Swarm intelligence and ant colony optimization in accounting model choices

Abstract

Current accounting methods for small and medium-sized enterprises (SMEs) have long running times and low user satisfaction. Therefore, a method for the selection of accounting models for SMEs based on accounting market big data (AMBD) is proposed in this paper. Firstly, some indicators such as the current ratio, quick ratio, asset-liability ratio, accounts receivable turnover rate, and other indicators taken from the solvency, operating capacity, profitability, and growth capacity of a company are selected to set up an AMBD constraint system. Then, the principal component analysis method is used to achieve the classification of the constraints of the AMBD. Finally, by combining particle swarm optimization with ant colony optimization, the optimal accounting model is obtained through iteration. Experimental results show that the proposed method has high efficiency and user satisfaction, and achieves a high coefficient of rationality. Furthermore, the method incorporates the constraints found in the AMBD, and meets the selection requirements of the SME accounting model.

Keywords

Ant colony optimization swarm intelligence accounting big data market constraints accounting models choice

1 Introduction

Current accounting methods are based on the generation and development of traditional data environments [1]. However, big data is having a huge impact on today’s global economy, and it has also caused setbacks to traditionally-developed accounting models. With the continuous emergence of relevant data, accounting market big data (AMBD)is bound to have an irreversible impact on current accounting methods [2, 3]. Therefore, the accounting model should be reformed to meet the current requirements. The environment is so big that we need to re-examine how to choose accounting modelsefficiently.

Ding Shenghong analyzed the general characteristics of “Internet Plus” from the perspective of human rights in [4]. Its impact on the transformation of property rights to human rights was obtained. According to Maslow’s Hierarchy of Needs, the choice of measurement method for human capital accounting confirmation is explored as one of the human rights accounting products in the era of “Internet Plus”. There are two alternative hypotheses of completely low-level demand and high-level demand, human capital accounting of their respective human rights accounting reporting modes. Under the above assumptions, Shenghong summarizes the exploration of human capital accounting infrastructure theory. The process is simple; however, user satisfaction from the process is low.

The current “three phases of superposition” in China, the “new normal” and the scientificconnotation of the grim situation at home and abroad are explained by Liu Jinbin in [5]. The new requirements of the “new normal” on corporate environmental accounting information disclosure are revealed. Using the “four comprehensive” elements of strategic thinking, meanwhile, relying on the state to promote the national governance system and the modernization of governance capabilities, different disclosure models in different companies based on the comprehensive classification of enterprises are proposed. The method discloses different environmental accounting information and accepts the construction of information disclosure modes of environmental accounting enterprises with different regulatory requirements. This method has a high operating efficiency; however, the rationality coefficient is low.

Tang Mei proposes that the tea market in the Central Plains Economic Zone is becoming more competitive [6]. If tea production enterprises are to gain a foothold and develop in such a fierce market, Mei claims, they must rely on and adopt more scientific and effective management methods. Furthermore, cost accounting is an important part of the production, operation, and management of tea companies. Tea companies can understand their own production and operation conditions and the dynamic needs of the tea market in a timely manner by accounting for costs in production and operations. This can help enterprises to achieve the optimal allocation of resources and rational use of tea production and operation, so as to obtain the benefits of growth. Combining the status and characteristics of tea production and operation as well as cost accounting, in the significance of tea enterprise value growth, Mei analyzes and discusses how to solve some cost accounting problems in tea production and management. Therefore, the method is more specific in its operation process. However, its operating efficiency is lower than other methods.

Big data is diverse and unstructured, and is difficult to store, process and mine [7]. It also exhibits a large size, multiple data types, fast propagation speed, authenticity, strong understanding, and strong innovation. Here, the choice of accounting model is explored based on characteristics of AMBD. The detailed structure of our paper is as follows.

Several representative indicators are selected to establish a market-based constraint system for (SME) AMBD based on the solvency, operating capability, profitability and growth ability of the company.

A combination of particle swarm optimization and ant colony optimization is used to select the optimal accounting model for small and medium-sized enterprises to improve selection rationality and user satisfaction.

