Indonesian J our nal of Electrical Engineering and Computer Science V ol. 37, No. 3, March 2025, pp. 1772 1784 ISSN: 2502-4752, DOI: 10.11591/ijeecs.v37.i3.pp1772-1784 1772 T omato leaf disease detection using T aguchi-based P ar eto optimized lightweight CNN Bappaditya Das, C. S. Raghuv anshi Department of Computer Science and Engineering, F aculty of Engineering and T echnology , Rama Uni v ersity , Kanpur , India Article Inf o Article history: Recei v ed Mar 12, 2024 Re vised Sep 30, 2024 Accepted Oct 7, 2024 K eyw ords: Deep learning Hyperparameters tuning Leaf disease detection Multiobjecti v e T aguchi method ABSTRA CT The prospect of food security becoming a global danger by 2050 due to the e xponential gro wth of the w orld population. An increase in production is indis- pensable to satisfy the escalating demand for food. Considering the scarcity of arable land, safe guarding crops ag ainst disease is the best alternati v e to maxi- mize agricultural output. The con v entional method of visually detecting agri- cultural diseases by skilled f armers is time-consuming and vulnerable to inac- curacies. T echnology-dri v en agriculture is an inte gral strate gy for ef fecti v ely addressing this matter . Ho we v er , orthodox lightweight con v olutional neural netw ork (CNN) models for early crop disease detection require ne-tuning to enhance the precision and rob ustness of the models. Disco v ering the optimal combination of se v eral h yperparameters might be an e xhausti v e process. Most researchers use trial and error to set h yperparameters in deep learning (DL) net- w orks. This study introduces a ne w systematic approach for de v eloping a less sensiti v e CNN for crop leaf disease detection by h yperparameter tuning in DL netw orks. Hyperparameter tuning using a T aguchi-based orthogonal array (O A) emphasizes the S/N ratio as a performance metric primarily dependent on the model’ s accurac y . The multi-objecti v e P areto optimization technique accom- plished the selection of a rob ust model. The e xperimental results demonstrated that the suggest ed approach achie v ed a high le v el of accurac y of 99.846% for tomato leaf disease detection. This approach can generate a set of optimal CNN models’ congurations to classify leaf disease with limi ted resources accurately . This is an open access article under the CC BY -SA license . Corresponding A uthor: C. S. Raghuv anshi Department of Computer Science and Engineering, F aculty of Engineering and T echnology Rama Uni v ersity Kanpur , 209217 Uttar Pradesh, India Email: drcsraghuv anshi.fet@ramauni v ersity .ac.in 1. INTR ODUCTION Plants are essential for human ci vilization as the y generate food and pro vide protection ag ainst harmful radiation. T omato is a popular , nutrient-dense v e getable with pharmacological properties [1]. The e xtensi v e use of tomatoe s escalates demand, resulting in an annual consumption of about 160 million tons [2]. T omatoes are a highly protable crop for agricultural households and can ha v e a signicant im pact on reducing po v erty [3]. As per F A O, plant diseases alone accounted for 14% of agricultural production losses, leading to an annual trade decit of $200 billion [2]. T imely identication of plant diseases can minimize the use of pesticides, thereby safe guarding consumer health and the en vironment. T raditional visual diagnosis of pests and pathogens is more J ournal homepage: http://ijeecs.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 1773 time-consuming and comple x. F armers f ace the formidable challenge of frequent ly monitoring their plants to pre v ent the spread of disease. Therefore, de v eloping an automated, rapid, and accurate leaf disease detection system is imperati v e for the early identication of diseases and holds immense importance. Con v olutional neural netw orks (CNNs) ha v e emer ged as a po werful tool for automated leaf dise ase detection [4]. Their success in accurately detecting diseases has fuelled a sur ge in research, focusing on de v el- oping no v el CNN architectures or applying e xisting models to v arious cr o ps [4]–[9]. The e xtensi v e culti v ation of tomatoes and the a v ailability of lar ge, publicly accessible datasets containing di v erse disease cate gories ha v e made tomato leaf disease detection a popular area of