Elymus Repens Optimization (ERO); A Novel Agricultural-Inspired Algorithm
محورهای موضوعی : IT Strategy
1 - Faculty of Engineering, University of Birjand
کلید واژه: Elymus Repens Optimization, meta-heuristic algorithms, Rhizome Optimization Operator, Stolon Optimization Operator,
چکیده مقاله :
Optimization plays a crucial role in enhancing productivity within the industry. Employing this technique can lead to a reduction in system costs. There exist various efficient methods for optimization, each with its own set of advantages and disadvantages. Meanwhile, meta-heuristic algorithms offer a viable solution for achieving the optimal working point. These algorithms draw inspiration from nature, physical relationships, and other sources. The distinguishing factors between these methods lie in the accuracy of the final optimal solution and the speed of algorithm execution. The superior algorithm provides both precise and rapid optimal solutions. This paper introduces a novel agricultural-inspired algorithm named Elymus Repens Optimization (ERO). This optimization algorithm operates based on the behavioral patterns of Elymus Repens under cultivation conditions. Elymus repens is inclined to move to areas with more suitable conditions. In ERO, exploration and exploitation are carried out through Rhizome Optimization Operator and Stolon Optimization Operators. These two supplementary activities are used to explore the problem space. The potent combination of these operators, as presented in this paper, resolves the challenges encountered in previous research related to speed and accuracy in optimization issues. After the introduction and simulation of ERO, it is compared with popular search algorithms such as Gravitational Search Algorithm (GSA), Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), and Firefly Algorithm (FA). The solution of 23 benchmark functions demonstrates that the proposed algorithm is highly efficient in terms of accuracy and speed.
Optimization plays a crucial role in enhancing productivity within the industry. Employing this technique can lead to a reduction in system costs. There exist various efficient methods for optimization, each with its own set of advantages and disadvantages. Meanwhile, meta-heuristic algorithms offer a viable solution for achieving the optimal working point. These algorithms draw inspiration from nature, physical relationships, and other sources. The distinguishing factors between these methods lie in the accuracy of the final optimal solution and the speed of algorithm execution. The superior algorithm provides both precise and rapid optimal solutions. This paper introduces a novel agricultural-inspired algorithm named Elymus Repens Optimization (ERO). This optimization algorithm operates based on the behavioral patterns of Elymus Repens under cultivation conditions. Elymus repens is inclined to move to areas with more suitable conditions. In ERO, exploration and exploitation are carried out through Rhizome Optimization Operator and Stolon Optimization Operators. These two supplementary activities are used to explore the problem space. The potent combination of these operators, as presented in this paper, resolves the challenges encountered in previous research related to speed and accuracy in optimization issues. After the introduction and simulation of ERO, it is compared with popular search algorithms such as Gravitational Search Algorithm (GSA), Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), and Firefly Algorithm (FA). The solution of 23 benchmark functions demonstrates that the proposed algorithm is highly efficient in terms of accuracy and speed.
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http://jist.acecr.org ISSN 2322-1437 / EISSN:2345-2773 |
Journal of Information Systems and Telecommunication
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Elymus Repens Optimization (ERO); A Novel Agricultural-Inspired Algorithm |
Mahdi Tourani1*
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1. Faculty of Engineering, University of Birjand |
Received: 01 Apr 2023/ Revised: 27 July 2024/ Accepted: 20 Aug 2024 |
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Abstract
Optimization plays a crucial role in enhancing productivity within the industry. Employing this technique can lead to a reduction in system costs. There exist various efficient methods for optimization, each with its own set of advantages and disadvantages. Meanwhile, meta-heuristic algorithms offer a viable solution for achieving the optimal working point. These algorithms draw inspiration from nature, physical relationships, and other sources. The distinguishing factors between these methods lie in the accuracy of the final optimal solution and the speed of algorithm execution. The superior algorithm provides both precise and rapid optimal solutions. This paper introduces a novel agricultural-inspired algorithm named Elymus Repens Optimization (ERO). This optimization algorithm operates based on the behavioral patterns of Elymus Repens under cultivation conditions. Elymus repens is inclined to move to areas with more suitable conditions. In ERO, exploration and exploitation are carried out through Rhizome Optimization Operator and Stolon Optimization Operators. These two supplementary activities are used to explore the problem space. The potent combination of these operators, as presented in this paper, resolves the challenges encountered in previous research related to speed and accuracy in optimization issues. After the introduction and simulation of ERO, it is compared with popular search algorithms such as Gravitational Search Algorithm (GSA), Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), and Firefly Algorithm (FA). The solution of 23 benchmark functions demonstrates that the proposed algorithm is highly efficient in terms of accuracy and speed.
