Micro, Small, and Medium Enterprises’ Business Vulnerability Cluster in Indonesia: An Analysis Using Optimized Fuzzy Geodemographic Clustering

Abstract

The COVID-19 pandemic has caused effects in many sectors, including in businesses and enterprises. The most vulnerable businesses to COVID-19 are micro, small, and medium enterprises (MSMEs). Therefore, this paper aims to analyze the business vulnerability of MSMEs in Indonesia using the fuzzy spatial clustering approach. The fuzzy spatial clustering approach had been implemented to analyze the social vulnerability to natural hazards in Indonesia. Moreover, this study proposes the Flower Pollination Algorithm (FPA) to optimize the Fuzzy Geographically Weighted Clustering (FGWC) in order to cluster the business vulnerability in Indonesia. We performed the data analysis with the dataset from Indonesia’s national socioeconomic and labor force survey (SUSENAS and SAKERNAS). We first compared the performance of FPA with traditional FGWC, as well as several known optimization algorithms in FGWC such as Artificial Bee Colony, Intelligent Firefly Algorithm, Particle Swarm Optimization, and Gravitational Search Algorithm. Our results showed that FPAFGWC has the best performance in optimizing the FGWC clustering result in the business vulnerability context. We found that almost all of the regions in Indonesia outside Java Island have vulnerable businesses. Meanwhile, in most of Java Island, particularly the JABODETABEK area that is the national economic backbone, businesses are not vulnerable. Based on the results of the study, we provide the recommendation to handle the gap between the number of micro and small enterprises (MSMEs) in Indonesia.

1. Introduction

The COVID-19 pandemic has caused a contraction in the global economy as a result of various efforts in countries to reduce the COVID-19 pandemic numbers, such as lockdown policies and large-scale social restrictions. With no exception, an economic decline has also been felt by Indonesia of up to −2.07% (YoY) [1,2,3,4,5,6,7]. The manufacturing sector and service operations are the main driving force for economic growth [8,9,10,11].

In 2019, the contribution of the manufacturing sector to the Indonesian economy was 19.70 percent. This contribution was higher than the business and agricultural sectors, which contributed 13.01 percent and 12.72 percent, respectively. Apart from contributing through value-added products, the manufacturing industry is also able to provide jobs. In 2019, the processing industry was able to employ a workforce of 14.96 percent of the total workforce in Indonesia. The era of globalization and information also encourages changes in the socioeconomic structure in society. Previously, economic policies that were centered on priority sectors, namely large-scale industries, have now changed to be more inclusive by helping all sectors to develop, including the SMEs businesses [12,13,14].

The development of a processing industry at the scale of the SMEs is seen as important. The 2015–2035 National Industrial Development Master Plan (RIPIN) places small-scale industries in the long run as a contributor to the national economy. The policies implemented include creating a supply chain in synergy between the subsectors of the manufacturing industry. In addition, equal distribution of industrial development and industrial estates is developed based on the potential resources of each region.

From the results of the 2019 Annual SMEs Survey, the number of SME businesses/companies in Indonesia was recorded at 4.38 million businesses/companies. Java Island is the island with the highest number of SMEs. The number of IMK in Java Island reached 62.26 percent of all SMEs in Indonesia. The provinces of Central Java, East Java, and West Java are the provinces with the highest number of IMK, where each has more than 500 thousand businesses/companies. This condition is very different from Maluku and Papua Provinces where the number of businesses in each reaches less than 30 thousand businesses/companies [15].

Economic indicators such as the SMEs have interregional interaction. In other words, the economic condition in a certain region can affect the nearest regions [16]. Consequently, the condition of SMEs also relies on the surrounding area, where they usually get production goods from the neighboring region [17]. As well as the economic conditions, the population dynamics in a region can affect the development of the regions nearby, particularly the vulnerability of businesses there [16].

Therefore, it is necessary to reanalyze business vulnerability to cluster which areas need special attention. One of the vulnerability analyses that can be used is the clustering approach that was implemented by Rufat [18] using hierarchical clustering. Moreover, it is also essential to consider the spatial interaction in analyzing the business vulnerability of SMEs. Nasution et al. [19] used fuzzy geographically weighted clustering (FGWC) with intelligent firefly algorithm (IFA) to assess the distribution of regional social vulnerability to natural hazards.

Cluster analysis, or so-called group analysis, is used to classify objects of observation, based on [19,20,21,22], which are divided into hard and soft (fuzzy) clustering [23,24,25]. Grouping in hard clustering is performed by maximizing the homogeneity of the observed objects and making them belong to a cluster [26,27,28,29], while fuzzy clustering is based on the fuzzy logic that assumes that an object can be belong to more than one cluster to a certain degree [30]. Considering the spatial interaction of economic conditions, we attempt to implement the hybrid fuzzy geographically weighted clustering (FGWC) with optimization algorithms to cluster the business vulnerability in Indonesia at a district level. The hybridization is important because FGWC has the disadvantages of sensitivity and the local optimum trap [19,31].

