Zebra Optimization Algorithm: A New Bio-inspired Optimization Algorithm for Solving Optimization Algorithm

In this paper, a new bio-inspired metaheuristic algorithm called Zebra Optimization Algorithm (ZOA) is developed; its fundamental inspiration is the behavior of zebras in nature. ZOA simulates the foraging behavior of zebras and their defense strategy against predators’ attacks. The ZOA steps are described and then mathematically modeled. ZOA performance in optimization is evaluated on sixty-eight benchmark functions, including unimodal, high-dimensional multimodal, fixed-dimensional multimodal, CEC2015, and CEC2017. The results obtained from ZOA are compared with the performance of nine well-known algorithms. The simulation results show that ZOA can solve optimization problems by creating a suitable balance between exploration and exploitation and has a superior performance compared to nine competitor algorithms. ZOA’s ability to solve real-world problems has been tested on four engineering design problems, namely, tension/compression spring, welded beam, speed reducer, and pressure vessel. The optimization results show that ZOA is an effective optimizer in determining the values of the design variables of these problems compared to the nine competitor algorithms.


I. INTRODUCTION
The optimization problem is a problem that has more than one feasible solution, and optimization is the process of achieving the best solution among all the available solutions to this problem. Each optimization problem is determined by its decision variables, constraints, and objective function [1]. Various analytical methods have been proposed to solve optimization problems, including gradient-based methods and numerical calculations. Methods such as gradient-based are limited to solving simple derivative functions, and when the condition of continuity and derivability of functions does not exist, the gradient method is unusable. On the other hand, the accuracy of numerical calculation methods depends on choosing the appropriate initial solution despite their wide application in solving optimization problems. In such methods, improper selection of initial solutions leads to the optimal local solution [2].
In an optimization problem, it is not only important to find a solution, but also the cost of achieving the solution and its efficiency. Global optimization problems in real applied optimization problems have high dimensions and complexity because they involve many multiple decision variables and many complex nonlinear relationships. The complex and nonconvex nature of the problems and their unknown search space in real-world applications make analytical methods almost unusable [3]. The weakness of analytical mathematical methods in solving optimization problems has led to the creation of a special type of intelligent search algorithms called meta-heuristic algorithms. Meta-heuristic algorithms are stochastic methods that, inspired by nature and its mechanisms, try to send their initial population to the global optimum and provide appropriate solutions close to the global optimum in a reasonable time [3]. Because these solutions may not be the same as the global optima of optimization problems, the solutions obtained from metaheuristic algorithms are called quasi-optimal [4].
Metaheuristic algorithms based on the two concepts of exploration and exploitation are able to find appropriate solutions to optimization problems. The concept of exploration represents the ability of the algorithm to globally search the search space to scan it to identify the optimal area accurately. The concept of exploitation represents the ability In the study of optimization algorithms, the main research question is that despite the numerous metaheuristic algorithms designed, what is the need to develop newer optimization algorithms? The answer to this question based on the No Free Lunch (NFL) theorem [47] is that the optimal performance of an algorithm in optimizing a set of objective problems and functions does not guarantee the optimal performance of that algorithm in solving other optimization problems. The NFL states that any algorithm can never be declared the best optimizer for all optimization issues. Hence, the NFL encourages researchers to design new metaheuristic algorithms to be able to solve optimization problems more effectively by providing better solutions. The NFL motivated the authors of this paper to develop a new metaheuristic algorithm that is highly efficient in achieving optimal solutions to optimization problems.
Zebras are herbivores whose main diet consists of various grasses and plant materials such as leaves and sprouts. The zebra is a social animal that always lives in a herd to protect itself from predators. Although the animal's first instinctive move is to escape the predator, it sometimes confuses or frightens the predator by gathering together to form a defensive structure.
Based on the best knowledge of the literature, simulation of zebra's social behavior in nature has not been employed in the design of any optimization algorithm. In this paper, a new optimizer based on simulation of foraging behavior and defensive strategy of zebras is developed to address this research gap. This paper's novelty and scientific contribution are to design a new metaheuristic algorithm called Zebra Optimization Algorithm (ZOA). ZOA's fundamental inspiration is to model the social behavior of herds of zebras in the wild. The ZOA steps are stated, its mathematical modeling is presented. ZOA performance has been tested on sixty-eight benchmark functions of a variety of unimodal, high-dimensional multimodal, fixed-dimensional multimodal, CEC2015, and CEC2017. The optimization results obtained from ZOA are compared with nine well-known algorithms. The claim of this study is that based on the mathematical simulation of zebras' life, a new and powerful metaheuristic algorithm can be designed for optimization applications. The results of optimization and experiments on objective functions, comparison of ZOA performance with several well-known metaheuristic algorithms, and various analyzes confirm that ZOA is highly efficient in optimization applications.
In the following, the paper is organized so that the proposed algorithm is introduced in Section 2. Simulation studies and analysis of the proposed algorithm are presented in Section 3. The efficiency of the proposed algorithm in solving engineering design problems is evaluated in Section 4. Conclusions and several suggestions for future studies are provided in Section 5.