Keywords: Elymus Repens Optimization; Meta-Heuristic Algorithms; Rhizome Optimization Operator; Stolon Optimization Operator.
1- Introduction
Today, the industry faces various pressing problems that require urgent solutions and optimal answers. Contributing to the resolution of these issues can greatly enhance efficiency across multiple fields. There exist diverse approaches to solving optimization problems, including one-by-one counting methods, classical mathematical methods, and optimization methods.
The one-by-one method involves a significant amount of time to solve problems, rendering it practical only for small-scale issues. However, its advantages encompass very high accuracy and zero error.
Conversely, classical mathematical methods, such as derivation methods, require adherence to specific principles and rules for continuous problems. These limitations can make it challenging to employ these methods for solving optimization problems. Nonetheless, classical mathematical methods offer high accuracy, making them an appealing option.
In optimization methods, algorithms begin in an initial space and move intelligently towards an optimal solution. With effective guiding operators, these algorithms conduct smarter searches in problem spaces, ultimately accelerating the process of reaching a final answer. Several desirable features of optimization methods include:
Ø No limitation in problem modeling
Ø Universality in covering a wide range of issues
Ø High speed in determining the optimal answer
In this paper, a powerful method is introduced for optimizing problems by harnessing the positive features of nature to address challenges. One such valuable feature is the growth mechanism of Elymus repens in agricultural land, which provides an innovative approach to problem-solving.
The paper proceeds as follows: Section 2 provides an overview of optimization algorithms. Section 3 introduces the Elymus repens mechanism, and Section 4 presents the new algorithm called Elymus repens optimization. Finally, in Section 5, the performance of this new algorithm is evaluated using 23 sample functions.
2- Literature review
Today, optimization algorithms are used as a method for obtaining the optimal solutions to optimization problems[1]. Unlike classical mathematical methods, these algorithms are much more efficient in solving optimization problems. The basis of optimization algorithms is usually nature, physics, and swarm. The final answer obtained from them has high accuracy and suitable speed. Optimization algorithms use two basic components of exploration and exploitation to search the problem space. These two features are very helpful in finding the optimal answer. Exploration provides the algorithm with the ability to search freely without paying attention to the accuracy of the results. On the other hand, paying attention to the information obtained in the previous loops is the basis of exploitation. With an increase of exploration, the algorithm finds random and unpredictable directions, and on the opposite side, with an increase of exploitation, the performance of the algorithm becomes cautious. By the exploration and exploitation, the algorithm will move towards the smart answer.
In the following, some of the popular optimization algorithms are reviewed [2]:
Genetic Algorithm [3], Genetic programming [4], Tabu Search [5], Evolution Strategy [6], Memetic Algorithm [7], Cultural Algorithm [8], Simulated Annealing [9], Differential Evolution [10], Evolutionary Programming [11], Co Evolutionary Algorithm [12], Gradient Evolution Algorithm [13], Imperialistic Competitive Algorithm [14], Biogeography-Based Optimization [15], States of Matter Search [16], Sine Cosine Algorithm [17], Multi-level Cross Entropy Optimizer [18]. These algorithms are modeled on Darwin's theories.