There are several modifications that have been done to improve the FGWC local and global weakness [31], such as metaheuristic optimization [30], spatial interaction [32], distance matrix [33], or context-based and fast computing such as CUDA [34]. A well-known modification of FGWC is using metaheuristic optimization algorithms. The FGWC with metaheuristic optimizations has been done in various cases such as the Artificial Bee Colony (ABC) for crime clustering in USA [30], Intelligent Firefly Algorithm (IFA) for social vulnerability profiling in Indonesia [22], and Particle Swarm Optimization (PSO) for the East Java dengue fever case [35]. The Gravitational Search Algorithm (GSA) has also been implemented and proven to optimize the FGWC clustering results [36].

However, the algorithms mentioned above have some weaknesses. For example, the PSO and ABC are easily trapped in local optima and have slow convergence [37,38]. Moreover, the dependency between agent interactions in the IFA and GSA increases computational costs [19,39]. On the other hand, there is also an algorithm that has been used in hard clustering [40], but has not yet been implemented in FGWC, namely the Flower Pollination Algorithm (FPA). The FPA is an algorithm that is inspired by the pollination process of flowers. The FPA has advantages in the balance between the local and global search to find the best solution and creates fast convergence [41]. The FPA has been proven to outperform many metaheuristic optimizations including ABC, GSA, IFA, and PSO [37,42,43,44]. Moreover, the FPA has been implemented to optimize various cases such as engineering, image processing, networks, and even clustering [40,44,45,46,47]. Thus, we propose the implementation of the FPA into FGWC to analyze business vulnerability. We evaluate the performance of the FPA along with the classical FGWC and its four predecessor algorithms, namely ABC, GSA, IFA, and PSO. These algorithms have been implemented in the naspaclust package in R [48].

This paper consists of five sections. Section 2 briefly explains the data source used in this study, which are SUSENAS and SAKERNAS, along with a brief explanation of the naspaclust package. Section 3 discusses the methodologies and research workflow used in this study, including the evaluation method to assess the clustering performance. Section 4 provides the performance and selected clustering results, with the addition of discussion for deeper analysis. This paper gives a summary of everything as well as policy implications in Section 5.

2. Materials and Methods

This research implements the use of machine learning [49,50]. The complexity of the characteristics dataset requires precision in selecting relevant statistical analysis methods and can overcome the balance and outliers of the classification process [51,52,53]. We have identified data distribution assumptions, minimized errors to get good accuracy, and have displayed the assumptions in the form of a dashboard. In answering the objectives of this study, we used data sourced from Statistics Indonesia, namely the National Socioeconomic Survey and the National Labor Force Survey. At the stage of establishing the MSME business vulnerability cluster (BVC), this study used locations that are included in the category of disadvantaged, frontier, and outer regions of Indonesia (

Table 1. SUSENAS question block.

Information, technology, and communication	[R701] Do you use a cell phone?
	[R702] Do you have a cell phone?
	[R703] Do you use a computer (pc/desktop, laptop/notebook/tablet?
	[R704] Have you ever accessed the internet (including Facebook, Twitter, BBM, and WhatsApp)?
Access to financial services	[R2101] How many adult household members (15 years and over) have savings in formal financial institutions (banks, cooperatives, etc.)?
Description of sources of income household	[R2301A] What is the main source of financing?

SUSENAS question block). This category was defined by Presidential Regulation (PERPRES) Number 63 of 2020 concerning the determination of frontiers, outermost and least developed regions in 2020–2024, often referred to as “3T” (terdepan, terluar, tertinggal) regions and including as many as 62 regions.

2.1. The National Socioeconomic Survey (SUSENAS)

SUSENAS is a source of socioeconomic data on households in Indonesia [54,55]. In general, the purpose of collecting data through SUSENAS is the availability of community welfare that can reflect the socioeconomic conditions of the community. Specifically, the SUSENAS targets are: availability of basic data on community welfare at the district/city level and compiling detailed data on housing and health at the provincial level. The compilation of detailed data on household consumption expenditure, both in rupiah value and in quantity, is used as a basis for estimating consumption patterns, population size, nutritional adequacy, distribution of expenditures, and poverty at the national level. The question blocks that will be used in this research are represented in Table 1.

2.2. The National Labour Force Survey (SAKERNAS)

SAKERNAS is a special survey to collect employment data. The manpower data collection through SAKERNAS has three main objectives. The three objectives are to determine: (1) employment opportunities and their relation to education, number of hours worked, types of work, employment opportunities, and employment status; (2) unemployment and underemployment; and (3) people who are included in the nonlabor force category, namely, those who go to school, take care of the household and carry out other activities.

Table 2. SAKERNAS question blocks.

