https://doi.org/10.31449/inf.v48i12.6029 Informatica 48 (2024) 81–96 81 Intelligent Classification Model for Interior Design Knowledge Graph based on Simulated Annealing Algorithm Jie Liu 1 , Feng Wang 2* , Bin Song 2 , Xiangyun Wang 2 1 Faculty of Mathematics, Qilu Normal University, Jinan 250200, China 2 School of Art Design, Shandong Youth University of Political Science, Jinan 250103, China Email: ljqlnu1018@163.com * Corresponding author Keywords: simulated annealing algorithm, knowledge graph, genetic algorithm, interior design, classification models Received: April 16, 2024 In real life, interior design is a complex and challenging job. Interior design solutions need to consider factors such as spatial layout, color matching, etc., and the emergence of knowledge graph provides a new method of summarizing design ideas for the interior design industry. However, in the face of a large number of knowledge graphs, how to achieve high-quality classification of knowledge graphs has become a hot topic of discussion in related industries. The work builds a knowledge graph intelligent classification model based on machine learning, simulated annealing, and genetic algorithms to accomplish effective knowledge graph classification. The global optimization of convolutional neural network parameters is accomplished by merging the model using the simulated annealing approach and the genetic algorithm. The experimental results indicated that the proposed model converged to an F1 score of about 95.03%, while the control model converged to an average F1 score of 94.37% and 94.26%. The average recall of the proposed model was 91.71% while the average recall of the control model was 87.06%. Based on the experimental findings, it can be said that the suggested model performs noticeably better than the control model, indicating that it is an improved knowledge graph classification method. In addition, the proposed model contributes to the development of interior design related industries. Povzetek: V članku je opisan razvoj inteligentnega modela za klasifikacijo grafov znanja na področju notranjega oblikovanja. Predlagan model temelji na algoritmu simuliranega ohlajanja in dosega boljšo točnost ter izboljšano klasifikacijo. 1 Introduction Interior design (InD) is a comprehensive field, which involves aesthetics, architecture and so on. Currently there are numerous InD styles of various types, such as minimalism, industrial style, Scandinavian style, etc. Each of these design styles has its own characteristics, which brings a wealth of choices for modern home life [1]. However, with the continuous development of the design field, the diversity and innovation of InD have become increasingly prominent. The rich and diverse design styles and creativity also create a considerable workload for InD solution summarization. But as different machine learning (ML) algorithms have evolved, the issue of InD solution summarization has been resolved with the introduction of knowledge graphs (KG). The term “knowledge domain visualization,” also known as “knowledge domain mapping map,” refers to a collection of several graphs that illustrate the structural links and knowledge production process [2-3]. Through KG, the association between design styles, design solutions and design objects can be visualized, thus assisting the planning and program construction of InD. KGs are usually constructed in a structured way, but the construction of KGs through this way will output a large number of KGs [4]. How to effectively categorize the generated KGs has become a difficult problem in KG research. Currently available optimization techniques include the genetic algorithm (GA) and the simulated annealing algorithm (SAA), which when combined with ML algorithms can increase the ML algorithm's convergence speed and computational efficiency [5]. In view of this, the study employs GA and SAA for combining and constructing a fusion optimization seeking algorithm to help convolutional neural networks (CNN) for KG classification. To address the problem of KG generation, the study found through reviewing the literature that a number of researchers have innovated the methods of KG generation and application methods. For example, Xue et al. found that the current mainstream KG still contains inaccurate or outdated entries, so they proposed a KG construction method that can be used for quality assessment and error detection. In comparison to existing models of the same kind in the KG creation process, the suggested method had superior accuracy and sophistication, as confirmed by 82 Informatica 48 (2024) 81–96 J. Liu et al. experimental verification in the final study [6]. Wang and other researchers used heterogeneous graphs to improve the KG generation process, and the KGs after the introduction of heterogeneous graphs can be represented in a low dimensional space. In addition, the study also analyzed the applicability of heterogeneous graph-based KGs in real industrial environments and