Some algorithms are physics-based optimization algorithms such as: Small-World Optimization Algorithm [19], Central Force Optimization [20], Magnetic Optimization Algorithm [21], Gravitational Search Algorithm [22], Charged System Search [23], Chemical-Reaction Optimization [24], Black Hole [25], Curved Space Optimization [26], Water Evaporation Optimization [27], Ideal Gas Molecular Movement [28], Multi-Verse Optimizer [29], Vibrating Particles System [30].
Some optimizers are swarm-based algorithms: Particle Swarm Optimization [31], Grasshopper Optimization Algorithm [32], Moth–flame Optimization [33], Artificial Fish Swarm Algorithm [34], Honey Bee Optimization [35], Termite Colony Optimization [36], Ant Colony Optimization [37], Shuffled Frog-Leaping [38], Monkey Search [39], Dolphin Partner Optimization [40], Firefly Algorithm [41], Bat Algorithm [1], Bird Mating Optimizer [42], Fruit Fly Optimization [43], Lion Pride Optimizer [44], Krill Herd [45], Grey Wolf Optimizer [46], Cuckoo Search [47], Soccer League Competition Algorithm [48], Dragonfly Algorithm [49], Whale Optimization Algorithm [50], Salp Swarm Algorithm [51], Harris Hawks Optimization [52], Flying Squirrel Optimizer [53], Ant Lion Optimizer [54]
In addition to these algorithms, some intelligence may be found in nature that can form the basis of other optimization algorithms. One of these is the Elymus Repens behavior.
The introduced algorithms are very effective in industry, energy, medicine and etc. References [55-59] in science, [60-64] in engineering and [65-69] in medical show part of the research conducted with these algorithms in the field of optimization.
3- Elymus Repens
Elymus repens (ER) is a highly competitive, allelopathic, perennial grass. This plant is considered one of the world's most troublesome weeds, reproducing both sexually through seeds and asexually through rhizomes. It is found in temperate regions worldwide, with the exception of Antarctica [70, 71, 72]. The structure and appearance of this plant are depicted in Fig. 1 and Fig. 2.
In Northern Europe, Elymus repens is a common and aggressive grass species favored by cereal-dominated crop rotations and nitrogen fertilization [73, 74]. This species can become a pernicious weed, spreading rapidly by underground rhizomes[72] and quickly forming a dense mat of roots in the soil. Even the smallest fragment of the root can regenerate into a new plant[75].
Elymus repens is propagated by seeds, rhizomes, or stolons. The creeping stems on the ground surface and the wire-shaped underground stems have numerous short branches and scaly leaves. New aerial organs are formed from the nodes of rhizomes and stolons.
This plant is highly resilient and can thrive in favorable conditions on the ground. These conditions include water, organic, and biological materials. Where these conditions are optimal, the growth of this plant flourishes. On the other hand, this plant can be considered as a "search engine" as it moves towards favorable agricultural positions and covers them using propagation tools such as rhizomes or stolons. Once introduced to an area, it swiftly moves to better conditions and occupies the desired area.
The power and speed of occupying fertile areas by this plant is so high that it prevents the growth of any other type of plant, thus making it one of the most destructive weeds.
Fig. 1. Elymus Repens [76]
Fig. 2. Elymus Repens in the agricultural land
4- Elymus Repens Optimization
This study is centered around the behavior patterns of Elymus Repens within their cultivation environment. In terms of growth and reproduction, this plant initially progresses through seeds and subsequently through rhizomes and stolons (illustrated in Fig. 3) within the cultivation environment. Elymus repens tends to move towards any part of the soil that provides more favorable conditions.
Fig. 3.Rhizomes and Stolons in Elymus Repens
In this paper, this process is modeled as a optimization search algorithm that is named Elymus Repens Optimization (ERO). In the ERO model, the cultivation land of the plant serves as the search space for the problem, with every position within this space being a candidate answer - representing a position of the land with the best cultivation conditions, i.e., the optimal answer. The rhizomes and stolons act as the ERO optimization operators.