deep learning (DL) research [10]. Both the restructured deep residual dense netw ork (RRDN) model [11] and impro v ed f aster re gion con v olutional neural netw ork (F aster RCNN) [12] emplo yed deep residual netw orks for feature e xtraction. Researchers ha v e de v eloped se v- eral ef cient, lightweight CNN models using DL to classify tomato leaf diseases. T oLeD [13], a CNN with a small parameter count of 0.2 M, achie v ed a maximum testing accurac y of 91%, where v alidation accurac y w as impro v ed by adjusting through h yperparameter tuning of the epoch, batch size, learning rate, dropout rate, number of con v olution layers, and pooling layers. The IN AR-SSD model [14], [15], combining rain- bo w concatenation with the SSD algorithm and the Inception module, achie v ed 98.49% and 78.80% accurac y for classifying v e common leaf diseases of tomato and apple, respecti v ely . Bhujel et al. [16], de v eloped a 20-layered lightweight CNN model (l w resnet20 cbam) by incorporating the con v olutional block attention module (CB AM), spatial attention (SA), squeeze and e xcitation (SE), and dual attention (D A) modules into the ResNet-20 architecture to classify tomato leaf diseases. The model attained a T op-1 accurac y of 99.51% with a v alidation loss of 0.0155. A customized CNN w as de v eloped using DenseNet201 as the base architecture, follo wed by adding three con v olutional layers and a attening layer [17]. This model achie v ed the highest v alidation accurac y of 98.26% in diagnosing tomato leaf diseases on the PlantV illage dataset. Hyperparameter tuning w as utilized for Ef cientNet-based transfer learning to achie v e 89% accurac y and 0.235 loss in identifying v e classes of cassa v a leaf diseases [18]. An e xperimental approach optimized h yperparameters, such as batch size, epochs, learning rate, optimizer , and loss function. Inte grating channel, spatial, and pix el attention using ResNet50, multi-feature fusion netw ork (MFFN), and the adapti v e attention mechanism achie v ed 99.8% v alidation accurac y for tomato leaf disease classication [19]. T rials were conducted for 100 epochs using v arious combinations of channel attention module (CAM), position attention module (P AM), and cross-position attention module (CP AM) with a batch size of 4 and a x ed learning rate of 0.0003. Optimal batch size and learning rate v alues can signicantly decrease the training time of the model [20], whereas adjusting the ratios of the dataset for training, testing, and v al idation impro v es the model’ s ac- curac y . Since ResNet50 outperforms visual geometry group (V GG)16 and V GG19 in detecting leaf diseases, an online application [21] for recommending initial treatment by utilizing ResNet50 achie v ed the highest ac- curac y of 98.98%. Datasets of v arying sizes were used to assess the v alidation accurac y and loss of the model. The principal component analysis (PCA) technique using V GG16 [22] and the tw o-stage transfer learning ap- proach emplo ying V GGNet [23] achie v e high accurac y in detecting tomato leaf diseases. This research uses semantic se gmentation to distinguish precisely between disease-af fected and health y re gions. Cutting-edge ap- proaches, such as the proposed U-Net design with skip connections and dilated con v oluti o ns , ensure accurate separation. Researchers emplo yed the T aguchi methodology to optimize h yperparameters within a CNN model for accurate breast histopathology image classication [24]. A similar approach w as applied to determine the optimal architectural conguration for a DL netw ork for mal w are detection [25]. Six of the nine control v ari- ables were assigned tw o le v els, while the number of lters per con v olutional operation w as assigned three le v els. The authors utilized ANO V A to e v aluate model performance and identify signicant parameters based on lar ger -is-better criteria. A generalized T aguchi method w as proposed for optimizing h yperparameters in multi-objecti v e CNN models [26]. The method in v olv ed dening a performance functional v ector , emplo ying e xtended orthogonal arrays(O As), and computing a performance inde x to identify optimal parameter settings. Optimizing h yperparameters is crucial yet challenging in de v eloping DL models. The traditional tri al- and-error method for determining