Enhancing hybrid genetic algorithm performance in reducing steel usage for shipbuilding through sensitivity analysis

Abstract

In ship construction, material costs constitute a substantial portion of the overall expenses. With the surging steel prices, the shipbuilding industry faces a pressing challenge. To counterbalance this issue, optimizing the structural components of ships has emerged as a viable solution. Genetic Algorithm (GA) methods, known for their application in structural optimization, have demonstrated their potential. However, the protracted computational time associated with GA remains a limiting factor. This research introduces a novel approach by merging GA with Finite Element Method (FEM) for optimizing plate sizes, resulting in a hybrid GA system. Moreover, the study incorporates sensitivity analysis (SA) due to its proven efficacy in enhancing optimization processes involving multiple variables. The SA component investigates plate interrelationships and effectively clusters them. After this grouping, the hybrid GA executes parallel optimization of plates that influence each other under tension. By integrating SA, the optimization process becomes faster and more time-efficient, while preserving optimal manufacturing costs. Remarkably, this methodology culminates in a substantial reduction in computational time when contrasted with the hybrid GA approach devoid of SA, all the while maintaining a parallel manufacturing cost trajectory. In conclusion, this study presents an innovative hybrid GA approach, supplemented with SA, as an effective strategy for mitigating the escalating steel costs in shipbuilding. The amalgamation of GA, FEM and SA synergistically simplifies the optimization process, ensuring optimal results in a faster way.

Keywords:

• Material selection
• sensitivity analysis
• hybrid genetic algorithm
• computation time
• material cost

REVIEWING EDITOR:

• Zhou Zude, Senior Editor, Wuhan University of Technology, China

SUBJECTS:

• Science
• Mathematics & Statistics
• Statistics & Probability
• Operations Research
• Optimization
• Technology
• Engineering & Technology
• Civil, Environmental and Geotechnical Engineering
• Marine and Offshore Structures
• Social Sciences
• Built Environment
• Architecture
• Structure, Materials and Detailing

1. Introduction

Constructing a ship entails significant expenses, especially in terms of material procurement. Lowering material costs can provide shipyards with a competitive edge and decrease overall ship manufacturing expenditures. Furthermore, the prices of fuel and materials have experienced substantial hikes, resulting in escalated ship production and operational expenditures. This trend has motivated stakeholders in the maritime sector to prioritize efficiency across all operational domains. To tackle these issues, optimizing material utilization and minimizing ship weight to reduce material costs and fuel consumption emerge as viable solutions. Numerous shipbuilding industries have initiated the use of high-strength steel as plate material to reduce weight and fuel consumption. Meanwhile, the automotive industry has previously employed this material in crafting lightweight vehicles (Kwon et al., 2010). The advantages of high-strength steel encompass exceptional energy absorption, enhanced strength and the capacity to diminish weight through the utilization of thinner materials (Sonsino, 2007).

However, the cost of high-strength steel is relatively higher in comparison to the commonly used mild steel. Therefore, an approach for material selection becomes necessary to achieve optimal material cost. This procedure holds significant importance in manufacturing industries, including the automotive and aircraft sectors (Poulikidou et al., 2015), as it aids in decreasing the weight of structures (Tawfik et al., 2016) and material expenses. The ultimate material selection involves striking a balance between the various materials, considering their advantages and drawbacks (Ahmad et al., 2023; Syed et al., 2023). Recent studies have demonstrated that applying the material selection method using the Genetic Algorithm (GA) (Putra et al., 2021; Putra & Kitamura, 2021) can effectively decrease material costs. However, GA faces a limitation concerning computational time, demanding a substantial duration to attain the optimal solution. Moreover, as the number of plates and material types in the selection process increases, the computation time for GA also lengthens. Hence, there is a necessity to introduce an approach that establishes relationships between plates and clusters according to their stress distribution. This method is anticipated to alleviate the computational load on GA by forming plate groups.

One method to establish relationships between plates and group them based on their stress distribution is Sensitivity Analysis (SA). SA is a relatively common approach for discerning relationships between factors and responses through a limited number of tests (He et al., 2022). The Response Surface Method (RSM) is a SA tool that has found application in numerous studies for estimating and optimizing solutions. For example, it has been employed to formulate prediction equations to estimate wave height in cases where there is insufficient or unavailable nearshore measurement data (Ti et al., 2018). RSM has also been utilized to optimize the parameters of a rectangular cambered otter board, aiming to uphold favorable fishing efficiency, particularly for fishing targets (Xu et al., 2021).