concluded that the proposed KG construction method has achieved some success in real application scenarios [7]. Yuan et al. constructed an exponential atlas generation model based on depth model using ML method, which achieves more accurate data keyword extraction by graph convolutional network for data extraction and fusion. It was experimentally proved that the atlas generated by the proposed KG generation method outperforms other similar models in terms of keyword summarization and keyword relationship processing, and the results show the advanced nature of the proposed model [8]. Steenwinckel et al. tried to add ML algorithm into the process of KG generation. The relationship between the data was characterized by the instance neighborhood of the knowledge in the deep learning-based KG construction, while the representation of the nodes of interest in the KG was in a binary way for easy processing by the ML algorithm. The final experiment indicated that the proposed new KG construction method has higher efficiency and accuracy compared to other methods [9]. Numerous research teams have also made innovations in the optimization and implementation of SAA. For example, Li et al. suggested a broadband passive interference technique based on SAA to address the technological challenges associated with broadband passive interference. Using the least amount of each chosen sub-element, the method employs SAA to produce the newly integrated foil element's amplitude-frequency profile with the least amount of variation. Experimental results showed that the new integrated foil element optimized with SAA has high interference efficiency [10]. A new path planning method for robotic systems was proposed by researchers such as Shi to address the logical rationality of robot trajectories and final states. In this path planning method, the SAA was employed for the optimization of each robot's path trajectory, thereby enabling the derivation of the optimal path solution for each robot within the current region. The study's findings indicate that, in terms of both computing cost and the quality of the solutions produced, the strategy proposed in the research performs better than the current strategies in use [11]. Shin et al. found that the traditional SAA has obvious shortcomings in coping with large-scale problems, so they chose to add an efficient storage hardware for memory optimization based on stochastic SAA, and designed relevant experiments to verify the optimization effect of the improved SAA on memory. The experimental results demonstrated that the proposed method achieved an absolute advantage in the maximum cut combination optimization problem [12]. Cloud cover can provide a significant challenge to microcosmic data transmission since optical remote sensing sensors are unable to detect through clouds. In view of this, Han et al. introduced SAA to optimize the cloud coverage uncertainty. The final results demonstrated that the proposed technique represents a significant advancement in AEOS scheduling, outperforming existing state-of-the-art methods in various scenarios [13]. The summary of relevant work is shown in Table 1. Table 1: Summary of related work Research topic Research methods and applications Main indicators Performance results Limitations Knowledge graph Xue et al.'s knowledge graph construction method [6] Quality assessment and error detection Improve the accuracy and complexity of knowledge graphs There may still be inaccurate or outdated entries Wang et al.'s heterogeneous graph method [7] Low dimensional space representation and practical industrial applicability Improve the practicality and applicability of knowledge graphs Further verification is needed for its wide applicability to actual industrial environments Yuan et al.'s deep model-based exponential graph generation model [8] Data keyword extraction and keyword summary Superior keyword processing and summarization performance compared to other models The complexity of deep models may increase computational costs Steenwinckel et al.'s deep learning method [9] Efficiency and accuracy Higher efficiency and accuracy There may be a high computational complexity issue in constructing large-scale knowledge graphs Intelligent Classification Model for Interior Design Knowledge… Informatica 48 (2024) 81–96 83 Simulated annealing algorithm Application of Li et al.'s simulated annealing algorithm in broadband passive interference technology [10] Interference efficiency Improving the interference efficiency of broadband passive interference technology Further validation is needed to evaluate the effectiveness in different environments Shi et al.'s path planning method based on simulated annealing algorithm [11] Optimal path solution and cost calculation Better path planning effect There may be challenges in real-time path planning for complex environments Shin et al.'s memory optimization simulated annealing algorithm [12] Memory optimization effect Maximum cut combination optimization