General characteristics	What is the highest certificate/STTB owned rank: Do not have SD certificate, Package A, SDLB, SD/MI, Package B, SMPLB, SMP/MTS, Package C
	Has (NAME) ever received any training/courses/training and obtained a certificate?
	Is (NAME) currently attending any training/courses/training (does not have to be certified)?
The main job	What was the main business field/line of work of the place (NAME) worked during the past week?
	What is the type of occupation/position of the main job (NAME) during the past week?
	How long has (NAME) been looking for a job/preparing for a business in the main job?
	Is there a certain party (individual/business/company) that regulates/coordinates the business/work (NAME)?
	How many workers/employees/employees are paid?
	Did (NAME) use digital technology in their main job during the past week?
	Did (NAME) use the internet in their main job during the past week?
	Is the internet used for: 1. Communication 2. Promotion 3. Carrying out the process of selling goods/services via email/social media (Instagram, Facebook, Twitter, etc.)/instant messaging services (LINE, Whatsapp, Telegram, etc.) 4. Carrying out the process of selling goods/services through the website/marketplace application (Tokopedia, Bukalapak, OLX, etc.) 5. Others, please explain……………………
	How does the agency/institution/company/business where (NAME) works do financial accounting?
	Are the goods/services produced from work a week ago prioritized for their own use?
	Number of working days, income and wages/salary.
	What is the type of agency/institution from the workplace/business of (NAME)?
	What is the main location of the workplace/business (NAME) at home?
Work experience	Has (NAME) ever had a previous occupation/main business?
	Has (NAME) stopped working from the main job/business in the past year?
	What was the main reason (NAME) stopped working at the main job/business during the past year? Layoffs 1 Business closes/goes bankrupt 2 Income is not satisfactory 3 Not suitable for the work environment 4 Out of work period/contract 5 Not in accordance with skills/skills gained 6 Pregnant/giving birth/childbirth 7 Taking care of the household 8 Cannot be classified into codes 1–8, write:……………………… 9
	What was the status/position of (NAME) before resigning from the last main job/business?
	Doing business alone (1) Doing business assisted by temporary workers/workers (2)

describes the question blocks that will be used in this study.

2.3. Nature-Inspired Spatial Clustering: The Naspaclust Package

Naspaclust is an abbreviation of nature-inspired spatial clustering. This is an R package that accommodates the optimization spatial clustering results of Fuzzy Geographically Weighted Clustering using nature-inspired metaheuristic algorithms [48]. There are two types of algorithm in the package: classical and optimized. The classical algorithm implements the FGWC that was developed by Mason and Jacobson in 2007 [56]. On the other hand, there are seven optimization algorithms that were developed in this package that was constructed from many previous studies (see [48] for details). However, this study limits the optimization algorithms to five, namely the ABC [14], FPA, GSA [36], IFA [19], and PSO [57,58,59,60]. The optimization of these algorithms mainly used the centroid approach that was developed by Runkler and Katz [61], and then this approach was implemented into FGWC [19,30,31,62] so that it could be used to produce a controllable parameter solution.

3. Methodology

3.1. Data and Algorithms

This study mainly uses data from two sources, the SUSENAS and SAKERNAS. We obtained the sample’s information with criteria that they be older than 15 years old and have an enterprise with paid employees. Subsequently, the data were aggregated into the district level. As the filtering rules applied, we obtained only 503 districts that fulfilled the criterion, instead of 514. All the algorithms mentioned above had been implemented in FGWC, except the FPA. Thus, this study also proposes the FPA algorithm to optimize the clustering results of business vulnerability in Indonesia. The FPA is a metaheuristic algorithm that was inspired by the pollination of the flower by the insects. FPA had previously been implemented in various studies, including those using FCM and was proven to optimize the FCM clustering results [40].

3.2. Flower Pollination Algorithm

The FPA is a metaheuristic algorithm that is inspired by the pollination of plants [37]. The goal of the FPA is the “survival of the fittest” of the plants by considering the parameters for the most optimal reproduction, which in this case is the best objective function [47]. In this study, the objective function to be optimized is fuzzy clustering with the centroid approach and the parameter is the centroid [19,30,61]. There are two types of pollination: crosspollination, or global pollination, and self-pollination, or local pollination. Local pollination is fertilization from the same plant, regardless of the flower difference. Normally, the self-pollination uses wind and water so that it cannot move at a long distance [46]. On the other hand, crosspollination occurs through pollen from a different plant. Usually, the pollen is carried by pollinators who are long-distance flyers such as insects [44]. Mathematically, the long flights correspond to the Levy Flights behavior which fulfils the Levy distribution [37]. The selection of cross and self-pollination depends on the switching probability between 0 and 1 [43]. In summary, the pseudocode of FPA implementation in FGWC can be seen in Appendix A.

3.3. Research Workflow

This study started by running the combination of methods as well as the number of clusters. Furthermore, we obtained the validation indices for each combination to be evaluated. We did not only compare the clustering performance based on the objective function but also the validation indices. We assessed which algorithm performed best in this study. The latter subsection briefly explains the evaluation methods.