To initiate the algorithm, Elymus repens is assumed to be spread across the environment. Any position in the cultivation environment where the reproductive parts of the plant are placed becomes an initial candidate answer. These positions are evaluated using the objective function. Subsequently, the Elymus repens will move towards the optimal answer through the use of rhizomes and stolons.
4-1- Stolon Optimization Operator
Among the reproducible parts of Elymus repens, the part that is in a better environmental condition will spread to its neighboring parts through stolons. The number of neighbors for each position will increase with the improved environmental conditions. Consequently, a part of the plant that is in unfavorable conditions will not be reproduced. This process guides the initial solution towards better alternatives. Equation 1 and Equation 2 demonstrate the new candidate solutions with the stolon operator.
| (1) |
| (2) |
where, it indicates iteration, T the maximum of iteration, XiÎneighbork,it show i-th neighbor from k-th best position, XkÎbestit-1 the k-th best choice position, unifrnd, a uniform random number between [-α,+α] and b is the relationship coefficient.
The best position (XiÎbest) for reproduction is selected using the roulette wheel. This method ensures that better positions have a higher chance of reproducing. This selection process is repeated for all positions, and the resulting new neighbors are generated from the best ones.
4-2- Rhizome Optimization Operator
In 4-1, the k-best position of population generate a number of neighbors. The neighbors related to each k-best position form a group. At this step, in each group, the best neighbor is selected from among the neighbors created by each previous k-best position, and the other neighbors move towards it. Equations 3 to 6 show the new candidate solutions using the rhizome operator.
| (3) |
| (4) |
| (5) |
| (6) |
where, Xiit is new candidate answer, rand shows the random value between [0,1] and Xbest neighbork,it-1 and XiÎother neihbork,it-1, are the best neighbor and other neighbors for k-th neighborhood group. Fig. 4 shows the visual performance of rhizomes and stolons operators in ER optimization.
Fig. 4. The stolon and rhizome operators view
The flowchart and the pseudo code of ERO algorithm are presented in Fig. 5 and Fig. 6.
Fig. 5. Flowchart of the Proposed ERO Algorithm
Step 1: Planting the elymus repen and spreading it in the cultivation environment Step 2: Evaluation of the cultivation environment Step 3: Propagation of the elymus repen by stolons Step 4: Propagation of the elymus repen by rhizomes Step 5: if stop criteria has not been reached, Go to step 2. |
Fig. 6. The pseudo code of ERO algorithm
5- Validation and Computational Experiment
To demonstrate the effectiveness and power of Elymus Repens Optimization as proposed in this paper, it has been evaluated for minimizing 23 case study functions [77]. Table 2 depicts these well-known functions. For the computational testing, the simulations were run on a PC with a 2.30GHz Intel Core i5 processor and 6 gigabytes of RAM.
The aim of the algorithm presented is to minimize the functions listed in the first and second columns of Table 2 in the shortest possible time. The number of variables and function constraints are provided in the fourth and fifth columns, establishing upper and lower bounds for the function variables. The two-dimensional representations of these functions can be seen in Fig.7 and Fig. 8.
The evaluation of computational algorithms is typically gauged using two criteria: 1- The accuracy of the final solution 2- The computational speed. In this section, following the determination of these criteria for the aforementioned functions, the performance of ERO will be compared with Gray Wolf Optimization (GWO), Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO), and Firefly Algorithm (FA).
The Gray Wolf Optimizer (GWO), introduced in 2014, is a novel meta-heuristic inspired by the hunting behavior of gray wolves. This algorithm emulates the hierarchical structure of gray wolf packs, utilizing four distinct types of wolves - alpha, beta, delta, and omega - in its simulation. The process involves three primary hunting stages: searching for prey, surrounding the prey, and ultimately attacking the prey [47].