solution with absolute Advantage Need to consider applicability in different hardware environments Han et al.'s simulated annealing algorithm for optimizing uncertainty in cloud coverage [13] Optimize cloud coverage and improve performance Better performance than current methods Performance improvement only under specific tasks, generalization needs further verification In conclusion, existing research has made notable advancements in knowledge graph generation and SSA optimization, with a particular focus on enhancing accuracy and efficiency. Nevertheless, existing methodologies present shortcomings, including suboptimal accuracy of KG and diminished algorithmic efficacy. The fusion optimization search algorithm proposed in the study combines a GA and an SSA, which can effectively address the classification problem in the process of knowledge graph generation, thereby improving accuracy and efficiency. This method can overcome the inaccuracies and obsolescence inherent in KG, while also exhibiting high algorithm convergence speed and computational efficiency. It thus represents a novel solution for the construction of KG in the field of InD. The paper is organized primarily into four sections. The first section is the introduction, which introduces the current research status of the technology used. The approach, which carries out the intelligent categorization and creation of the KG of InD by SAA and GA, is covered in the second section. The third section is the model performance test, which verifies the advancement of the proposed model by designing controlled experiments. The fourth section is the discussion section, which mainly compares and analyzes the performance results of the proposed model. The last section is the conclusion, which mainly summarizes the research results and shortcomings. 2 Methods and materials This subsection explores the keyword-based generation of KG for InD and its classification method. In order to realize the classification problem of KG of InD, the study introduces SAA and GA for ICM construction, and GA is utilized to improve SAA in order to solve the local convergence problem of SAA so as to improve the classification effect of ICM. 2.1 Intelligent classification model construction based on SAA To carry out the intelligent classification of KG for InD, the study adopts a structured approach for KG construction with InD as the main body. The structured KG construction includes four steps: data entity extraction, data fusion, data constraints, and KG output [14]. Data entity extraction is to construct the relationship between InD data into a ternary group, which consists of a predicate and two formal parameters, and the data in the ternary group determine the existence of the relationship through the formal parameters. The study obtains the triad of data relationships before data fusion [15]. The feature data of different InDs exists in the form of triples, so the fusion process only needs to perform the merging of like terms of the triples. The data constraint process mainly carries out the normalization calculation and de-weighting of the data, and the constrained data is persisted into the KG through data persistence. Figure 1 depicts the precise flow of KG construction. 84 Informatica 48 (2024) 81–96 J. Liu et al. Structured data Term extraction Term extraction Term extraction Rule definition Entity Link Solid fill Knowledge graph Ontology construction Ontology Learning Physical learning Figure 1: Schematic diagram of knowledge graph construction After constructing the KG generation framework, iterative updating is also required to get the complete KG. In structural optimization methods, the iterative update of KG is usually carried out by incremental update [16]. Incremental updating can update only the changed data, so this updating method plays an important role in saving system resources and time. Although the traditional KG construction has formed a more complete system, the KG constructed by the above method still has obvious drawbacks, such as long construction period, low accuracy of data relationship processing, etc. In view of the above drawbacks of KG construction, the study adopts keyword entity extraction instead of traditional data entity extraction. In order to accurately extract keywords from data, the research also needs to use ML algorithms for assistance. By investigating and analyzing the application effects of current common ML algorithms, the study selects the simple, fast, and easy-to-understand term frequency-inverse document frequency (TF-IDF) method to extract keywords from InD data. This method mainly evaluates the importance of keywords in the input dataset by calculating term frequency (TF) and inverse document frequency (IDF) of the input InD data [17]. Where the expression for TF calculation is shown in Equation (1). , , ij fj k f TF f =  (1) In Equation (1), j i f , denotes the times a word appears in the input data set. tf denotes the meaning of the proportion of a word