This study proposes the grouping of plates with close relationships to reduce the GA’s load. To achieve this, the suggested approach involves SA before integrating the hybrid GA, which aims to curtail the number of genes, thereby reducing computational time. The plate material options encompass mild steel, AH32 and AH36, each differing in mechanical properties, notably in strength. The optimization process centers on curtailing material costs through adeptly selecting plate materials and reducing thickness. SA is employed to cluster plates based on their stress distribution, thereby diminishing the number of genes in the optimization process. The hybrid GA combines GAs and other optimization techniques to ascertain the optimal plate material type and thickness. The incorporation of SA into the optimization process anticipates a substantial reduction in computation time.

2. Optimization method

Ships are primarily constructed using plates and stiffeners, which are essential components focused on optimization to decrease plate thickness and the size of stiffeners. However, the extensive quantity of plates needed in ship construction adds complexity to the optimization process, particularly when it comes to selecting the right plate type and determining the appropriate size for stiffeners. Previous research has employed the hybrid GA method to cut down on material costs and reduce the weight of ships. However, this optimization process tends to be time-consuming (Putra & Kitamura, 2023). Consequently, there is a pressing need for a more streamlined approach to ease the burden on the GA during optimization.

2.1. Sensitivity analysis

The proposed SA method aims to determine plate grouping in the optimization process, as depicted in Figure 1. This technique involves analyzing uncertainties in the output of a numerical model or other factors that can contribute to reducing uncertainty in the model (Saltelli, 2002). SA is a powerful tool that can aid in predicting better models by qualitatively and/or quantitatively studying the model’s response to changes in input variables or by analyzing the interactions between variables to better understand the phenomena under study (Pichery, 2014). By incorporating SA into the plate grouping process, it is expected that the optimization process can be made more efficient and effective in reducing the computational burden of the hybrid GA method. In other words, SA can help enhance optimization performance and guide the informed decision-making process (Zhang et al., 2023).

Figure 1. Workflow of optimization method.

Furthermore, SA provides a systematic and quantitative approach to evaluating the significance of input variables or factors on the model’s output. It can help identify the most influential factors and reduce the computational burden by minimizing the number of factors to be considered in the optimization process (Ma et al., 2022). This is particularly useful in complex systems like ship structures, where many input variables can significantly increase the computational time and complexity of the optimization process.

In this study, SA is employed to group plates with the closest stress relationship, based on the stress distribution within the structure, as depicted in Figure 2. This grouping of plates reduces the number of genes in the chromosome, subsequently lessening the computational burden on the GA. This approach has the potential to decrease the time and resources required for optimization while still achieving desired outcomes. Overall, by integrating SA with the hybrid GA method, this study aims to enhance the efficiency and accuracy of the optimization process for material selection in ship structures, while also decreasing computational time and resource needs. This approach could hold significant implications for the shipbuilding industry, potentially resulting in substantial cost savings and improved design efficiency.

Figure 2. SA procedure.

2.2. Genetic algorithm

In this study, the primary objective was to reduce the material cost and decrease the weight of the structure through a meticulous material selection procedure. To achieve this goal, the researchers proposed applying the GA, a widely employed optimization technique for addressing material selection challenges. Within this context, GA was used to distinguish the most suitable plate material type among the options of mild steel and high-strength steel (Beasley et al., 1993; Sen & Yang, 2011). The GA method encompassed a solution set and employed selection, reproduction and mutation procedures. The selection process was inspired by the principle of natural selection, commonly called survival of the fittest, where the more robust entities endure, and the weaker ones fade away (Futuyma, 2014). By utilizing the capabilities of GA, the researchers desired to obtain an optimal solution for material selection that effectively reduces both material cost and structural weight.

The process of material selection is a pivotal step in identifying the optimal material for a given application, considering both material properties and design constraints. It requires integrating material properties derived from datasheets with specific design requirements to establish a ranking system that determines the most suitable material for the application. This process is essential to ensure that the selected material aligns with the precise application needs and ultimately enhances the overall success of the design.