Table 2. The 23 Benchmark Functions used in experimental study [77]
Name Function | Function | n | Range |
Sphere Model |
| 30 | [-100,100] |
Schwefel’s problem 2.22 |
| 30 | [-10,10] |
Schwefel’s problem 1.2 |
| 30 | [-100,100] |
Schwefel’s problem 2.21 |
| 30 | [-100,100] |
Generalized Rosenbrock’s function |
| 30 | [-30,30] |
Step function |
| 30 | [-100,100] |
Quartic function with noise |
| 30 | [-1.28,1.28] |
Generalized Schwefel’s problem 2.26 |
| 30 | [-500,500] |
Generalized Rastrigin’s Function |
| 30 | [-5.12,5.12] |
Ackley’s function |
| 30 | [-32,32] |
Table 2. The 23 Benchmark Functions used in experimental study [77] (continues)
Name Function | Function | n | Range |
Generalized Griewank Function |
| 30 | [-600,600] |
Generalized Penalized Functions |
| 30 | [-50,50] |
Generalized Penalized Functions |
| 30 | [-50,50] |
Shekel’s Foxholes function |
| 2 | [-65.536,65.536] |
Kowalik’s function |
| 4 | [-5,5] |
Six-hump camel back function |
| 4 | [-5,5] |
Table 2. The 23 Benchmark Functions used in experimental study [77] (continues)
Name Function | Function | n | Range |
Branin function |
| 2 | [-5,5]×[0,10] |
Goldstein-Price function |
| 2 | [-2,2] |
Hartman’s family |
| 3 | [0,1] |
Hartman’s family |
| 6 | [0,1] |
Shekel’s family |
| 4 | [0,10] |
Shekel’s family |
| 4 | [0,10] |
Shekel’s family |
| 4 | [0,10] |
Fig. 7. Graphs of functions (F1- F12) for n=2
Fig. 8. Graphs of functions (F13- F23) for n=2
Another algorithm discussed in this paper is the Gravitational Search Algorithm (GSA), which operates based on physical laws such as gravity. In GSA, a collection of masses follows rules of movement that affect each other and lead to an improved final optimal answer. GSA was developed in 2009 [78].
The Firefly Algorithm (FA) was introduced by Xinshe Yang, a scholar from Cambridge, in 2008 [79]. FA is a random search algorithm inspired by swarm intelligence, simulating the attraction mechanism between individual fireflies in nature [80].
In 1995, an algorithm based on the intelligent collective behavior of animals in nature was discovered for stochastic optimization. This algorithm, called Particle Swarm Optimization (PSO), has seen advanced versions published. Numerous studies have been conducted and published regarding the effects of its parameters [81].
Table 3 presents the simulation results of the algorithm introduced in this paper (ERO) and compares it with PSO, GSA, FA, and GWO. The results include the mean run time and mean fitness of the best values found in 30 independent runs with separate seeds. The best accuracy of the algorithms is highlighted in green in Table 3, while yellow indicates that ERO is the second-most accurate.