optimal h yperparameter congurations for CNNs is e xhausti v e and time- consuming. Despite their established impact on DL model performance, optimizing CNN h yperparameters for detecting tomato leaf diseases requires further e xploration. This paper proposes a frame w ork that inte grates T aguchi-based h yperparameter ne-tuning and multi-objecti v e P aret o optimization to de v elop a lightweight CNN model for accurately detecting tomato leaf disease. The signicant contrib ution of this research is as: i) T o preprocess the image, we perform v arious augmentations, such as rotation, scaling, ipping, brightness adjustment, normalization, color enhancement, and noise reduction. T omato leaf disease detection using T a guc hi-based P ar eto optimized ... (Bappaditya Das) Evaluation Warning : The document was created with Spire.PDF for Python.
1774 ISSN: 2502-4752 ii) W e designed a lightweight CNN model with less than three million parameters, achie ving superior accu- rac y in tomato leaf disease detection compared to pre vious classical CNN models. This model’ s memory ef cienc y mak es it suitable for deplo yment in resource-constrained en vironments, such as mobile or em- bedded de vices. iii) W e emplo yed a systematic approach to optimize h yperparameters rather than relying on trial and error . In our performance re vie w , we consider v alidation accurac y and loss f actors rather than depending e xclusi v ely on the standard S/N ratio based solely on accurac y . W e e xpand the population to a x ed size by adjusting the de v eloped model’ s h yperparameters. i v) W e de v eloped the most rob ust and least vulnerable model by making a trade-of f between multi-objecti v es using P areto front optimization. The rest of the paper is structured as follo ws: section 2 outlines the proposed methodology . Section 3 pro vides detailed e xplanations and discussions of the research ndings. Final ly , section 4 concludes with dif ferent application areas of our research. 2. METHOD This comprehensi v e approach ensures accurate crop disease identication through a str eamlined process, as depicted in Figure 1. Figure 1. Process o w diagram of proposed model 2.1. Datatset pr eparation A total of 18,160 tomato leaf images with laboratory backgrounds were used from 10 classes col- lected from the publicly a v ailable Kaggle dataset. These images were di vided into training (13,083), v alidation (3,265), and testing (1,812) sets. Representati v e images from each class are sho wn in Figure 2. T o ensure compatibility with our proposed model, all images were resized to 224 × 224 pix els. 2.2. Data pr epr ocessing 2.2.1. Data augmentation In preprocessing, data augmentation i s a v aluable machine learning (ML) technique that combats o v er - tting by generating di v erse modied v ersions of e xisting data. This process often applied to images, in v olv es ipping, cropping, rotation, resizing, and more transformations. Random rotation is a common approach that repositions objects in the frame by applying arbitrary clockwise or anticlockwise rotations. Scaling refers to resizing a digital image while maintaining its aspect ratio to ensure it does not appear distorted. Flipping or mirroring pix els horizontally or v er tically creates a mirror ef fect and can increase dataset di v ersity . Enhancing image brightness through pix el intensity adjustments during preprocessing di v ersies data. Indonesian J Elec Eng & Comp Sci, V ol. 37, No. 3, March 2025: 1772–1784 Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 1775 Figure 2. Representati v e tomato leaf image from each class 2.2.2. Normalization Normalization in preprocessing adjusts pix el intensity ranges, which is benecial for impro ving glare- damaged images by contrast or histogram stretching. It enhances ML algorithm ef cienc y and accurac y . The normalization process can be mathematically represented as: x nor m = x x min x max x min (1) where x is the original pix el v alue, x min and x max are the minimum and maximum pix el v alues in the image, respecti v ely , and x nor m is the normalized pix el v alue. 2.2.3. Color enhancement Color enhancement reduces illumination and camera-related v ariations by enhancing color cons is- tenc y . The specialized algorithms correct color discrepancies to impro v e data quality , aiding in accurate disease detection on agricultural crop images. 