The selection method of SME accounting model based on AMBD is verified by experimentation and analysis.

The proposed method is summarized, and future research directions are proposed.

2 The choice of accounting models for small and medium-sized enterprises under the constraints of accounting big information market data

2.1 Principles of accounting model selection

Principle of the rational division of labor

A reasonable division of labor means that any relevant work is divided into several processing steps to be completed by different people, which prevents anyone from completing the accounting process alone. Therefore, by this principle, the entire process of any economic business should be divided amongst two or more people. For example, a business should not have one person be responsible for accounts receivable as well as shipping, or else errors will surface in the work.

The principle of separation of money and goods

Money management and property management are required in the principle of separation of money and goods. This means that management and accounting staff responsible for money and goods should be completely dispersed, and accounting should not be both accountable and managed. SMEs tend to make the same staff responsible for both accounting and cashier duties because of their small size and to save on labor costs, which means that errors are prone to occur in both work.

Principles of inspection

The principle of inspection includes the procedure for the superior to verify the lower level review, internal review, and independent inspection. The internal review refers to the accounting documents of the financial institution. When accounting documents are filled out, they must be submitted to an accountant for review before the cashier can make a payment or register a transaction. Independent inspection mainly refers to the regular inspection of accounting materials by internal audit institutions or full-time auditors.

Principle of economic responsibility

Under this principle, when there is a problem in filling out accounting vouchers, it must be submitted to the accountant for re-examination and the view before payment or registration. Trading SMEs tend to be operated directly by operators in most cases, with the same staff in charge of accounting and cashier duties. Therefore, they are small and labor-saving. On this basis, responsible people can not only effectively control managers, but also improve their work responsibilities.

2.2 Establishment of accounting Big information market data constraints

SMEs as mentioned earlier refers to economic units with relatively small numbers of employees and amounts of assets compared to large enterprises [8]. The employment and turnover of such enterprises are very small, and they are usually funded by one or a small number of individuals. In most cases, the business is managed directly by the operator and is rarely subject to outside interference. The accounting model means that a certain currency and a certain method are used to provide the necessary accounting information for the accounting supervision accounting object by using certain procedures. Meanwhile, the program formed by combining them scientifically is a fixed program in accounting. The formulation of the accounting model can be done either by a government department or an enterprise, and doing so is a mandatory accounting code of conduct and norms. It is also a general term for a country, a region and a corporate accounting method and procedure [9]. The accounting model can be defined by either administrative regulations or corporate regulations. As an administrative regulation, the unified accounting model formulated by the government department is mandatory; As a corporate regulation, the internal accounting model of the enterprise is relatively small. Therefore, the formulation of the enterprise unit accounting model should be designed on the basis of the relevant national accounting model [10].

The information market refers to the complete exchange relationship between the information product producers, the information service operators and the information product demanders in the market. It covers the entire distribution and exchange process, and the circulation of commoditized information products from production to consumption. Specifically, the information market is a multi-faceted, multi-level, multi-form market system which meets the needs of social information, using information products and information services like content and using information labor law to conduct transactions [11].

On the basis of the principles of comparability, completeness, accessibility, non-overlapability, etc., we refer to the relevant literature and combine the status quo of SMEs in China. Several representative indicators have been selected from the solvency and operation of SMEs, capacity, profitability and growth ability. These indicators reflect the growth characteristics of accounting data of SMEs from different angles, which constitutes the market constraint system for SME accounting big data [12].

Among them, the solvency ratio is the basis for responding to the growth of SMEs. It mainly includes the current ratio (X₁), quick ratio (X₂), and debt ratio (X₃). Only if the debt-to-capacity ratio of the company is reasonable, the financial structure is considered to be sound and the accounting model is considered to be rational, under which conditions it is possible to expand the business [13, 14].