Previously, the GA was extensively employed to obtain the most suitable type of plate material from the entire plate arrangement. This issued a substantial load on GA due to the escalating number of combinations, leading to longer computation times.

By dividing several plates into smaller groups, the number of combinations can be significantly reduced, thus lightening the burden on GA. As depicted in Figure 3, the outcomes of SA produce plate data with the closest relationships, subsequently arranging the plates to be optimized in order of significance, from the most influential to those with minimal impact. The final step involves segmenting them into several smaller groups, aiming to expedite the GA process in generating suitable combinations for these groups. This is achieved because fewer genes translate to fewer combinations, enabling GA to converge rapidly.

Figure 3. Plate grouping to GA process.

2.3. Size optimization

In the context of physical products, size optimization can encompass the redesign of a product to reduce its physical dimensions while preserving its intended functionality. This might require the incorporation of lighter materials, more streamlined designs, or other innovative approaches. Size optimization holds significance due to its potential to produce various advantages, including cost reduction, enhanced performance and increased efficiency. (1) $$t_{{\sigma }_{\mathit{\text{ax}}}}^{a+1}=\frac{{\sigma }_{\mathit{\text{ax}}}^a}{{\sigma }_c}{t}^a\mathrm{ }$$(1) (2) $$t_{{\sigma }_{\mathit{\text{bd}}}}^{a+1}=\sqrt{\frac{{\sigma }_{\mathit{\text{bd}}}^a}{{\sigma }_c}}{t}^a\mathrm{ }$$(2) (3) $$t_{a+1}=\mathrm{\text{max}}\hspace{0.17em}\left(t_{{\sigma }_{\mathit{\text{ax}}}}^{a+1},t_{{\sigma }_{\mathit{\text{bd}}}}^{a+1}\right)$$(3)

The plate thickness optimization process involves the application of stress formulas to derive two distinct thickness values, which are critical in ensuring structural integrity. Equations (1)(1) $$t_{{\sigma }_{\mathit{\text{ax}}}}^{a+1}=\frac{{\sigma }_{\mathit{\text{ax}}}^a}{{\sigma }_c}{t}^a\mathrm{ }$$(1) and (2)(2) $$t_{{\sigma }_{\mathit{\text{bd}}}}^{a+1}=\sqrt{\frac{{\sigma }_{\mathit{\text{bd}}}^a}{{\sigma }_c}}{t}^a\mathrm{ }$$(2) represent these formulas, where σ_ax signifies axial stress, σ_bd stands for bending stress and σ_c means the allowable stress for the material. Equation (3)(3) $$t_{a+1}=\mathrm{\text{max}}\hspace{0.17em}\left(t_{{\sigma }_{\mathit{\text{ax}}}}^{a+1},t_{{\sigma }_{\mathit{\text{bd}}}}^{a+1}\right)$$(3) , the maximum value between the two thicknesses determined by the stress formulas, is selected as the optimal plate thickness. This selection process is integrated into the GA process, resulting in a powerful hybrid GA approach. This combination, depicted in Figure 4, utilizes the strengths of both techniques to yield an optimized plate thickness that meets structural requirements efficiently.

Figure 4. Hybrid GA procedure.

Plate thickness optimization is a prime example of size optimization in engineering. This process revolves around finding the ideal thickness for a plate while upholding the necessary strength and functionality criteria. The advantages of plate thickness optimization are multifaceted, encompassing reduced material consumption, lower weight and cost-efficient production. Essentially, techniques like plate thickness optimization are geared toward enhancing efficiency and performance while simultaneously curbing waste and production costs. In this specific study, plate thickness optimization involves a meticulous procedure of ascertaining the optimal plate thickness. This determination is made employing axial and bending stress formulas, which serve as pivotal metrics in the optimization process. It is crucial to note that plate thickness optimization often forms an integral part of a broader optimization endeavor, where advanced methodologies like GAs may be harnessed to pinpoint the optimal material type, further enhancing the overall efficiency of structural design.

This optimization process follows a SA of the plate grouping, a crucial preparatory step. The core of the hybrid GA is its ability to discern the most suitable plate material type while simultaneously determining the optimal plate thickness, all in accordance with specific problem requirements and constraints. This selection process weighs various material types against cost, strength and weight, resulting in a comprehensive and efficient structural design.