2.2.4. Noise r eduction Noise reduction, a typical digital image processing task, remo v es unw anted pix el v alue uctua tions, enhancing clarity and aiding visual analysis, often using lters and Gaussian blur . A Gaussian blur , achie v ed through a Gaussian function, is a standard graphics ef fect that reduces visual noise and detail. It dif fers signi- cantly from bok eh or shado ws, crea ting a smooth, translucent screen-lik e appearance. A Gaussian blur applies a weight to nearby pix els based on the tw o-dimensional Gaussian function gi v en by (2). g ( X , Y ) = 1 2 π σ e X 2 + Y 2 2 σ 2 (2) Where X represents the horizontal axis, Y the v ertical axis, and σ the standard de viation in a Gaussian distri- b ution. The Gaussian function peaks at (0,0), and its magnitude diminishes with increasing X or Y . 2.3. Pr oposed lightweight CNN Our proposed lightweight CNN architecture le v erages ef cient b uilding blocks to achie v e accurat e tomato leaf disease classication. The architecture incorporates v e distinct block types: Con vBlock, Incep- tionBlock, FireBlock, GhostBlock, and AttentionBl ock as sho wn in Figure 3. A Con vBlock is a fundamental block consisting of three stack ed Con vModules. Each Con vModule utilizes a tw o-dimensional (2D) con v olu- tional layer follo wed by a 2D max-pooling layer . The con v olutional layer e xtracts features by applying trainable lters to the input image, generating unique feature maps for dif ferent image locations. The subsequent max- pooling layer do wnsamples the feature maps while retaining the most signicant information by selecting the maximum v alue within non-o v erlapping re gions. This do wnsampling reduces model parameters, impro v es translation in v ariance, and promotes spatial re gularization to mitig ate o v ertting. T omato leaf disease detection using T a guc hi-based P ar eto optimized ... (Bappaditya Das) Evaluation Warning : The document was created with Spire.PDF for Python.
1776 ISSN: 2502-4752 Figure 3. Proposed lightweight CNN architecture detailing inception, re, and ghost modules The InceptionBlock recei v es the output from the Con vBlock and comprises tw o consecuti v e inception modules. While structurall y similar to the modules used in GoogLeNet, our implementation utilizes v arying k ernel sizes and lter quantities in the rst incept ion module to enable feature learning across multiple scales. This approach enhances model accurac y by mitig ating the v anishing gradient problem, a common issue in deep neural netw orks. Additionally , a 1 × 1 con v olutional lter within the inception module allo ws the netw ork to learn patterns across the entire image depth, reducing feature map dimensionality . The FireBlock comprises three re modules in series, recei ving an output from the InceptionBlock as input. FireBlock e xpands the channel depth by 12 on input. Each of the initial tw o re modules stretches the input channel depth by 4 of their input, while the third one by 3. The re module primarily focuses on optimizing computation and e xtr acting features in an ef cient w ay . The re module increases the number of channels of input feature maps while preserving height and width. The rst re module in our architecture transforms feature maps from (27, 27, 32) to (27, 27, 128). MaxPooling2D of Con vModule reduces feature map dimensions by do wnscaling and preserving essential features while reducing the computation and mem- ory requirem ents. The Con v olution2D operation in Con vModule generates multiple feature maps that capture dif ferent patterns without altering the spatial dimensions. As a result, the Con vModule reduces the dimensions of the input feature maps from (27, 27, 128) to (14, 14, 96). The input of the ne xt re module will be feature maps with dimensions (14, 14, 96). Thus, a Con vModule acts as a bridge between tw o sequentially connected re modules. Our modied approach has allo wed us to reduce the input dimension by 50%, leading to remark- able ef cienc y in learning high- and lo w-le v el input features. The GhostBlock, composed of tw o sequentially connected ghost modules [27], ef ciently generates additional feature maps through linear operations. Each ghost module rst em p l o ys standard con v olut ions follo wed by linear