II. ZEBRA OPTIMIZATION ALGORITHM
In this section, the proposed nature-inspired Zebra Optimization Algorithm (ZOA) is introduced and its mathematical modeling is presented.

A. INSPIRATION
Zebras are equine animals and come from eastern and southern Africa. This animal is famous for its black-and-white striped coat on its body. These stripes are usually located vertically on the neck and body, and they are effective in hiding zebras from predators as well as an inhibitory agent against biting flies. Specifications and descriptions of their conditions are as follows: They have a body length of 210-300 cm with a tail long 38-75 cm, 110-160 cm shoulder height, and weigh 175-450 kg [48]. The zebra is a heavy animal whose long and slender legs help the animal run at high speeds if necessary. Like wild equines, zebras have only one toe on each foot, a long neck, and a head that makes it easy to feed on the grass on the ground [49]. Among the social life behavior of zebras in nature, the two types of behavior are the most important: foraging and defense strategy against predators. In the foraging process, a pioneer zebra opens the way for other zebras to move to the forage. Therefore, other zebras in the herd move in the plains under the guidance of this pioneer zebra [50]. The zebras' first strategy against predators is to escape in a zigzag motion pattern. However, sometimes by gathering, they try to confuse or frighten the predator [48]. Mathematical modeling of these two types of intelligent zebra behavior is the fundamental inspiration for the proposed ZOA design.

B. MATHEMATICAL MODELLING
In this subsection, mathematical simulations of zebra's natural behaviors are presented to model ZOA.

1) INITIALIZATION
ZOA is a population-based optimizer that zebras are members of its population. From a mathematical point of view, each zebra is a candidate solution to the problem and the plain in which the zebras are in the search space for the problem. The position of each zebra in the search space determines the values for the decision variables. Thus, each zebra as a member of the ZOA can be modeled using a vector, while the elements of this vector represent the values of the problem variables. The population of zebras can be mathematically modeled using a matrix. The initial position of the zebras in the search space is randomly assigned. The ZOA population matrix is specified in (1).
where is the zebra population, is the th zebra, , is the value for the th problem variable proposed by the th zebra, is the number of population members (zebras), and is the number of decision variables.
Each zebra represents a candidate solution to the optimization problem. Therefore, the objective function can be evaluated based on the proposed values of each zebra for the problem variables. The values obtained for the objective function are specified as a vector using (2).
where is the vector of objective function values, and is the objective function value obtained for the th zebra.
Comparing the values obtained for the objective function effectively analyzes the quality of their corresponding candidate solutions and identifies the best candidate solution for the given problem. In minimization problems, the zebra with the least value of objective function is the best candidate solution. In contrast, in maximization problems, the zebra with the highest value of the objective function is the best candidate solution. Since in each iteration, the positions of the zebras and consequently the values of the objective function are updated, the best candidate solution must also be identified in each iteration. Two natural behaviors of zebras in the wild have been used to update ZOA members. These two types of behavior include (i) foraging and (ii) defense strategies against predators. Therefore, in each iteration, members of the ZOA population are updated in two different phases.