After selecting the best algorithm, we then determined the optimum number of clusters by comparing the objective function as well as the validation indices. Despite determining the optimum value via the minimum or maximum values, we also used the elbow method and considered the optimum value in determining the optimum number of clusters. The elbow method has been widely used in order to get the optimum clusters in a certain algorithm [19]. Moreover, we could also use the maximum or minimum value of the indices to get the optimum number of clusters [63]. The selected number of clusters was used to analyze the business vulnerability condition in Indonesia.

3.4. Evaluation Method

The objective function is not enough to evaluate the performance of fuzzy clustering. Thus, the performance between the algorithms was compared using fuzzy clustering validation indices. Since the metaheuristic optimization has a random characteristic, this study performed 50 simulations for each combination of algorithm and number of clusters with different initialization. The sample of 50 is considered as a large random sample according to the statistical principle that uses a minimum sample of 30 [64]. Moreover, the previous study of Mehdizadeh [65] only used 10 simulation runs in his study of Fuzzy PSO, which is small enough to become a random sample. Subsequently, this study calculated the average of each evaluation method to be compared between the algorithms. We also performed a Nonparametric Kruskal-Wallis test to assess whether there was a difference between each algorithm’s average performance [64]. A brief explanation of the validation indices can be seen as follows:

(1)

Partition coefficient (PC)

The partition coefficient reflects the overlap between the fuzzy subsets and relies on the membership coefficients. Therefore, it lacks the additional consideration of the data and centroid. The partition index is calculated using [20].

$$PC=\frac{1}{n}{{\displaystyle \sum }}_{i=1}^c{{\displaystyle \sum }}_{j=1}^n{\mu }_{ij}^2$$

(1)

(2)

Classification entropy (CE)

CE represents the fuzziness between clusters. Based on the equation, CE index value will always range from 0 to ${\log }_{a}c$. Thus, low CE index shows a more optimal cluster. The CE index is calculated as follows [20]

$$CE=-\frac{1}{n}{{\displaystyle \sum }}_{i=1}^c{{\displaystyle \sum }}_{j=1}^n{\mu }_{ij}{\log }_a{\mu }_{ij}$$

(2)

(3)

Separation index (S)

The S index is a proportion of the objective function value to the minimum cluster separation. The minimum S index displays a an optimal cluster partition. On the other hand, the sum of the distances between centroids reflects the cluster separation [66].

$$S=\frac{{{\displaystyle \sum }}_{j=1}^c{{\displaystyle \sum }}_{i=1}^n{\mu }_{ij}^m\Vert x_i-v_j{\Vert }^2}{n{\min }_{j,k}\Vert v_k-v_j{\Vert }^2}$$

(3)

(4)

Xie and Beni index (XB)

Along with the SC index, the XB index shows the variation magnitude between clusters as well as the separation clarity [66].

$$XB=\frac{{{\displaystyle \sum }}_{j=1}^c{{\displaystyle \sum }}_{i=1}^n{\mu }_{ij}^m\Vert x_i-v_j{\Vert }^2}{n{\min }_{i,j}\Vert x_i-v_j{\Vert }^2}$$

(4)

(5)

IFV index

The IFV index is often used to validate spatial clustering due to its robustness and stability [67]. A maximum IFV index value reflects a good spatial cluster separation. The IFV index is measured using the equation:

$$IFV=-\frac{1}{c}{{\displaystyle \sum }}_{j=1}^c\{\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n{\mu }_{ij}^2{\left[{\log }_{2}c-\frac{1}{n}{\log }_2{\mu }_{ij}\right]}^2\}\frac{{\max }_{k,j}\Vert v_k-v_j{\Vert }^2}{\overline{{\sigma }_d}}$$

(5)

$$\overline{{\sigma }_d}=\frac{1}{c}{{\displaystyle \sum }}_{j=1}^c(\frac{1}{n}{{\displaystyle \sum }}_{i=1}^n\Vert x_i-v_j{\Vert }^2)$$

(6)

3.5. Parameter Setups

There are two kinds of parameters in this study, namely the FGWC and optimization algorithms. For the FGWC, we first set the fuzzifier = 2. Subsequently, we increased the spatial effect, as recommended by Mason and Jacobson [56], of the membership configuration to 70% so that $\alpha =0.3$. On the other hand, for the spatial weight, we made the same influence of interregional population and distance that was adapted from previous studies [30,56], so that a = b = 1. Last but not least, we set epsilon = 1 × 10⁻⁶ for the error tolerance, which is lower than Nasution et al. [19], to make sure that we obtained the best solution.

From the optimization point of view, we set the number of populations for the candidates to 15. Next, we set the extra termination for each algorithm when the global solution did not change 15 times. For the PSO algorithm, we set the inertia weight update using the simulated annealing. This is because the simulated annealing is one of the weights that produced optimum solutions in a previous study [68]. The rest of the parameter setups can be seen in

Table 3. Optimization algorithm parameter setups.