tr ansformations to produce additional feature maps. Attention module enables the netw ork to focus on the most critical features and generates a feature map. Global a v erage pooling is a process that reduces the spatial dimension of the feature map generat ed by the AttentionBlock and con v erts it into a x ed-length feat ure v ector . Each element of the v ector is assigned a channel wise singular v alue. A dense layer with the rectied linear unit (ReLU) acti v ation function is added follo wing the global a v erage pooling operation. The ReLU acti v ation function helps to speed up the training process by reducing the lik elihood of v anis hing gradients. The dropout layer follo ws the dense layer . The dropout layer randomly drops neurons after each iteration to pre v ent o v er -reliance on specic features. Indonesian J Elec Eng & Comp Sci, V ol. 37, No. 3, March 2025: 1772–1784 Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 1777 2.4. Hyper parameters optimization 2.4.1. Contr ol factors and le v el selection This study e xamined the inuence of six k e y h yperparameters on a CNN model’ s perform ance: epochs, learning rate, batch size, optimizer , number of neurons in the nal dense layer , and dropout rate. W e assigned a discrete set of le v els to each h yperparameter to enable a systematic e v aluation. All h yperparam- eters, e xcept dropout rate, were assigned equal le v els to ensure a balanced e xploration of the h yperparameter space. Utilizing the data presented in T able 1 and the formulas in section 2.4.2, we constructed an ef fecti v e O A, as sho wn in T able 2. This array allo ws us to assess e v ery possible combination of h yperparameter v alues systematically . T able 1. Le v el of h yperparameters and corresponding v alues Le v el Hyperparameters Neurons at dense layer Epoch Optimizer Learning rate Dropout rate Batch size Le v el 1 90 10 RMSprop 0.0001 0.10 16 Le v el 2 120 25 AdamW 0.0002 0.20 32 Le v el 3 50 Nadam 0.0003 0.30 64 Le v el 4 75 Adam 0.0005 0.40 128 2.4.2. Design of orthogonal array The minimum number o f e xperiments for N number of control f actors in the T aguchi method is dened as [18], ( D O E ) min = N X j =1 ( D O F ) j + 1 (3) and DOF of a control f actor with L le v el is dened as, ( D O F ) L = L 1 (4) In this study , we in v estig ated six v ariables, comprising v e control v ariables, each with four le v els and one binary v ariable. This e xperimental setup resulted in a total of 16 de grees of freedom. An L 16 (4 5 ) T aguchi O A w as emplo yed to e xplore the design space for the initial v e v ariables ef ciently . Subsequently , to accommodate the binary v ariable and e xpand the e xperimental scope, we e xtended the array to 32 e xperimental runs. This e xpansion w as achie v ed by i ncorporating the tw o le v els of the sixth v ariable while ensuring a uniform distrib ution of le v els across all parameters. This approach not only s atised b ut e xceeded the minimum requirements for e xperimental size, thereby enhancing the statistical rob ustness of the analysis. 2.4.3. T aguchi method The T aguchi method, a rob ust optimization frame w ork de v eloped by Genichi T aguchi, has signi- cantly enhanced product and process quality across v arious industries [28]. Unlik e the e xhausti v e full f actorial approach, T aguchi’ s methodology reduces the e xperim ental b urden while ef fecti v ely identifying optimal pa- rameter combinations. V alidation accurac y and loss are critical metrics for assessing DL model performance. Hyperparameters, such as epoch, learning rate, optimizer , batch size, and dropout, substantially impact these metrics. T raditionally , researchers ha v e relied on time-consuming trial-and-error methods to optimize these h yperparameters. The T aguchi method of fers a more ef cient alternati v e using O A to e xplore the design space systematically . O As enable the in v estig ation of multiple f actors and their interacti ons with a minimal number of e xperiments. Although the selection of O As is inuenced by the number of control parameters and their le v els [29], researchers can customize the array size to meet specic e xperimental requirements [30]. The T aguchi method is notably more ef cient than the full f actorial approach, requiring signicantly fe wer e xperi- ments ( L × ( P 1) compared to L P ), where L represents the number of le v els, and P denotes the number of parameters. This ef cienc y is particularly adv antageous when computational resources or time constraints are limiting f actors. The T aguchi method uses the signal-to-noise ratio (S/N) as an optimization criteri on, which is dened by (5). S/N = Desired signal strength Unw anted noise po wer (5) T omato leaf disease detection using T a guc hi-based P ar eto optimized ... (Bappaditya Das) Evaluation Warning : The document was created with Spire.PDF for Python.
