be used as a propose in future studies. The propose approach can be used for different methodologies and technologies.