in the input text. In addition, the expression for calculating IDF is shown in Equation (2). || |1 { : }| lg ij D j w d IDF + = (2) In Equation (2), D is the total number of keywords in the dataset related to the input InD. } : { j i d w j  is the occurrences of a word i w among all the keywords. j d denotes all words in the input dataset. The final output of the keywords can be obtained by synthesizing the output of TF and IDF, and the expression of the synthesized output is shown in Equation (3). ( ) ( ) ( ) || |1 { : }| , , lg ij ii D j w d ij i fj k TF w IDF w f TF IDF w f +  = − =   (3) The output result after processing by TF-IDF is a data sequence, and the elements in this data sequence are the keywords of KG [18]. To extract the keywords of the InD data and construct the KG, CNN is selected for the study to perform the keyword relationship extraction, while the powerful classification ability of CNN can also be used for the classification model (CM) construction of the KG. After extracting the relationships between keywords, the generated KG of InD is shown in Figure 2. Intelligent Classification Model for Interior Design Knowledge… Informatica 48 (2024) 81–96 85 Nordic Style House type Balcony Solid wood furniture Sofa Living room Study Height Chinese style wind Minimalist wind Area Background wall Full shading Figure 2: Interior design knowledge graph display In this study, the CNN algorithm is not only used for the extraction of keyword relationships, but also involved in the classification of KG, but the traditional CNN algorithm also has the obvious defect of the difficulty of convergence of the objective function (OF) [19]. In order to solve this problem, the fully connected layer (FCL) of CNN needs to be made to find the globally optimal parameters during feature computation. Therefore, the study introduces SAA for OF optimization based on the traditional CNN algorithm. The fundamental goal of SAA, a universal optimization technique inspired by the solid matter annealing process, is to simulate the solid annealing process in order to obtain the global optimal solution for the OF [20-21]. The temperature decay function is one of the most important parameters in SAA, and the computational expression of this parameter is shown in Equation (4). 1kk TT  + = (4) In Equation (4),  denotes the temperature decay coefficient also known as the cooling rate parameter, which is used to control the rate of temperature change. 1 k T + denotes the temperature of the 1 k + th iteration and k T denotes the temperature of the k th iteration. To adapt SAA to the EucD computation of CNN, the study adds new inversion parameters to the algorithm, and therefore the algorithm's temperature decay function computation is changed accordingly. The new temperature decay function calculation expression of SAA is shown in Equation (5). ( ) 1 1 00 N K N T k T EXP Ck T   = − =   (5) In Equation (5), k denotes the iterations of the algorithm, which is consistent with the iterations of the CNN algorithm. 0 T denotes the initial temperature set before the start of the iteration, and ( ) . EXP denotes the exponential operation. C denotes a random constant and N denotes the number of parameters to be inverted. After determining the temperature decay function and the initial temperature, the algorithm needs to generate the initial solution and set up a perturbation mechanism to generate a new solution [22]. The computational expression for the perturbation mechanism is shown in Equation (6). ( ) ( ) |2 1| 1 0.5 1 1 i i i i i U i m m y B A y Tsgn u T −  = + −      = − + −         (6) In Equation (6), i m is the i th variable of the solution in the current iteration number. i m denotes the i th variable of the new solution and T is the temperature in the current iteration number. | .| denotes taking absolute values. u denotes a constant generated by a random number function that takes values in the range [0, 1]. ( ) sgn . denotes the sign function. i A denotes the lower limit of the i th variable and i B denotes the upper limit of the i th variable. i y denotes the intermediate variable in the perturbation mechanism. In addition, Metropolis criterion also has an important role in SAA. By Metropolis criterion, it makes the algorithm to receive worse solutions, so the algorithm can better search the global solution [23-24]. The mathematical expression of Metropolis criterion is shown in Equation (7). 86 Informatica 48 (2024) 81–96 J. Liu et al. 12 21 12 1, , EE H EE EXP E E T    = −   −     (7) In Equation (7), 1 E denotes the state energy of the algorithm at the current moment and 2 E denotes the state energy of the algorithm after the state update. The SAA calculation flow is shown in Figure 3. Determine the initial temperature T 0 , temperature decay coefficient A, maximum number of iterations K, and initial solution x Start Initialize calculation of fitness value f (x 0 ) Generating disturbance to generate new street x 1 Calculate fitness value f (x 1 ) f （x 1 ）