1778 ISSN: 2502-4752 The S/N v alue is determined based on the problem type and e v aluated using one of three performance criteria: lar ger -is-better , smaller -is-better , or nominal-is-better . F or the lar ger -is-better criterion, the S/N ratio is gi v en by: η l = ( S / N ) l = 10 log   1 n n X i =1 1 y 2 i ! (6) for the smaller -is-better criterion, the S/N ratio is: η s = ( S / N ) s = 10 log   1 n n X i =1 y 2 i ! (7) for the nominal-is-better criterion, the S/N ratio is: η a = ( S / N ) a = 10 log y 2 s 2 y (8) here, y i represents the outcome of the i -th run of a collection of n observ ations, y 2 denotes the mean squared response, and s 2 y is the v ariance. 2.4.4. P ar eto optimization P areto optimization, also kno wn as P areto front optimization, is a technique for multi-objecti v e op- timization in v arious elds, i ncluding engineering and mathematics. P areto dominance is the k e y concept in P areto front optimization. The domination between tw o solutions is dened as [31], [32]: A solution P1 is considered to dominate another solution P2 if and only if both of the follo wing conditions are satised: a) The solution P1 is superior or equal to P2 in all objecti v es. b) The solution P1 is superior to P2 in at le ast one objecti v e. The non-dominant points are represented as a non-domination front. In Figure 4, the curv e passing through P 3 , P 5 , and P 6 labeled as ”Non-dominated front” of the graph with tw o conicting objecti v es - f 1 and f 2 respecti v ely . Figure 4. A set of points along with the rst non-dominated front 2.4.5. Pr oposed T aguchi-based P ar eto fr ont optimization algorithm The o wchart of our proposed algorithm is sho wn in the Figure 5. In our Algorithm 1, the size of the O A(R) depends solely on the number of control f actors (P) and the le v els for each control f actor (le v elF actor). The proposed T aguchi-based P areto front optimization (TPFO) tak es a parameter named totalT rials equal to R. Indonesian J Elec Eng & Comp Sci, V ol. 37, No. 3, March 2025: 1772–1784 Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 1779 The v alue of R is deri v ed using the formula and technique e xplained in section 2.4.2, le v elF actor = [ j k | j { 1 , . . . , P } , k { 1 , . . . , L i } ] be a set of arrays where j k refers to the k -th le v el of the j -th f actor . The function CREATE OA generates an O A of size R ( L R ) with P number of control f actors and levelFactor . The literature re vie w established the function ar guments. A v ector with P components represents each input for P h yperparameters and is mathematically represented as, H = [ h 1 ( τ ) , h 2 ( τ ) , . . . , hP ( τ )] where hi ( τ ) represents the le v el of the i -th h yperparameter at the τ -th trial. Each SETFACTOR operation uses a unique combination of parameter le v els f rom the T aguchi table. CONDUCT EXP runs the e xperiment using that setting as input and records the outcomes in T . T is a 2D table wi th R (total number of trials/runs) ro ws and tw o columns for storing v alidation accurac y and loss v alues. F or ins tance, T [ τ ][1] and T [ τ ][2] contain the v alidation loss and accurac y for the τ -th trial. The SORT and FILTER functions arrange T s v alidation accurac y records in descending order and discard those records belo w a user -dened threshold. Create a scatter plot of ltered records where each point P τ represents a feasible solution in the objec- ti v e space dened by objecti v e 1 and objecti v e 2 for the τ -th entry of the O A. FIND SOLUTIONS compares each solution with e v ery other solution to determine whether an y other solution dominates. Add the solution to the Best Response set only if no other solutions dominate it. H is a set of combinations of h yperparam- eters considered the best possible settings for achie ving optimal results, i.e., H H . Highlight the P areto front by sk etching non-dominated solutions. Figure 5. Flo wchart of T aguchi-based pareto optimized CNN T omato leaf disease detection using T a guc hi-based P ar eto optimized ... (Bappaditya Das) Evaluation Warning : The document was created with Spire.PDF for Python.