Algorithm	Parameters
ABC	$n_{onlooker }=5, limit=5$
FPA	$\gamma =1.2, \mathsf{\lambda }=1.5,\mathrm{p}=0.7$
GSA	$G=1,v_{max}=0.7$
IFA	$\mathsf{\gamma }=1,\mathsf{\beta }=1.5,{\mathsf{\alpha }}_{\mathrm{k}}=1$
PSO	$v_{max}=0.7,c_1=0.7,c_2=0.6,w_{min}=0.2,w_{max}=0.9$

.

In ABC, $n_{onlooker}$ is the number of onlooker bees, and $limit$ is number of turns to do the elimination. In FPA, $\gamma$ and $\mathsf{\lambda }$ is the levy step size factor and shift, while $\mathrm{p}$ is the switch probability. Furthermore, $G$ in GSA is the initial gravitational constant and $v_{max}$ is the maximum velocity for the agents. In IFA, $\mathsf{\gamma }$ and $\mathsf{\beta }$ represent the scaling factor for distance and attractiveness, while ${\mathsf{\alpha }}_{\mathrm{k}}$ is the randomization constant. PSO had more parameters than the other algorithms. $v_{max}$ is the maximum velocity for particles, $c_1$ and $c_2$ are the cognitive and social scaling parameters, while $w_{min}$ and $w_{max}$ are the minimum and maximum inertia weight, respectively.

4. Results

4.1. Performance Evaluation

Table 4. Performance evaluation summary.