After identifying the most suitable material type, the optimization process proceeds to the size optimization stage, a pivotal step in determining the optimal plate thickness. This stage operates based on the specific requirements and constraints defined for the project. Typically, it involves minimizing the weight of the plate while adhering to critical constraints such as the minimum required strength or the maximum allowable deflection. The advantage of a hybrid GA with size optimization is its capacity to enhance the efficiency and precision of the optimization process by capitalizing on the strengths of both techniques. The GA excels at traversing the expansive search space and identifying promising solutions, effectively acting as an explorer. On the other hand, size optimization excels at the fine-tuning aspect of design, delicately adjusting the parameters to ascertain the truly optimal size.

This symbiotic relationship between GA and size optimization streamlines the design process, expedites decision-making and results in a highly efficient and accurate optimization process. By synergizing these complementary strengths, this hybrid approach stands as a robust solution for achieving optimal plate structures in engineering design.

3. Case study

3.1. Model

The model used is like that used in previous studies—namely the hatch cover which consists of the top plate, bottom plate and support beams and stiffeners attached to the top and bottom plates. In the Finite Element Method (FEM) program, shell elements are used for plates and girders, while beam elements are utilized for stiffeners. Detailed information regarding the main dimensions, loads and material types is provided in Table 1. These data are essential for creating a FEM model, incorporating predetermined loads and depicting boundary conditions, as typically illustrated in Figure 5. The longitudinal, transverse and vertical displacements are represented by u, v and w, respectively, while the angular displacements around the x-, y- and z-axes are indicated by θx, θy and θz. The initial hatch cover design consists of two material types: NS (Normal Strength) and AH32 (Higher Strength) as shown in Table 2.

Figure 5. Hatch cover design (A type).

Table 1. Initial data.

Item	Unit	Initial design
L (length)	mm	10,675
W (width)	mm	9462
H (height)	mm	815
Load	N/mm^2	0.0343
Material	–	NS, AH32
Density	kg/m^3	7800
Stiffener (top plate)	mm^2	1362
Stiffener (bottom plate)	mm^2	2736

Table 2. Initial structure design.

Structure	Material type	Thickness (mm)
Plate 0-1	NS	9
Plate 2-3	AH32	11
Plate 4-5	NS	9
Plate 6-8	AH32	10
Plate 9	NS	8
Plate 10	AH32	14
Plate 11-12	AH32	10
Plate 13	AH32	16
Plate 14	NS	8
Plate 15	NS	10
Plate 16	NS	8
Plate 17	NS	10
Plate 18-19	NS	8

Based on the preliminary design data provided in Tables 1 and 2, along with Figure 5, the total material cost required for the structure is estimated to be $7330. The incorporation of different material types within the same model is attributed to variations in load distribution among the top, bottom and transverse plates of the hatch cover.

3.2. Design variables

Within the optimization process of the hatch cover design, two pivotal design variables came under investigation: the plate material type (m_i) and the plate thickness (t_i). The choice of these variables was studied, given their substantial influence on both the mechanical performance and cost considerations of the hatch cover. The plate material type presented three distinct options: Normal Strength (NS), Higher Strength (AH32) and Higher Strength (AH36) as outlined in Table 3. These choices encapsulated the range of materials that could be employed, each with its distinct mechanical properties and cost implications.

Table 3. Material properties.

Material type	Tensile strength (MPa)	Yield strength (MPa)	Density (kg/m^3)	Price ($/ton)^a
NS (normal strength)	400–502	235	7800	533
AH32 (higher strength)	440–590	315	7800	733
AH36 (higher strength)	490–620	355	7800	800

^aSteel Price (2019).

Meanwhile, the plate thickness emerged as an important variable. This dimension was subjected to thorough exploration, spanning a range from 6 mm to 20 mm. The objective was to determine the optimal thickness that would meet the balance between mechanical resilience and cost-effectiveness, ultimately shaping the performance and efficiency of the hatch cover.