The ratio of operational capacity is an indicator reflecting the growth level of SMEs. It mainly includes the accounts receivable turnover rate (X₄) and inventory turnover rate (X₅). Under normal circumstances, the higher the asset turnover capacity, the higher the capital utilization. In addition, the faster the financial growth of the company, the more rational the choice of accounting model.

The index of profitability is a decisive indicator reflecting the growth of SMEs [15]. The return on net assets (X₆) directly reflects the profitability of the company. However, the profit rate of the main business (X₇) reflects the profit rate created by the main products of the company, or the revenue from its main business operations. Under the premise of increasing corporate profits, whether profits mainly come from the main business is an inevitable manifestation of whether the company has grown. The gross profit margin (X₈) directly determines whether the company has sustainable growth.

Enterprise development ability is a fundamental part of the growth of SMEs. The growth rate of the main business income of the company (X₉) can reflect the expansion of the main business income scale and a market expansion capability of the company. The stronger the market expansion ability of the company, the greater the market share, and therefore the higher the growth [10, 11]. The three indicators of profit growth rate (X₁₀), net profit growth rate (X₁₁), and shareholder equity growth rate (X₁₂) of the main business can dynamically reflect the profitability of the company and its ability to increase the corporate equity of its shareholders. They can also reflect the constraints of AMBD to a certain extent. Integrating the above-mentioned various market AMBD constraints can effectively enhance the rationality of the selection of accounting models for SMEs and increase user satisfaction.

Principal Component Analysis (PCA) is a statistical analysis method that converts multiple variables into several comprehensive indicators. This is a way to improve the efficiency of accounting choice for SMEs. We substitute the above-mentioned AMBD constraints into the principal component analysis. The principal component analysis is a statistical analysis method that converts multiple variables into a few comprehensive indicators. Each of the principal components can reflect most of the information of the original variables, and the information contained in them is not repeated [18]. This method combines complex factors into several principal components while introducing multi-faceted variables, which simplifies the problem and allows for more scientific and effective data information.

In essence, principal component analysis is a statistical analysis method that converts multiple variables into a few comprehensive indicators. From the perspective of mathematics, this is a dimensionality-reduction processing technique that can improve the efficiency of accounting choices for small and medium-sized enterprises. Assume that there are n samples, each of which has a total of p variable descriptions. This forms an n × p-order data matrix. p-dimensional random vectorx = (X₁, X₂, ⋯ , X_p) · n samples x_i = (x_i1, x_i2, ⋯ , x_ip), i = 1, 2 ⋯ , n. The accounting big information market data constraint standard function can be expressed as Equation 1. $Z_{ij} = \frac{x_{ij} - x_{j}}{s_{j}}$ (1) In Eq. 1, s_j represents the standard deviation of the data sample.

According to Eq. 1, the following correlation coefficient function R can be solved. $R = \frac{Z}{n - 1}$ (2) where R is the valid function value; n is the number of samples; and Z is the sample.

Assuming 86% utilization of accounting big data information, Eq. 3 can be obtained. $\frac{\sum_{j = 1}^{n} λ_{j}}{\sum_{j = 1}^{p} λ_{j}} \cdot R \geq 86 %$ (3)

In Eq. 3, λ_j represents the utilization of accounting big data information.

For λ_j, there is a system of equations R = λ_j, then according to the equation, the unit eigenvector $b_{j}^{o}$ expression is obtained in Eq. 4. $U_{ij} = Z_{i} b_{j}^{o}, j = 1, 2, \dots, n$ (4)

In Eq. 4, U₁ is called the first principal component, U₂ is called the second principal component, and so on, so that U_p is called the pth principal component.

Conventional cluster analysis methods can be adopted for cluster analysis of the constraint factors of AMBD in SME accounting. However, due to research on the classification of information constraints of accounting big data from SMEs, the objects that are clustered are often composed of multiple elements [19]. The data of different factors often have different units and dimensions, and the their values may vary greatly, which will affect the classification results [20]. Therefore, after the objects of the classification elements are determined, the cluster elements must be processed before cluster analysis. We standardize the data of X and record the resulting data as Z_i,j. Then, Eq. 5 is obtained. $Z_{ij} = \frac{X_{ij} - X_{j}}{S_{j}} \cdot U_{ij}$ (5) where Z_ij denotes the sample size; X and Y denote the sample value represented by two parts; and S denotes the specific range value.