Performance Measurement	C	FGWC Algorithms
		CLASSIC	ABC	FPA	GSA	IFA	PSO
Objective function	2	1.3546 × 106	1.3538 × 106	1.3497 × 106	1.3544 × 106	1.3545 × 106	1.3544 × 106
	3	9.0303 × 105	9.0241 × 105	8.9936 × 105	9.0288 × 105	9.0295 × 105	9.0288 × 105
	4	6.7728 × 105	6.7696 × 105	6.7426 × 105	6.7719 × 105	6.7722 × 105	6.7719 × 105
	5	5.4182 × 105	5.4162 × 105	5.3957 × 105	5.4176 × 105	5.4178 × 105	5.4175 × 105
	6	4.5152 × 105	4.5136 × 105	4.4970 × 105	4.5147 × 105	4.5149 × 105	4.5146 × 105
	7	3.8701 × 105	3.8689 × 105	3.8554 × 105	3.8698 × 105	3.8699 × 105	3.8698 × 105
	8	3.3864 × 105	3.3856 × 105	3.3740 × 105	3.3861 × 105	3.3862 × 105	3.3861 × 105
	9	3.0101 × 105	3.0090 × 105	3.0002 × 105	3.0099 × 105	3.0100 × 105	3.0099 × 105
	10	2.7091 × 105	2.7084 × 105	2.7009 × 105	2.7089 × 105	2.7090 × 105	2.7089 × 105
PC Index	2	5.0000 × 10−1	5.0722 × 10−1	5.2241 × 10−1	5.1076 × 10−1	5.0093 × 10−1	5.0354 × 10−1
	3	3.3333 × 10−1	3.4143 × 10−1	3.5743 × 10−1	3.4124 × 10−1	3.3418 × 10−1	3.3974 × 10−1
	4	2.5000 × 10−1	2.5882 × 10−1	2.7072 × 10−1	2.5596 × 10−1	2.5080 × 10−1	2.5246 × 10−1
	5	2.0000 × 10−1	2.0537 × 10−1	2.1398 × 10−1	2.0492 × 10−1	2.0053 × 10−1	2.0380 × 10−1
	6	1.6667 × 10−1	1.7195 × 10−1	1.7687 × 10−1	1.7186 × 10−1	1.6712 × 10−1	1.6815 × 10−1
	7	1.4286 × 10−1	1.4687 × 10−1	1.5209 × 10−1	1.4701 × 10−1	1.4324 × 10−1	1.4289 × 10−1
	8	1.2500 × 10−1	1.2891 × 10−1	1.3141 × 10−1	1.2884 × 10−1	1.2525 × 10−1	1.2503 × 10−1
	9	1.1111 × 10−1	1.1425 × 10−1	1.1630 × 10−1	1.1459 × 10−1	1.1134 × 10−1	1.1113 × 10−1
	10	1.0000 × 10−1	1.0201 × 10−1	1.0412 × 10−1	1.0257 × 10−1	1.0014 × 10−1	1.0002 × 10−1
CE Index	2	6.9315 × 10−1	6.8589 × 10−1	6.7032 × 10−1	6.8229 × 10−1	6.9221 × 10−1	6.8958 × 10−1
	3	1.0986 × 100	1.0866 × 100	1.0603 × 100	1.0868 × 100	1.0973 × 100	1.0890 × 100
	4	1.3863 × 100	1.3688 × 100	1.3390 × 100	1.3744 × 100	1.3847 × 100	1.3814 × 100
	5	1.6094 × 100	1.5961 × 100	1.5680 × 100	1.5972 × 100	1.6081 × 100	1.5999 × 100
	6	1.7918 × 100	1.7761 × 100	1.7534 × 100	1.7762 × 100	1.7904 × 100	1.7873 × 100
	7	1.9459 × 100	1.9322 × 100	1.9051 × 100	1.9314 × 100	1.9446 × 100	1.9458 × 100
	8	2.0794 × 100	2.0641 × 100	2.0463 × 100	2.0641 × 100	2.0784 × 100	2.0793 × 100
	9	2.1972 × 100	2.1834 × 100	2.1672 × 100	2.1816 × 100	2.1962 × 100	2.1971 × 100
	10	2.3026 × 100	2.2927 × 100	2.2764 × 100	2.2897 × 100	2.3019 × 100	2.3025 × 100
S Index	2	4.6807 × 107	1.0339 × 102	1.5034 × 101	3.1627 × 102	1.0507 × 103	4.9634 × 102
	3	6.8092 × 1010	1.2966 × 103	2.5468 × 103	1.2263 × 103	9.5055 × 103	4.3475 × 103
	4	9.6128 × 1011	1.1329 × 103	1.3652 × 104	2.8750 × 103	1.3684 × 104	8.5458 × 103
	5	2.4582 × 1012	2.7337 × 103	2.4891 × 104	1.2615 × 104	2.6536 × 104	1.1127 × 104
	6	3.6300 × 1013	1.8326 × 103	8.0931 × 104	5.1090 × 102	2.1415 × 104	9.7044 × 103
	7	4.1404 × 1013	6.9357 × 103	5.1912 × 104	2.6892 × 103	6.6719 × 104	1.7776 × 104
	8	2.5955 × 1013	7.8481 × 103	9.2450 × 104	1.6523 × 103	5.4829 × 104	3.0956 × 104
	9	2.3469 × 1013	7.0561 × 103	1.0135 × 105	1.4089 × 103	3.3104 × 104	2.4702 × 104
	10	2.5988 × 1015	1.0877 × 104	1.9946 × 105	1.7557 × 104	4.1839 × 104	4.1954 × 104
XB Index	2	4.0829 × 100	4.2544 × 100	4.1573 × 100	4.2736 × 100	4.1352 × 100	4.1909 × 100
	3	2.7219 × 100	2.8401 × 100	2.8319 × 100	2.8610 × 100	2.7720 × 100	2.8337 × 100
	4	2.0414 × 100	2.1693 × 100	2.1693 × 100	2.1557 × 100	2.0831 × 100	2.1092 × 100
	5	1.6331 × 100	1.7233 × 100	1.7308 × 100	1.7263 × 100	1.6655 × 100	1.7135 × 100
	6	1.3609 × 100	1.4438 × 100	1.4379 × 100	1.4574 × 100	1.3914 × 100	1.4078 × 100
	7	1.1665 × 100	1.2400 × 100	1.2446 × 100	1.2472 × 100	1.1928 × 100	1.1910 × 100
	8	1.0207 × 100	1.0864 × 100	1.0690 × 100	1.0923 × 100	1.0418 × 100	1.0399 × 100
	9	9.0729 × 10−1	9.5956 × 10−1	9.5982 × 10−1	9.7005 × 10−1	9.2428 × 10−1	9.2411 × 10−1
	10	8.1656 × 10−1	8.5981 × 10−1	8.5519 × 10−1	8.6651 × 10−1	8.3250 × 10−1	8.3358 × 10−1
IFV Index	2	2.3289 × 10−8	1.1365 × 10−2	8.2913 × 10−2	4.1144 × 10−3	1.2061 × 10−3	2.6313 × 10−3
	3	4.0231 × 10−8	3.2324 × 10−2	2.0135 × 10−1	1.4923 × 10−2	4.7535 × 10−3	1.3659 × 10−2
	4	4.9924 × 10−8	3.7302 × 10−2	3.2216 × 10−1	1.7016 × 10−2	6.0455 × 10−3	1.2509 × 10−2
	5	4.0018 × 10−8	3.6548 × 10−2	3.7416 × 10−1	2.0551 × 10−2	7.0764 × 10−3	1.8697 × 10−2
	6	2.9146 × 10−8	4.2314 × 10−2	4.1691 × 10−1	2.4747 × 10−2	8.3875 × 10−3	1.5328 × 10−2
	7	2.4576 × 10−8	4.1615 × 10−2	4.5595 × 10−1	2.2740 × 10−2	7.8361 × 10−3	9.4770 × 10−3
	8	2.2690 × 10−8	3.4981 × 10−2	4.6065 × 10−1	2.3783 × 10−2	7.6422 × 10−3	9.2776 × 10−3
	9	2.2372 × 10−8	5.4328 × 10−2	4.8662 × 10−1	2.3515 × 10−2	7.4486 × 10−3	9.1279 × 10−3
	10	2.0450 × 10−8	3.7936 × 10−2	4.3299 × 10−1	2.1008 × 10−2	7.1109 × 10−3	8.5118 × 10−3
Computational time (seconds)	2	0.561	108.347	32.218	13.996	86.177	16.162
	3	0.799	100.495	30.331	12.932	77.502	13.480
	4	0.734	112.403	36.463	15.897	94.718	17.125
	5	0.910	83.480	31.878	14.340	85.477	13.678
	6	0.906	103.444	38.463	17.064	105.026	21.565
	7	0.974	124.028	41.173	18.286	108.363	19.510
	8	1.013	94.965	33.810	16.148	82.565	15.617
	9	1.111	118.785	40.832	20.101	118.395	21.933
	10	1.118	104.519	38.686	17.916	81.331	11.986
Number of iterations	2	11.440	32.380	36.940	15.080	17.840	18.140
	3	12.420	34.420	38.280	15.440	17.840	16.740
	4	12.780	30.420	38.100	15.440	17.800	17.300
	5	13.320	26.480	36.340	15.440	17.840	17.260
	6	13.640	25.300	36.200	15.000	17.840	19.820
	7	13.780	29.380	36.960	15.160	17.840	19.820
	8	13.860	26.880	34.140	15.040	17.880	20.460
	9	13.900	25.520	33.340	15.040	17.880	20.360
	10	13.960	27.260	35.720	15.400	17.920	19.020