2) PHASE 1: FORAGING BEHAVIOR
In the first phase, population members are updated based on simulations of zebra behavior when searching for forage. The main diet of zebras is mainly grasses and sedges, but if their favorite foods are scarce, they may also eat buds, fruits, bark, roots, and leaves. Depending on the quality and availability of vegetation, zebras may spend 60-80 percent of their time eating [51]. Among the zebras, there is a zebra called the plains zebra, which is a pioneer grazer, by devouring the canopy of upper and less nutritious grass, provides conditions for other species that need shorter and more nutritious grasses below [50]. In ZOA, the best member of the population is considered as the pioneer zebra and leads other population members towards its position in the search space. Therefore, updating the position of zebras in the foraging phase can be mathematically modeled using (3) and (4).
where , 1 is the new status of the th zebra based on first phase, , , 1 is its th dimension value, , 1 is its objective function value, is the pioneer zebra which is the best member, is its jth dimension, is a random number in interval [0, 1], = round(1 + ), where is a random number in the interval [0, 1]. Thus, ∈ {1,2} and if parameter = 2, then there are much more changes in population movement.

3) PHASE 2: DEFENSE STRATEGIES AGAINST PREDATORS
In the second phase, simulations of the zebra's defense strategy against predator attacks are employed to update the position of population members of ZOA in the search space. The main predators of zebras are lions; however, they are threatened by cheetahs, leopards, wild dogs, brown hyenas, and spotted hyenas [48]. Crocodiles are another predator of zebras when they approach water [52]. Zebras' defense strategy varies depending on the predator. The zebra's defensive strategy against lion attacks is to escape in a zigzag pattern and random sideways turning movements [53]. Zebras are more aggressive against attacks by smaller predators, such as hyenas and dogs, which confuse and frighten the hunter by gathering [48]. In the ZOA design, it is assumed that one of the following two conditions occurs with the same probability: (i) the lion attacks the zebra, and thus, the zebra chooses an escape strategy; (ii) other predators attack the zebra, and the zebra will choose the offensive strategy.
In the first strategy, when the zebras are attacked by lions, the zebras escape from the lion's attack in the vicinity of the situation in which they are located. Therefore, mathematically, this strategy can be modeled using the mode 1 in (5). In the second strategy, when other predators attack one of the zebras, the other zebras in the herd move towards the attacked zebra and try to frighten and confuse the predator by creating a defensive structure. This strategy of zebras is mathematically modeled using the mode 2 in (5). In updating the position of zebras, the new position is accepted for a zebra if it has a better value for the objective function in that new position. This update condition is modeled using (6).
where , 2 is the new status of the th zebra based on second phase, , , 2 is its th dimension value, , 2 is its objective function value, is the iteration contour, is the maximum number of iterations, is the constant number equal to 0.01, is the probability of choosing one of two strategies that are randomly generated in the interval [0,1], is the status of attacked zebra, and is its th dimension value.

B. REPETITIONS PROCESS, FLOWCHART, AND PSEUDO-CODE OF ZOA
Each ZOA iteration is completed by updating the population members based on the first and second phases. The process of updating the algorithm population continues based on (3) to (6) until the end of the full implementation of the algorithm. The best candidate solution is updated and saved during successive iterations. Once fully implemented, ZOA makes the best candidate solution available as the optimal solution to the given problem. The ZOA steps are presented as flowcharts in Figure 1 and its pseudocode in Algorithm 1.
Input: The optimization problem information.

2.
Set the number of iterations (T) and the number of zebras' population (N).

3.
Initialization of the position of zebras and evaluation of the objective function.
Calculate new status of the th zebra using (3). 9.
Calculate new status of the th zebra using mode 2 in (5). 17. end if 18. Update the th zebra using (6). 19. end for i=1:N 20. Save best candidate solution so far. 21. end for t=1:T 22. Output: The best solution obtained by ZOA for given optimization problem. End ZOA.

B. COMPUTATIONAL COMPLEXITY
In this subsection, the computational complexity of ZOA is investigated. ZOA initialization preparation is equal to ( • ) where is the number of zebras and is the number of problem variables. ZOA includes the number of iterations, so that in each iteration, each population member is updated in two phases and its objective function is evaluated. The computational complexity of this update process is equal to (2 • • • ). Thus, the total computational complexity of ZOA is equal to ( • • (1 + 2 • )).