3.3. Constraints

The optimization process imposes specific constraint conditions, crucial for maintaining structural integrity and safety while minimizing material usage and weight. These constraints are outlined in the following equations: (4) $$\delta \le 0.0056\bullet l_{\mathrm{\text{max}}}\left(\mathrm{\text{mm}}\right)$$(4) (5) $${\sigma }_{\mathrm{\text{max}}}\le 0.8R_{\mathit{\text{eH}}}(\mathrm{N}/{\mathrm{\text{mm}}}^2)$$(5) (6) $${\sigma }_{\mathrm{\text{sh}}}\le 0.46R_{\mathit{\text{eH}}}(\mathrm{N}/{\mathrm{\text{mm}}}^2)$$(6)

In Equation (4)(4) $$\delta \le 0.0056\bullet l_{\mathrm{\text{max}}}\left(\mathrm{\text{mm}}\right)$$(4) , δ represents the deflection limit and l_max represents the greatest span of the primary supporting members. In Equation (5)(5) $${\sigma }_{\mathrm{\text{max}}}\le 0.8R_{\mathit{\text{eH}}}(\mathrm{N}/{\mathrm{\text{mm}}}^2)$$(5) , σ_max represents the maximum stress on the structure, and R_eH represents the yield strength of the material as shown in Table 3. Additionally, in Equation (6)(6) $${\sigma }_{\mathrm{\text{sh}}}\le 0.46R_{\mathit{\text{eH}}}(\mathrm{N}/{\mathrm{\text{mm}}}^2)$$(6) , σ_sh represents the shear stress on the structure. These constraints are not only integral to the optimization process but also instrumental in achieving the study’s objective: optimizing material selection without endangering the ship’s structural integrity.

3.4. Objective function

The main objective of this optimization process is to achieve a reduction in the material cost of the structure. To accomplish this objective, a hybrid optimization method that combines GA with SA has been employed. This comprehensive approach allows for a more efficient and effective optimization process. The core of this optimization effort is expressed through the objective function presented in Equation (7):

(7) $$\mathrm{\text{min}}f\left(t,C\right)={\sum }_{i=0}^{n-1}{t}_i{L}_x{L}_y\rho C_i\mathrm{ }(\mathrm{\text{Rp}})$$(7)

where n is the number of plates, L_x is the length in the x direction (mm), L_y is the length in the y direction (mm), $\rho$ is the density of material (kg/mm³), t_i is the plate thickness (mm), and C_i is the material price (Rp/kg).

4. Result and analysis

To execute the SA in this study, a meticulous stress analysis was conducted for each individual plate within the simulation framework. This analysis aimed to evaluate how stress levels varied under different plate thickness scenarios. Specifically, the thickness of the existing plates was systematically altered by increments of 2 mm, 3 mm and 4 mm to assess their impact on stress distribution. Von Mises Stress was selected as the parameter of choice due to its suitability in designing ductile components, as established in previous research (Bai & Bai, 2014). Using Von Mises Stress as a criterion allowed for the identification of plates that exhibited significant differences in stress values under varying thickness conditions. In essence, when notable disparities in this stress parameter were observed, it signified a relationship between the two plates. Moreover, a 4% change threshold was applied to filter out minor variations. Only changes exceeding this threshold were considered for grouping purposes, ensuring that only the most substantial alterations were utilized in the SA process.

By employing these meticulous methods, the SA process achieved two crucial objectives. First, it effectively reduced the multitude of potential plate combinations, streamlining the optimization process. Second, it led to a notable reduction in the computational time required for optimization, enhancing the overall efficiency of the study’s approach. Figure 6 provides a visual representation of the stress change distribution resulting from the SA tests. This graphic depiction allows for a clear understanding of how stress levels vary across the plates. Notably, plates that exhibit significant changes in stress are singled out as having the closest relationship to the plate subjected to testing. This information is crucial in the subsequent stages of the study.

Figure 6. Stress changed distribution: (a) –2 mm, (b) +2 mm, (c) +3 mm and (d) +4 mm.

Drawing insights from the SA results, Table 4 serves as a valuable summary. It effectively identifies specific plate groupings that are chosen for further examination and inclusion in the subsequent simulation process. These groupings, namely 0-18, 3-9 and 6-13, emerge as the most relevant based on the findings. The simulation phase itself involves a population size of 50 and spans over two generations. The method employed for simulation follows a specific sequence, mirroring the order of stress analysis results outlined in Figure 7. This sequence delineates the progression of the plate simulation, providing a structured and methodical approach to the optimization process.

Figure 7. Plate simulation sequence.

Table 4. Summary of SA.