Bold: the values are the average values from 50 simulations for each combination.

disseminates the clustering performance summary based on the algorithms and number of clusters. The bolded values show the best performance value in the number of clusters. We compile the average results of each simulation regarding the performance in this study, namely the objective function, PC, CE, S, XB, and IFV indexes. Based on the table, it can be seen that from the objective function, PC, CE, and IFV, the FPA performs best among all algorithms. In contrast, the classical algorithm performs best in most numbers of clusters in terms of the XB index. Meanwhile, the other validation indices such as FPA showed various best algorithms depending on the index and number of clusters. If we look at the details, the optimum performance was principally obtained by the FPA, although in some numbers of clusters, the ABC and GSA performed best.

In terms of computational cost, traditional FGWC provided the lowest computational cost compared to the other algorithms. By looking at the number of iterations, it can be seen that FGWC had the lowest iterations below 20 iterations with the poorest performance. The same pattern also occurred with the GSA and IFA optimization. However, looking at the performance evaluation, it can be seen that they performed worse than the FPA. This means that in the case of business vulnerability, the algorithms other than the FPA tended to converge toward the local optimum. Meanwhile, the FPA had more optimum solutions, although it required more iterations.

Figure 1 supports the finding of the comparison of the methods. We employed the Kruskal-Wallis test to see whether there was a significant difference in the evaluation results between each method and plotted them using tile plot to make the interpretation straightforward. To make the comparison fairer, we only compared the optimized algorithms. Based on Figure 1, it can be seen that the chi-square value of the test inside of the tile plot is high for all the combinations of number of clusters and evaluation methods. In other words, there is a difference in the evaluation metrics among the optimization methods. By combining the previous finding and the statistical significance, we can conclude that the FPA is suitable to optimize the clustering results of business vulnerability.

4.2. Clustering Results

The previous subsection showed that the FPA is the best method to be used in this study. This subsection explains the clustering results using FPAFGWC. This section starts from the selection of the optimum number of clusters and then the interpretation of clustering results.

Figure 2 shows the FPAFGWC clustering results based on the objective function and validation indices. We visualized the results to make a more straightforward decision about the optimal number of clusters. Based on the figures, it can be seen that the objective function, PC index, and XB index in Figure 2a,b,e tend to make the same pattern where the values decrease as the number of clusters increases. On the other hand, the CE and IFV index in Figure 2c,f shows the opposite. Surprisingly, the SC index in Figure 2d shows volatility between the number of clusters.

Based on the figures, it can be seen that the objective function, XB, and IFV indexes could be used as our basis for using the elbow method because the PC and CE indexes showed an inversed relationship than they should have across the number of clusters. From the objective function and XB index, it can be seen that the “elbow” was formed in four clusters. Subsequently, the values tend to decrease slightly. Meanwhile from the IFV index, the “elbow” was directly formed in three clusters, with the following tending to have close value. From the PC and CE indexes, the optimal number of clusters was two, considering the best value. Moreover, from the SC index, it can be seen that the values increased from two to three clusters, although it decreased when the number of clusters was four and five. From the analysis above, we found that two and three were the optimal number of clusters for the business vulnerability analysis. Considering the purpose of this study to find which regions are vulnerable, we chose two clusters to be analyzed.

Figure 3 shows the business vulnerability profile and

Table 5. Cluster mean using FPAFGWC.