III. SIMULATION STUDIES AND DISCUSSION
In this section, the efficiency of the proposed algorithm in optimizing and providing optimal solutions is evaluated. Sixty-eight benchmark functions have been employed to test the performance of the proposed algorithm. These functions include unimodal, high-dimensional multimodal, fixeddimensional multimodal, CEC2015, and CEC2017. The ability of the proposed algorithm is compared with the performance of the nine famous metaheuristics GWO, TLBO, GA, MPA, PSO, QANA, TSA, WOA, and GSA. Table 2 shows the values of the control parameters of these algorithms. The proposed algorithm and each of the mentioned algorithms are employed in twenty independent implementations, while each execution contains 1000 repetitions. The experiments are done in the Matlab R2020a version in the environment of Microsoft Windows 10 with 64 bits on the Core i-7 processor with 2.40 GHz and 6 GB memory. The optimization results obtained for the benchmark functions have been reported using two indicators: the average of the optimal solutions obtained (avg) and the standard deviation of these solutions (std).

A. EVALUATION OF UNIMODAL BENCHMARK
The unimodal functions F1 to F7 are a good set to evaluate the exploitability of optimization algorithms because they have only one main solution without having any local solutions. Table 3 shows the results of optimizing the functions F1 to F7. The optimization results show that ZOA with high exploitation power has provided the global optimal in F6 solution. ZOA is the first best optimizer compared to the competitor algorithms in optimizing F1, F2, F3, F4, F5, and F7. The simulation results show that ZOA has a superior performance in optimizing the unimodal functions F1 to F7 against nine competitor algorithms.

B. EVALUATION OF HIGH-DIMENSIONAL MULTIMODAL BENCHMARK
The high-dimensional multimodal functions F8 to F13 are a good set to evaluate the exploration power of optimization algorithms because in addition to the main optimal solution, they also have several local solutions in the search space. Table 4 presents the optimization results of functions F8 to F13 using the proposed ZOA and nine competitor algorithms. ZOA with high exploration power has been able to provide the global optimum for functions F9 and F11 after identifying the optimal area. ZOA is the first best optimizer for functions F10 and F12. In optimization of F8, ZOA is the fourth optimizer after GA, TLBO, and PSO. In optimization of F13, ZOA is the second-best optimizer after GSA. The simulation results show the acceptable exploration power of ZOA in accurately scanning the search space and passing local optimal areas.

Input information of optimization problem.
Set parameters of and .
Create initial population.
Evaluate objective function based initial population.
Print the best candidate solution.
Save the best solution found so far. population.

C. EVALUATION OF FIXED-DIMENSIONAL MULTIMODAL BENCHMARK
The fixed-dimensional multimodal functions F14 to F23 challenge the exploration ability of optimization algorithms to find the optimal region in low-dimensional problems. Table 5 releases the implementation results of the proposed ZOA and nine competitor algorithms in solving functions F14 to F23. ZOA is the first best optimization for F15 and F20 functions. In addition, the simulation results show that in solving the functions F14, F16, F17, F18, F19, F21, F22, and F23, although ZOA is similar in avg criterion to some competitor algorithms, but has better std criterion. Therefore, ZOA is a more effective optimizer in solving these objective functions. The simulation results show that ZOA has a superior performance in solving fixed-dimensional multimodal functions compared to nine competitor algorithms.
The performance of ZOA and nine competitor algorithms in optimizing functions F1 to F23 as boxplot is presented in Figure 2. In addition, Figure 3 plots the convergence curves of ZOA and competing algorithms to achieve a solution.

D. STATISTICAL ANALYSIS
In this subsection, a statistical analysis is presented to determine whether the superiority of ZOA over nine competitor algorithms is statistically significant. Wilcoxon rank sum test [54] is a statistical test that is used to compare two data samples with the aim of detecting significant differences between them. In this test, a -value is the criterion for determining the superiority of one algorithm over another algorithm. The Wilcoxon rank sum test is implemented on the optimization results of ZOA and nine competitor algorithms and the results are presented in Table 6. What can be deduced from the results of statistical analysis is that ZOA has a significant superiority over the corresponding competitor algorithm in cases where the -value is less than 5%.
The Friedman test [55] is used to analyze the superiority of ZOA based on ranking its performance in achieving solutions to optimization problems. The results of the Friedman test on the performance of optimization algorithms in handling the functions F1 to F23 are presented in Table 7. What is evident from the simulation results is that ZOA offers superior performance compared to competitor algorithms.