1780 ISSN: 2502-4752 Algorithm 1. TPFO for h yperparameters tuning 1: Pr ocedur e TPFO(totalT rials) 2: Declare τ , T [1 ..R , 1 .. 2] , P , LP , Threshold 3: Input: H = { [ h 1 ( τ ) , h 2 ( τ ) , . . . , hP ( τ )] , 1 hi ( τ ) L i and 1 τ R , follo wing T aguchi orthogonal array } 4: Initialize total T r ial s R , τ 0 , H , B est R esponse { [ −∞ , + ] } 5: Set numF actor s P , l ev el F actor [ L 1 , L 2 , L 3 , . . . , L P ] 6: // Create a T aguchi orthogonal array with R number of ro ws // 7: LR C R E AT E O A ( P , l ev el F actor ) 8: // Perform the e xperiments for each trial // 9: while τ < R do 10: SET F A CT ORS( H τ ) 11: [ V al Accur acy , V al Loss ] C O N D U C T E X P ( τ ) 12: T [ τ , 1] V al Accur acy 13: T [ τ , 2] V al Loss 14: τ τ + 1 15: end while 16: SOR T DESCEND( T .V al Accur acy ) { Sort the table by V alAccurac y in descending order } 17: FIL TER( T ) based on ( T .V al Accur acy T hr eshol d ) 18: PLO T((Filtered( T ))) 19: B est R esponse B est R esponse { F I N D S O L ( F il ter ed ( T )) } 20: H H { H associated with B est R esponse } 21: Dra w P areto front. 3. RESUL TS AND DISCUSSION W e performed our in v estig ations on a laptop equipped with an AMD Ryzen 5 5600H processor , an NVIDIA GeF orce GTX 1650 GPU, and a 64-bit W indo ws 11 operating system. T ensorFlo w with K eras in Python 3.9.12 w as the DL frame w ork, utilizing CUD A 11.6 for GPU acceleration. Additionally , we beneted from the high-performance GPU P100 setup of fered by Kaggle accelerators for computationally intensi v e tasks. An e xperimental design based on a T aguchi O A w as emplo yed to in v estig ate the inuence of h yperpa- rameters on model performance. The results, presented in T able 2, stem from multiple trials using tw o distinct models with v arying h yperparameters. Each trial in v olv ed dif ferent settings for the number of ne u r on s in the dense layer , epochs, optimizer , learning rate, dropout rate, and batch size. The primary objecti v e of the se trials w as to identify the most ef fecti v e combinations of these h yperparameters. W e conducted paired and unpaired t- tests to assess the impact of the number of neurons on model performance. The results, summarized in T able 3, indicate no statistically signicant dif ferences between model 1 and model 2 re g arding v alidation accurac y and loss. W e ha v e used the Pearson correlation coef cient to analyze the linear relationship between numeric h yperparameters and model performance. The optimizer , being a cate gorical v ariable, w as e xcluded from this analysis. The results, visualized in Figure 6, re v ealed a strong positi v e correlation between epochs and learning rate with v alidation accurac y (r = 0.7476 and r = 0.7370, respecti v ely). These r v alues indicate that increases in these h yperparamet ers are associated with impro v ed model performance. Con v ersely , epochs and learning rate e xhibited the strongest ne g ati v e correlation with v alidation loss (r = -0.7334 and r = -0.7289, respecti v ely), suggesting that increasing these h yperparameters leads to a decline in model error . Both h yperparameters e xhibited statistically signicant (p-v alue < 0.05) positi v e correlations with v alidation accurac y and ne g ati v e correlations with v alidation loss. Dropout sho wed ne gligible correlations with v alidation accurac y (r = -0.2518, p = 0.1795) and v alidation loss (r = 0.2748, p = 0.1416), suggesting that dropout may not ha v e been a critical f actor in impro ving model performance within the e xplored parameter space. Similarly , batch size had minimal impact on v alidation accurac y (r = -0.2161, p = 0.2514) and v alidation loss (r = 0.2118, p = 0.2612), indicating that the range of batch sizes tested had a ne gligible ef fect on model generalization. The res ults indicate that epochs and learning rate are the most critical h yperparameters inuencing model performance. Careful tuning of these parameters can lead to signicant