Assume that the distance between the projection point of a test sample in the feature space and the center point of the point group is y_i. The following formula to completes the SME AMBD cluster analysis. $y_{i} = Z_{ij} \cdot x \cdot R$ (6)

In Eq. 6, y_i is the clustering result of the AMBD constraint factors, and is also the clustering result of the AMBD constraints.

The above process’ main purpose is to roughly divide the constraint factors of the AMBD. Then, the component level of each constraint factor is obtained based on the principal component analysis to complete the final classification of the constraints of AMBD and complete the establishment of those constraints [21].

2.3 Choice of accounting models for small and medium-sized enterprises

Ant colony optimization (ACO) is a group-intelligent optimization algorithm that is inspired by the natural behavior of ants searching for food. It utilizes collaboration processes which are based on the collective foraging behavior of real ant colonies in nature. The algorithm constructs a solution path taken by several “ants”. It improves the quality of the solution by leaving and exchanging pheromones on the solution path to achieve the goal of optimization [22]. As a general stochastic optimization method, ACO has been successfully applied in a series of applications. Combinatorial optimization problems, such as TSP, have achieved good results. However, since the algorithm is a typical probabilistic algorithm, the parameters in the algorithm are usually determined experimentally. This means that the optimization performance of the method is closely related to human experience in determining the parameters, and that it is difficult to optimize the performance of the algorithm. The ant colony algorithm has a slow convergence rate, and can easily fall into a local optimum. The lack of initial pheromones in the ant colony algorithm generally results in a long search time, and its complexity can reflect this. Moreover, the method is prone to stagnation, in that after the search progresses to a certain extent, the solutions found by all individuals are completely consistent, and the solution space cannot be further searched, which is not conducive to finding any better solutions that may exist.

Particle swarm optimization (PSO) has a fairly fast rate of approximating the optimal solution. Its essence is to use the current position, global extremum and individual extrema to guide particles to their new positions at each iteration. The use of the individual particle’s own experience and the group’s collective experience to adjust its own state is the key to the excellent characteristics of the particle swarm algorithm. The advantage of the PSO algorithm is to solve optimization problems of continuous functions. Based on the ABMD constraints, the selection of enterprise accounting model is an advantage algorithm. Here, PSO and ACO are combined to overcome the shortcomings of ant colony algorithms and get the required optimization results.

Based on the AMBD constraints, the selection of the enterprise accounting model is accomplished using a merit algorithm. Here, PSO and ACO are combined, so that PSO overcomes the shortcomings of ACO, and the optimal results are obtained. The main steps are as follows.

Part I: Selecting the initial population of the ant colony algorithm using particle swarm optimization.

The ant colony representing particle swarms with different combinations of accounting models is initialized. The position and velocity of the particles are denoted as $x_{i}^{'} (x_{i^{'} 1}^{'}, x_{i^{'} 2}^{'}, \dots, x_{i^{'} m}^{'})$ and v_i′ = (v_i′1, v_i′2, ⋯ , v_i′m). The learning factor and the maximum number of iterations are set respectively.

The fitness values for all particles is calculated based on the fitness function in Eq. 7. $f (x) = y_{i} \cdot \frac{w_{2} \sum_{i^{'} = 1}^{n} \sum_{j^{'} = 1}^{p^{'}} q_{i^{'} j^{'}} u_{i^{'} j^{'}}}{w_{1} \sum_{i^{'} = 1}^{n} \sum_{j^{'} = 1}^{p^{'}} c_{i^{'} j^{'}} u_{i^{'} j^{'}} + w_{3} \sum_{i^{'} = 1}^{n} \sum_{j^{'} = 1}^{p^{'}} t_{i^{'} j^{'}} u_{i^{'} j^{'}} + w_{4} \sum_{i^{'} = 1}^{n} \sum_{j^{'} = 1}^{p^{'}} r_{i^{'} j^{'}} u_{i^{'} j^{'}}}$ (7)

In Eq. 7, w₁, w₂, w₃ and w₄ represent weights, and q_i′j′, u_i′j′, c_i′j′, t_i′j′, and r_i′j′ represent different accounting models, respectively.