Group	Plate pairing
	−2 mm	+2 mm	+3 mm	+4 mm
1	3, 9	0, 18	0, 18	0, 18
2	4, 18	3, 9	3, 9	3, 9
3	6, 19	6, 13	6, 13	6, 13

The decision to group the plates in pairs, as illustrated in Figure 7, is grounded in the pursuit of efficiency. When two plates are combined, it leads to a considerably reduced number of potential combinations, facilitating a much faster convergence process. Consequently, each sequence can be executed expeditiously, with the outcomes from each simulation serving as the building blocks for determining the optimal thickness and material type in the subsequent sequence of simulations. This strategy ensures a streamlined and efficient optimization process, ultimately saving time and computational resources.

The simulation outcomes of the hybrid GA with sequences 1–10 initially took 1062 min to complete. However, when the SA process was incorporated, the total time increased slightly to 1067 min, which is approximately 18 h in total. This time investment was accompanied by a noteworthy reduction in material costs. Specifically, the initial cost of $7330 decreased substantially to $3981, resulting in an efficiency gain of approximately 54%, as detailed in Table 5. Upon closer examination of the data, it becomes evident that the hybrid GA simulation integrated with SA outperformed its counterpart that lacked SA. Without the SA component, the simulation process demanded a considerably longer timeframe, stretching to 54 h, with material costs amounting to $3971. This discrepancy in simulation time is striking, with the SA-enhanced approach being 36 h quicker, representing a remarkable 67% reduction in time compared to the non-SA method. Furthermore, while the cost differential was more pronounced with SA, it was not of significant concern.

Table 5. Results of comparison of SA with hybrid GA.

	Without optimization	Hybrid GA (I)	SA + Hybrid GA (II)	Difference (I and II)
Time (h)	–	54	18	−67%
Material cost ($)	7330	3971	3981	+0.25%

A more comprehensive view of the simulation results is provided through Figures 8 and 9, which depict the changes in plate thickness and material type. Figure 8 shows that many plates tend to converge toward a minimum thickness of 6 mm. However, it is worth noting that several plates exhibit an increase in thickness, specifically plates 10, 12 and 19. This increase is primarily attributable to the influence of stress distribution from other plates that experience a decrease in thickness. As a result, these three plates undergo a thickness increase. Nevertheless, when considering the entire structure, it becomes evident that there is an overall reduction in thickness. This reduction not only contributes to a lighter structure but also leads to a decrease in material costs, as described in Table 5.

Figure 8. Plate thickness change.

Figure 9. Material type change.

In essence, these findings underscore the substantial advantages of employing SA within the hybrid GA simulation, demonstrating the potential for significant time savings in the optimization process, which could have significant implications for efficiency and cost-effectiveness in the shipbuilding industry.

Conversely, the transition in material types is notably substantial when compared to the initial design, which featured a well-balanced combination of NS and AH32 materials. Following the comprehensive material selection process, guided by the predefined constraints and the objective of minimizing material costs, there emerges a tendency toward NS as the primary material choice. Notably, the transformation leaves only one plate retaining the AH32 classification, while two plates shift to the AH36 category, as shown in Figure 9. This transition signifies a shift towards more cost-efficient material choices that harmonize with the optimization goals.

5. Conclusions

The findings of this study underscore the transformative impact of integrating SA into the hybrid GA approach. This novel approach translates into a remarkable enhancement in optimization efficiency, with a time reduction of over two-fold when compared to the hybrid GA without SA. It is important to note that the marginal increase in cost, which remains below 1%, can be attributed to factors related to hardware, particularly the processor employed for executing the optimization process. However, it is essential to contextualize this cost difference within the broader framework of substantial time savings and increased computational efficiency. In essence, the adoption of SA in synergy with the hybrid GA methodology emerges as a strategic move, yielding more optimal results while significantly expediting the optimization process. This development holds promising implications for industries, particularly in shipbuilding, where cost-efficiency and timely design processes are of paramount importance.

Acknowledgment

This work was partially supported by Program Pendanaan Inovasi Tahun 2023 Skema Program Pengembangan Produk (P4) No: PKS-138/UN2.INV/HKP.05/2023.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Jos Istiyanto

Jos Istiyanto Finite Element Analysis Gerry Liston Putra: Develop Algorithm and Writing Muhammad Rifqi Ramadhan: Algorithm Analysis and Writing.