Table 3. The average of final best fitness and the mean running time for 30 runs of minimizing benchmark functions, number of iterations=100
Algorithm | PSO | GSA | FA | GWO | ERO | |||||||||||||||
F1(x) | Mean Fitness | 2.75 | 59137 | 0.26 | 1.61×10-5 | 6.23×10-6 | ||||||||||||||
Mean Time | 3.29 | 11.89 | 17.6 | 0.65 | 0.086 | |||||||||||||||
F2(x) | Mean Fitness | 0.55 | 2.22 | 2.37 | 6.92×10-4 | 0.01 | ||||||||||||||
Mean Time | 3.73 | 12.43 | 15.72 | 0.79 | 0.09 | |||||||||||||||
F3(x) | Mean Fitness | 1035 | 99701 | 1278 | 17.85 | 4.6×10-3 | ||||||||||||||
Mean Time | 3.27 | 21.8 | 13.37 | 0.64 | 0.089 | |||||||||||||||
F4(x) | Mean Fitness | 4.75 | 82.65 | 6.25 | 0.19 | 3.07×10-4 | ||||||||||||||
Mean Time | 3.56 | 14.63 | 13.16 | 0.44 | 0.09 | |||||||||||||||
F5(x) | Mean Fitness | 252 | 3.85×107 | 294 | 28.23 | 9.2×10-3 | ||||||||||||||
Mean Time | 3.4 | 13.42 | 13.37 | 0.49 | 0.09 | |||||||||||||||
F6(x) | Mean Fitness | 6.67 | 5.96×104 | 0.87 | 0.03 | 0 | ||||||||||||||
Mean Time | 3.49 | 23.9 | 11.74 | 0.63 | 0.087 | |||||||||||||||
F7(x) | Mean Fitness | 0.029 | 0.27 | 0.046 | 0.005 | 0.0098 | ||||||||||||||
Mean Time | 2.97 | 22.9 | 14.09 | 0.77 | 0.10 | |||||||||||||||
F8(x) | Mean Fitness | -67993 | -2546 | -2705 | -6003 | -10727 | ||||||||||||||
Mean Time | 2.96 | 13.97 | 12.85 | 0.87 | 0.01 | |||||||||||||||
Algorithm | PSO | GSA | FA | GWO | ERO | ||||||||||||||||
F9(x) | Mean Fitness | 37.54 | 62 | 97 | 21.16 | 0.0027 | |||||||||||||||
Mean Time | 2.91 | 21.63 | 12.21 | 0.6548 | 0.09 | ||||||||||||||||
F10(x) | Mean Fitness | 1.42 | 19 | 0.91 | 0.001 | 0.0014 | |||||||||||||||
Mean Time | 3.03 | 24.83 | 6.43 | 1.138 | 0.1 | ||||||||||||||||
F11(x) | Mean Fitness | 0.97 | 563 | 0.21 | 0.018 | 5.8×10-7 | |||||||||||||||
Mean Time | 3.43 | 24.9 | 11.26 | 0.5157 | 0.09 | ||||||||||||||||
F12(x) | Mean Fitness | 0.54 | 2.52×108 | 0.29 | 0.071 | 3.08×10-7 | |||||||||||||||
Mean Time | 4.49 | 22.82 | 13.5 | 1.912 | 0.14 | ||||||||||||||||
F13(x) | Mean Fitness | 0.5 | 4.91×108 | 1.17 | 0.79 | 2.6×10-7 | |||||||||||||||
Mean Time | 4.88 | 18.91 | 12.55 | 1.69 | 0.13 | ||||||||||||||||
F14(x) | Mean Fitness | 1.75 | 1.77 | 3.91 | 2.18 | 6.14 | |||||||||||||||
Mean Time | 3.88 | 6.62 | 12.73 | 0.72 | 0.11 | ||||||||||||||||
F15(x) | Mean Fitness | 0.001 | 0.001 | 0.001 | 0.0032 | 7.3×10-7 | |||||||||||||||
Mean Time | 0.99 | 15.99 | 12.49 | 0.4846 | 0.09 | ||||||||||||||||
F16(x) | Mean Fitness | -1.03 | -1.03 | -1.03 | -1.03 | -1.00 | |||||||||||||||
Mean Time | 3.45 | 15.2 | 5.89 | 0.33 | 0.08 | ||||||||||||||||
F17(x) | Mean Fitness | 0.4 | 0.4 | 0.4 | 0.4 | 2.29 | |||||||||||||||
Mean Time | 3.44 | 12.58 | 13.25 | 0.37 | 0.08 | ||||||||||||||||
F18(x) | Mean Fitness | -592103 | -576415 | -592103 | -529210 | -591830 | |||||||||||||||
Mean Time | 3.96 | 13.92 | 12.29 | 0.3452 | 0.08 | ||||||||||||||||
F19(x) | Mean Fitness | -3.89 | -3.85 | -3.86 | -3.86 | -3.67 | |||||||||||||||
Mean Time | 3.35 | 14.68 | 12.06 | 0.45 | 0.09 | ||||||||||||||||
F20(x) | Mean Fitness | -3.27 | -3.03 | -3.22 | -3.23 | -2.40 | |||||||||||||||
Mean Time | 4.02 | 15.28 | 13.22 | 0.53 | 0.09 | ||||||||||||||||