The fitness value of each particle is compared with the fitness value of the best position $p_{i^{'}}^{'}$ . If its fitness value is larger, $p_{i^{'}}^{'}$ is considered to be the current best position.

The fitness value of each particle is compared with the fitness value of the global best position g_best = (g_i′1, g_i′2, ⋯ , g_i′m). If it is larger, g_best is reset.

The particle velocity and position are updated by using Equations 8-9. $v_{i^{'} d}^{k + 1} = {wv}_{i^{'} d}^{k} + C (p^{'} i^{'} d k - x_{i^{'} d}^{' k})$ (8) $x_{i^{'} d}^{' k + 1} = x_{i^{'} d}^{' k} + v_{i^{'} d}^{k + 1}$ (9)

In Eqs. 8-9, C represents the learning factor, $v_{i^{'} d}^{k + 1}$ represents the speed after the update, $v_{i^{'} d}^{k}$ represents the current speed, $x_{i^{'} d}^{' k}$ represents the current position, $p_{i^{'} d}^{' k}$ represents the current local optimum and $x_{i^{'} d}^{' k + 1}$ represents the updated particle position.

After updating the particle velocity and position, it is judged whether or not the algorithm end condition is satisfied. If the assumption is satisfied, the end condition is considered to be satisfied. Otherwise, the process is repeated from step 2.

Part II: Solving the ant colony algorithm based on the information obtained in the Part I.

According to the fitness function of the chromosome in the population selected by the above particle swarm algorithm, all possible paths between candidate accounting models τ (·) are set up based on the ant colony algorithm for SME accounting model selection model diagrams, using the expression shown in Eq. 10. $τ {(e, l)}^{new} = γ \cdot τ {(e, l)}^{old} + Δ τ {(e, l)}^{k^{'}}$ (10)

In Eq. 10, τ (e, l) ^new represents the updated path, τ (e, l) ^old represents the current path, and Δτ (e, l) ^k′ represents the amount of pheromones released after the k′-th ant passes the accounting mode e and the accounting mode l.

The search iteration G is set to 1 and the optimal objective function value F_max is set to 0. An ant is placed on each candidate accounting model, and n′ is defined as the total number of ants.

The initial solution set and feasible set for each ant is defined. Assuming that the starting point of ant k′ is u₁, the initial solution set is tabu_k′ ={ u₁ }, and the initial feasible set is allowed_k′ ={ u₂, ⋯ , u_m }.

The probability $p_{i^{'} i^{″}}^{' k^{'} (j^{'} j^{″})}$ is calculated by the ants using Eq. 11 and is moved to the next accounting model. The selected accounting model is added to tabu_k′ and the feasible set allowed_k′ is updated. $p_{i^{'} i^{″}}^{' k^{'} (j^{'} j^{″})} (t) = \frac{τ {(e, l)}^{new} η}{(η (u_{i^{'}}^{j^{'}}, u_{i^{″}}^{j^{″}}))}$ (11)

In Eq. 11, η represents the inertia factor, $u_{i^{'}}^{j^{'}}$ and $u_{i^{″}}^{j^{″}}$ represent two candidate accounting models, respectively.

After n moments, a search is traversed and completed by all ants. Then, the amount of information on all paths is updated by Eq. 10, and G is incremented by 1.

The above process is iterated until the most suitable accounting model is selected. The expression to select the best accounting model is defined by Eq. 12. $F_{max} = \frac{p_{i^{'} i^{″}}^{' k^{'} (j^{'} j^{″})} (t)}{{tabu}_{k^{'}} \cdot {allowed}_{k^{'}}} \cdot η$ (12)

In Eq. 12, F_max is the finally selected accounting model.