E. POPULATION DIVERSITY ANALYSIS
Population diversity plays an important role in increasing the global search capability of optimization algorithms in order to prevent optimization algorithms from getting stuck in local optimal solutions. In this subsection, population diversity analysis on the performance of ZOA in the optimization process is presented. In order to analyze the ZOA's population diversity while achieving the solution, the index is employed, which is calculated according to (7) and (8) [56].
where , = 1,2, … , , are the centroids, and is the index of the spreading of population members.
The population diversity analysis in optimizing objective functions F1 to F23 is shown in Figure 4. For each objective function, ZOA's convergence curve and its population diversity are presented. Simulation results and Figure 4 show that ZOA has a high population diversity in the optimizing process of most objective functions.

F. SCALABILITY ANALYSIS
In this subsection, the scalability analysis of ZOA in the optimization process is presented. In this analysis, ZOA is implemented on functions F1 to F13 for different dimensions of 10, 30, 50, 100, 500, and 1000. The simulation results are presented in Table 8. What emerges from the review of the results is that the ZOA, while increasing the dimensions of the problem, still maintains its efficiency and provides acceptable solutions.

G. SENSITIVITY ANALYSIS
ZOA is able to solve optimization problems in an iterationbased process and based on scanning the search space by its population members. As a result, changes in the number of zebras' population ( ) and the maximum number of iterations ( ) affect ZOA performance. In this subsection, a sensitivity analysis on ZOA performance with respect to the parameters and are presented.
To sensitivity analyze to parameter , the proposed ZOA has been employed for zebras' populations of sizes 20, 30, 50, and 100 in the optimization of F1 to F23. The results of sensitivity analysis to parameter are presented in Table 9. ZOA convergence curves under the influence of parameter changes are shown in Figure 5. What can be deduced from the simulation results is that increasing the value of improves the algorithm's exploration power in identifying the optimal area and thus ZOA provides better solutions.
In order to sensitivity analyze to parameter , the proposed ZOA has been employed for the maximum number of iterations of 100, 500, 800, and 1000 in the optimization of F1 to F23. The behavior of the ZOA convergence curves under the sensitivity analysis to the parameter is shown in Figure  6. The simulation results of this analysis are reported in Table  10. What is evident from the results of ZOA sensitivity analysis to the parameter is that increasing the value of gives the algorithm more opportunity to converge towards better solutions based on the exploitation power. VOLUME XX, 2017 9

F. EVALUATION OF CEC 2015 BENCHMARK
The ability of ZOA and nine competitor algorithms to optimize CEC1 to CEC15 functions of the CEC2015 benchmark test has been evaluated. The simulation results are presented in Table 11. Analysis and comparison of the results show that ZOA has performed better than the nine competitor algorithms in optimizing CEC1, CEC3, CEC5, CEC6, CEC7, CEC8, CEC9, CEC10, CEC11, CEC12, CEC13, CEC14, and CEC15. TSA has performed better in optimizing CEC2 and CEC4, while ZOA is the second optimizer to solve these functions. Analysis of the CEC2015 optimization results shows the superior performance of ZOA over the nine compared algorithms in most cases.

G. EVALUATION OF CEC 2017 BENCHMARK
The performance of ZOA and nine competitor algorithms have been tested on the optimization of benchmark functions C1 to C30. The optimization results of CEC2017 test functions are presented in Table 12. What can be deduced from the simulation results is that ZOA has provided the optimal solution for C1 , C2, C3, C4, C5, C6, C7, C8, C9, C10, C11,  C12, C13, C15, C16, C17, C18, C21, C22, C23, C24, C25,  C26, C27, C28, C29, and C30. TSA is the first-best optimizer to solve C14, C19, and C20 while ZOA is the second-best optimizer in these functions. Based on the analysis of CEC2017 simulation results, it is clear that ZOA is superiority optimizer over nine competitor algorithms for optimization in most cases.

IV. ZOA APPLICATION FOR ENGINEERING DESIGN PROBLEMS
In this section, the ability of the proposed algorithm to solve real-world problems is tested on four engineering design challenges including tension/compression spring, welded beam, speed reducer, and pressure vessel design problem.