impro v ements in v alidation accurac y and reductions in v alidation loss. Dropout and batch size, within the ranges e xplored, ha v e minimal impact on the model’ s performance. W e accomplished a comparati v e analysis of four optimizers (Adam, Nadam, AdamW , and RMSprop) to e v aluate their impact on model performance. Adam demonstrated superior performance across all metrics, achie ving the highest v alidation accurac y (99.794%) with the lo west v alidation loss (0.00653). Ne v ertheless, it displayed a broader range of performance, indicating a possible sensiti vity to h yperparameter settings or dataset Indonesian J Elec Eng & Comp Sci, V ol. 37, No. 3, March 2025: 1772–1784 Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 1781 characteristics. Nadam e xhibited e xceptional performance, achie ving the highest accurac y of 99.846% and the lo west loss of 0.00703. While its performance w as consistent, it did not consistently surpass Adam. AdamW and RM Sprop generally underperformed compared to Adam and Nadam. The performance of RMSprop w as characterized by the broadest range of outcomes, suggesting potential instability . T able 2 illustrates that o v er 93% of the trials achie v ed an accurac y e xceeding 90%, with 30% of cases surpassing 99% accurac y . W e ha v e selecti v ely presented data points with v alidation accurac y greater than 99% to visualize top-performing models. T rials 15 and 32 demonstrated e xceptional performance, achie ving v alidation accuracies of 99.846% and 99.794%, respecti v ely , with corresponding losses of 0.00703 and 0.00653. Both trials belong to the rst non- dominated P areto front as sho wn in Figure 7, pro viding options for selecting optimal models. The choice of optimizer signicantly impacts model performance, with Adam demonstrating superior o v erall results. Ho w- e v er , its sensiti vity suggests that it may only be uni v ersally optimal for some scenarios. Nadam emer ged as a reliable alternati v e, balancing performance and stability . RMSprop and AdamW generally underperformed compared to Adam and Nadam. Future research should focus on e xpanding the dataset and e xploring a broader range of h yperparameter v alues. Additionally , in v estig ating adapti v e optimization techniques that inte grate the strengths of v arious optimizers could be a promising direction for future w ork. T able 2. Performance e v aluation of h yperparameter combinations using O A with multiple objecti v es T rials Model Hyperparameters Objecti v es Neurons at dense layer Epoch Optimizer Learning rate Dropout Batch size V alidation accurac y V alidation loss 1 Model 1 1 1 1 1 1 1 94.425% 0.18000 2 1 1 2 2 2 2 93.016% 0.19360 3 1 1 3 3 3 3 93.690% 0.19640 4 1 1 4 4 4 4 88.730% 0.32100 5 1 2 1 2 3 4 96.202% 0.11780 6 1 2 2 1 4 3 95.160% 0.13580 7 1 2 3 4 1 2 96.018% 0.11360 8 1 2 4 3 2 1 97.672% 0.07540 9 1 3 1 3 4 2 97.978% 0.06000 10 1 3 2 4 3 1 93.720% 0.18100 11 1 3 3 1 2 4 98.890% 0.03845 12 1 3 4 2 3 1 99.264% 0.02160 13 1 4 1 4 2 3 98.500% 0.04890 14 1 4 2 3 1 4 99.660% 0.01350 15 1 4 3 2 4 1 99.846% 0.00703 16 1 4 4 1 3 2 99.755% 0.00700 17 Model 2 2 1 1 1 1 1 93.660% 0.17460 18 2 1 2 2 2 2 95.069% 0.14500 19 2 1 3 3 3 3 95.038% 0.13590 20 2 1 4 4 4 4 87.351% 0.34750 21 2 2 1 2 3 4 92.890% 0.19380 22 2 2 2 1 4 3 97.703% 0.06658 23 2 2 3 4 1 2 96.477% 0.09570 24 2 2 4 3 2 1 97.152% 0.07570 25 2 3 1 3 4 2 97.700% 0.07362 26 2 3 2 4 3 1 95.957% 0.17560 27 2 3 3 1 2 4 99.173% 0.02460 28 2 3 4 2 1 3 99.387% 0.01880 29 2 4 1 4 2 3 98.652% 0.04483 30 2 4 2 3 1 4 99.690% 0.01010 31 2 4 3 2 4 1 99.720% 0.01160 32 2 4 4 1 3 2 99.794% 0.00653 T able 4 presents a comparati v e analysis of v arious CNN models for tomato leaf dise ase classi cation based on the number of trainable parameters and achie v ed accurac y . The proposed TPF O CNN outperforms all other models with a v alidation accurac y of 99.84% while maintaining a reduced number of trainable parameters ( < 3 M). Inte grating an attention mechanism ef fecti v ely captures rele v ant features, contrib uting to enhanced performance. In contrast, LMBRNet [9] achie v es a high accurac y of 99.70% b ut with a lar ger parameter count. T omato leaf disease detection using T a guc hi-based P ar eto optimized ... (Bappaditya Das) Evaluation Warning : The document was created with Spire.PDF for Python.