F21(x) | Mean Fitness | -6.97 | -6.24 | -7.81 | -9.54 | -9.86 | |||||||||||||||
Mean Time | 5.05 | 14.31 | 12.72 | 0.97 | 0.13 | ||||||||||||||||
F22(x) | Mean Fitness | -7.88 | -8.82 | -10.14 | -10.12 | -10.37 | |||||||||||||||
Mean Time | 5.24 | 14.39 | 13.9 | 1.21 | 0.13 | ||||||||||||||||
F23(x) | Mean Fitness | -6.6 | -8.82 | -10.53 | -10.24 | -10.45 | |||||||||||||||
Mean Time | 5.57 | 17.1 | 14.37 | 1.68 | 0.14 | ||||||||||||||||
To obtain the performance rating for these 5 algorithms (ERO, PSO, GSA, FA and GWO), the Eq. (7) is suggested:
| (7) |
where Mean R indicates the average weighted rank and #Rank i represents the number of rank i in all test functions. Tables 4 and 5 display the results of the number of ranks for each algorithm across all test functions, as well as the final rank among the algorithms based on Eq. (7). In these tables, #Ri denotes the number of rank i in all test functions. The green color in Tables 4 and 5 highlights the best performance of the algorithms.
Table 4. The results of the number of accuracy ranks for each algorithm in the all test functions and the final rank among the algorithms
| #R1 | #R2 | #R3 | #R4 | #R5 | Mean R | Final Rank |
ERO | 15 | 2 | 1 | 0 | 5 | 2.93 | 1 |
GWO | 1 | 14 | 5 | 1 | 2 | 3.86 | 2 |
PSO | 6 | 3 | 6 | 6 | 2 | 4.27 | 3 |
FA | 1 | 3 | 10 | 7 | 2 | 5 | 4 |
GSA | 0 | 1 | 1 | 9 | 12 | 6.73 | 5 |
Table 5. The results of the number of running time ranks for each algorithm in the all test functions and the final rank among the algorithms
| #R1 | #R2 | #R3 | #R4 | #R5 | Mean R | Final Rank |
ERO | 23 | 0 | 0 | 0 | 0 | 1.53 | 1 |
GWO | 0 | 23 | 0 | 0 | 0 | 3.06 | 2 |
PSO | 0 | 0 | 23 | 0 | 0 | 4.6 | 3 |
GSA | 0 | 0 | 19 | 4 | 0 | 4.86 | 4 |
FA | 0 | 0 | 4 | 19 | 0 | 5.86 | 5 |
When comparing algorithms to determine the best performance, both speed and accuracy should be considered together. Therefore, based on the results, it is evident that Elymus Repens Optimization (ERO) demonstrates the best overall performance in terms of accuracy and speed indexes.
6- Conclusions and Future Work
Optimization is one of the most important processes in the industry. Among the various methods, meta-heuristic algorithms are the most powerful for optimization. This paper introduces a new algorithm called Elymus Repens Optimization (ERO) based on the behavior of Elymus Repens in agricultural land. The effectiveness and power of ERO are then evaluated using 23 well-known benchmark functions to demonstrate its capabilities. Following this simulation, the performance of ERO is compared with other optimization algorithms such as Gray Wolf Optimization (GWO), Firefly Algorithm (FA), Particle Swarm Optimization (PSO), and Gravitational Search Algorithm (GSA). Results indicate that the proposed algorithm is highly efficient in terms of accuracy and speed.
Based on the desirable result of the algorithm, presented in this paper (ERO), it is recommended that this be implemented for optimization problems in the industry.
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*Mahdi Tourani
tourani.mahdi@birjand.ac.ir