In the realization of accounting mode selection for SMEs, the optimal accounting model is found through the combination of PSO and ACO based on the constraints of AMBD. This improves the overall effect of the proposed method, as well as user satisfaction.

3 Experimental results and analysis

To verify the feasibility of the selection method of the SME accounting model based on market constraints of accounting big data information, a Matlab program is written to implement the proposed method. Experimental data comes from 3 medium-sized companies and 2 small businesses. According to the comparison between the simulation results and the actual selection results, the rationality of the proposed method, user satisfaction, and efficiency of the accounting model selection are verified. Then, different methods are compared in those aspects, and the superiority of the proposed method is observed. Among them, the method proposed in [4] is Method 1, the method proposed in [5] is Method 2, and the method proposed in [6] is Method 3. The experimental index is as follows.

Mode rationality

Mode selection user satisfaction

Mode selection efficiency

The experimental results are as follows.

Fig. 1 shows that the stability curve of method 1 is less stable. Method 2 proposes a strategy based on a comprehensive classification of enterprises and different companies adopting different disclosure models to achieve a choice of accounting models. The process does not analyze the specific financial indicators of each company, and the division of the classification results is not clear, leading to poor rationality. When the choice of accounting model is based on the constraints of the AMBD, the factors affecting the choice of accounting model are considered comprehensively and the rationality of the choice of accounting model is improved [34 –37].

Fig.1

Comparison of rationality for different methods. (a) Method 1, rationality. (b) Method 2, rationality. (c) The rationality of choice of an accounting model for SMEs based on AMBD.

Fig. 2 shows that the choice of SME accounting methods is more user-friendly than current methods based on the accounting big data market constraints. Several representative indicators of company solvency, operational capacity, profitability, and growth ability are selected to form a market-based constraint system. Using the combination of PSO and ACO, the optimal accounting model for SMEs was found, and user satisfaction was improved.

Fig.2

Comparison of user satisfaction for different methods. (a) Method 2, User Satisfaction. (b) Method 1, User Satisfaction. (c) User satisfaction based on the selection method of accounting mode for SMEs under accounting big information market data.

Fig. 3 shows that the method of selecting an accounting mode is to substitute the AMBD constraint factors into the principal component analysis method in the running process. The principal component analysis is a kind of statistical analysis method that converts multiple source variables into a few comprehensive indicators [26 –32]. Principal component analysis is a kind of dimension reduction processing technology, which can improve the efficiency of SME accounting model selection.

Fig.3

Comparison of operating efficiency for different methods. (a) Method 2, operating efficiency. (b) Method 3, operating efficiency. (c) Operation efficiency of the selection method of accounting mode for SMEs based on AMBD.

4 Conclusion

The choice of accounting model is very important. If SMEs can find a suitable model for the development of accounting model, suitable for the development of the company, the authenticity of their accounting information will be improved. This will help to promote the development and innovation of small and medium-sized enterprises. The financial reports of SMEs are detailed, so many unnecessary economic disputes can be avoided. It can help promote the development and innovation of economic business for SMEs through the research and implementation of the choice of accounting models. By studying and implementing the selective accounting model, the accounting model of SMEs based on ABMD constraints is proposed. Firstly, the selection of AMBD is effectively improved by using a variety of AMBD constraints. SME accounting model is used to improve customer satisfaction. Then, the constraints of AMBD are aggregated by principal component analysis. This reduces the time spent in choosing accounting models and improves the efficiency of the method. Finally, the scope of research on the selection of accounting models for large enterprises is expanded to provide more comprehensive services in this regard.

Conflicts of interest

We declare that there are no conflicts of interest in this paper.

Footnotes

Acknowledgments

The study was supported by “Social Science Foundation of Fujian Province of China (Grant No. FJ2018C037)” and “Education and Scientific Research Project for Young Teachers in Fujian Province of China” (Grant No. JAS170344). We also thank Logan Praznik for his thorough editing work.

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