A. TENSION/COMPRESSION SPRING DESING OPTIMIZATION PROBLEM
Tension/compression spring design is a minimization problem, in which the main goal in this design is to reduce the tension/compression spring weight. Figure 7 shows the schematic of the tension/compression spring design problem. The values obtained for the design variables in the tension/compression spring design problem are presented in Table 13. The simulation results show that ZOA provides the optimal solution for this engineering design with the values of the decision variables equal to (0.0520983, 0.366644, 10.7299), and the value of the corresponding objective function is equal to 0.012668010. The statistical results of the performance of the proposed ZOA and nine competitor algorithms are presented in Table 14. These results show that ZOA with outstanding values in statistical indicators performs better than competitor algorithms. The convergence curve of the proposed ZOA while achieving the solution to the tension/compression spring design problem is shown in Figure 8.

B. WELDED BEAM DESING OPTIMIZATION PROBLEM
This engineering design is a minimization problem whose main challenge is to reduce the fabrication cost of the welded beam. Figure 9 shows the schematic of the welded beam design problem. The simulation results obtained from the ZOA and nine competitor algorithms in solving the welded beam design problem are presented in Table 15. The analysis of the results of this table shows that the proposed ZOA has presented a better performance in optimizing this design with the values of decision variables equal to (0.205739, 3.470261, 9.036623, 0.205740), and the value of the corresponding objective function equal to 1.724916. Statistical results for the welded beam design problem obtained from the mentioned algorithms are presented in Table 16. It can be concluded from this table that the proposed ZOA has provided a more efficient performance in optimizing this problem. The convergence curve behavior of ZOA in optimizing the welded beam design problem is shown in Figure 10.

C. SPEED REDUCER DESING OPTIMIZATION PROBLEM
The design of the speed reducer is one of the minimization problems because the primary goal of this problem is to find its structure so that this speed reducer has the minimum weight. Figure 11 shows the schematic of the speed reducer design problem. The values obtained for decision variables in speed reducer design are reported in Table 17. The proposed ZOA provides the optimal solution with the values of the decision variables equal to (3.50112, 0.7, 17,7.3423, 7.80116, 3.35194, 5.28818), and the value of the corresponding objective function is equal to 2998.5189. The statistical results obtained from the performance of ZOA and nine competitor algorithms on the speed reducer design problem are presented in Table 18. According to this table, the ZOA is superior to competing algorithms with a better position in statistical indicators. The convergence curve of the proposed ZOA in achieving the solution to the speed reducer design problem is shown in Figure 12.

D. PRESSURE VESSEL DESING OPTIMIZATION PROBLEM
This engineering design is a minimization problem whose objective function is to reduce the total cost of material, forming, and welding of a cylindrical vessel. Figure 13 shows the schematic of the pressure vessel design problem. The proposed values for the decision variables in the design of the pressure vessel are presented in Table 19. The simulation results show that ZOA provides the optimal solution to this problem by giving the values of the decision variables equal to (0.7781084, 0.3859585, 40.31504, 199.9663), and the value of the corresponding objective function is equal to 5887.2057. The statistical results of the proposed ZOA and nine competitor algorithms are reported in Table 20. This table shows the superiority of ZOA over competitor algorithms in having better statistical indicators for optimizing the pressure vessel design problem. The behavior of the ZOA's convergence curve when solving the problem of design of a pressure vessel is shown in Figure 14.

V. CONCLUSION AND FUTURE WORKS
I In this paper, a new metaheuristic algorithm called Zebra Optimization Algorithm (ZOA), which mimics the natural behaviors of zebras in the wild, was developed. These types of behavior include foraging and defense strategies against predators. The ZOA steps were stated, and then its mathematical modeling was presented. ZOA performance in solving optimization problems was evaluated on sixty-eight benchmark functions, including types of unimodal, highdimensional multimodal, fixed-dimensional multimodal, CEC2015, and CEC2017. The optimization results showed that ZOA is able to provide optimal solutions for objective functions by creating the appropriate balance between exploitation and exploration. To evaluate the quality of the ZOA, we compared its results with nine other known algorithms, GWO, TLBO, GA, MPA, PSO, TSA, WOA, and GSA. The simulation results show that ZOA performs better in most cases and has better performance against nine competitor algorithms by providing better solutions. ZOA's ability to optimize real-world problems was studied in four engineering design problems. The optimization results showed the high capability of ZOA to provide optimal solutions in engineering design applications.
The authors make several suggestions for future studies, such as developing binary and multi-objective versions of ZOA. The application of ZOA in solving optimization problems in various sciences and other real-world problems is another future perspective of this study.      Hybrid Function 2 ( = 3) 1200 C13