Cluster	Use_Cellph	Have_Cellph	Use_Pc	Acc_Int	Saving	Credit_A	Credit_B	Credit_C	Credit_D
1	88.25552	80.55931	15.37845	27.27296	34.50903	9.506159	10.82205	2.227692	4.093793
2	89.42493	85.69444	27.77035	47.54352	45.87103	11.127022	12.41292	3.176292	5.00927
	sour_money	edu	course	job_dur	no_empl_14	no_empl_519	digitech1	digitech2	digitech3
1	96.96485	46.61807	88.37956	44.57606	84.07763	14.43613	10.33827	39.21705	24.71888
2	96.38307	63.90895	83.51627	47.63658	80.92	16.39125	24.34142	68.87062	40.24244
	job_int	jobint_use1	jobint_use2	jobint_use3	jobint_use4	financebook	work_org	work_loc	prev_work
1	25.97092	25.30045	11.53989	10.93522	2.296787	55.59538	94.41761	30.41872	49.09258
2	61.53131	60.9503	33.52371	34.04755	9.251676	71.5543	92.99104	38.11023	59.03073

displays the cluster mean using FPAFGWC with two clusters. The details of the variable names in Table 5 can be seen in Appendix B. Based on the figure, it can be seen that Cluster 1 dominates almost the whole of Indonesia. Meanwhile, Cluster 2 mostly spreads around Java Island, including the JABODATABEK (Jakarta, Bogor, Depok, Tangerang, and Bekasi) area, though it includes some districts in Kalimantan and one district in Sumatera. Based on the cluster mean, it seems that there are some variables with a slight mean difference between clusters, such as the money source from the working household member, which produce relatively the same percentage. On the other hand, the means in Cluster 1 tend to be smaller than Cluster 2, except for training, micro enterprise, and household work organization. Thus, we can conclude that Cluster 1 is the vulnerable cluster and Cluster 2 is the nonvulnerable cluster. The vulnerability in Cluster 2 occurred because of the lower percentage of people who are trained, the lower percentage of micro enterprises, and the household work organization. This is due to the fact that Java is the most developed area in Indonesia and has many industrial areas.

5. Discussion

Our results showed that the optimization algorithm produced better results in optimizing the FGWC. This is consistent with the previous studies that found that the modification of FGWC can lead to a better clustering quality. The modification is not just limited to the metaheuristic optimization but also the modification of the spatial interaction [32], distance matrix [33], or the hybridization of context-based and fast computing like CUDA [34]. On the other hand, comparing the optimization algorithms, the FPA has the best performance in optimizing the FGWC clustering result in the business vulnerability context. This finding is consistent with the previous studies that found that the FPA outperforms the other metaheuristics algorithms [37,43,44]. Furthermore, Dhal [40], Kaur et al. [47], as well as Agarwal and Mehta [46], also found that the FPA performs well in optimizing clustering results. This study also used a switching probability of 0.7, which is close to Yang [37], who stated that 0.8 works better in several studies. Future studies may improve FPA optimization using some modifications, such as multiobjective FPA [69], distance steps setting using other distributions as in [70], implementing CUDA for increasing speed [34], etc.

Furthermore, for the clustering results, we found that Cluster 1 tends to be vulnerable. The regions are mostly spread through the whole of Indonesia except Java island. In 2020, the government imposed Act. No. 63 concerning the “3T” region. Interestingly, all the regions which comprise Cluster 1 were included. The “3T” regions are mostly located outside of Java island and are spread out. The data from BPS-Statistics Indonesia showed that only 37.74 percent of SMEs are located outside Java Island [71]. This should be concerning to government. The area outside Java mostly lacks phone signal. Moreover, the population of the border areas that are not often visited still live traditionally. The only customers of the businesses in these areas are the local people. An internet signal would be useful to increase the marketing strategy and promote their enterprises. When enterprises have internet access, their shops will be more easily noticeable to customers, and this will increase the chance of sales.

On the other hand, Cluster 2 is not a vulnerable area. It is mostly spread on Java island, particularly the JABODETABEK area. Based on the BPS, 62.26 percent of SMEs were located in Java island in 2019 [71], which shows the domination of SMEs by Java. Moreover, the area in Cluster 2 that is outside Java island are mostly city areas, such as Lhokseumawe in Aceh, Bandar Lampung and Metro in Lampung, Palangkaraya and Kota Baru (Baru City) in Central Kalimantan, etc. Nonetheless, the cities on Java island in Cluster 2 were mostly included in the Inflation City Survey by BPS-Statistics Indonesia. City areas tend to have easier access to the internet. The dense population triggers economic activity and with the addition of the internet, marketing to engage customers is easier.

Although there are some cities in Cluster 1, they also have problems that make them vulnerable in business. The Ministry of Cooperation and Small-Medium Enterprises (MCSMEs) asserted that there are four main problems in SMEs [72]. One of the main problems is the limitation of human resources. The limitation of knowledge access about business as well as the lack of business mentors makes it difficult for the SMEs to grow. From the marketing side, the lack of creativity and difficulties in goods and services distribution becomes the main problem. However, the online approach and increasing personal branding are ways to overcome this problem. The third problem is lack of access to enterprise capital, which limits production or optimal usage. Last but not least, the unlegalized SMEs still dominate the sector, making up approximately 98.68%.