Startseite Technik Dynamic random walk-based sled dog optimization algorithm and artificial neural network for optimizing design engineering problems
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Dynamic random walk-based sled dog optimization algorithm and artificial neural network for optimizing design engineering problems

  • Sadiq M. Sait

    Dr. Sadiq M. Sait received his Bachelor’s degree in Electronics Engineering from Bangalore University, India, in 1981, and his Master’s and Ph.D. degrees in Electrical Engineering from the King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, in 1983 and 1987, respectively. He is currently a Professor of Computer Engineering and Director of the Center for Communications and IT Research, KFUPM, Dhahran, Saudi Arabia.

         , Pranav Mehta

    Pranav Mehta is an Assistant Professor at the Department of Mechanical Engineering, Dharmsinh Desai University, Nadiad-387001, Gujarat, India. He is currently a Ph.D. research scholar at Dharmsinh Desai University, Nadiad, Gujarat, India. His major research interests include metaheuristics techniques, multiobjective optimization, solar-thermal technologies, and renewable energy.

         , Dildar Gürses

    Dr. Dildar Gürses is a lecturer at Bursa Uludağ University, Bursa, Turkey. She completed her BSc, MSc and Ph.D. degrees at Uludağ University, Bursa, Turkey. Her research interests are thermodynamics, electric vehicles, meta-heuristic optimization algorithms, and applications to industrial problems.

     EMAIL logo     und Ali Riza Yildiz

    Dr. Ali Riza Yildiz is a Professor in the Department of Mechanical Engineering, Bursa Uludağ University, Bursa, Turkey. His research interests are the finite element analysis of structural components, lightweight design, vehicle design, vehicle crashworthiness, shape and topology optimization of vehicle components, meta-heuristic optimization techniques, and additive manufacturing.
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Abstract

This research presents a modified version of the sled dog optimizer (SDO) to enhance optimization performance across various benchmark functions and real-world applications. The proposed modification introduces adaptive mechanisms to balance exploration and exploitation, thereby improving convergence speed and solution accuracy. Experimental results demonstrate that the modified SDO outperforms the standard SDO and other contemporary metaheuristic algorithms in terms of optimization efficiency and robustness. Comparative analysis of standard test functions and engineering design problems confirms the superiority of the proposed approach.

Keywords: sled dog optimization algorithm; engineering optimization problem; nature-inspired algorithms; structural optimization; brake pedal

1 Introduction

Industrial design optimization problems are challenging to solve due to their complex nature in terms of transient functions, multiple objectives, real-life operating conditions, and constraints. Classical optimization techniques trapped in local optimum solutions for critical optimization problems. Moreover, multi- and many-objective optimization problems are challenging tasks to solve as these problems tackle multiple fitness functions and Pareto fronts. Hence, researchers have developed nature-based optimization algorithms typically known as metaheuristics (MHs) algorithms. These algorithms are based on the physics phenomena that occur in nature, optics-based, human behavior-based, swarm intelligences-based, and evolutionary techniques-based. Furthermore, these developments of these algorithms are carried out by rigorous testing over the critical test functions, mainly Congress on evolutionary computations (CEC test suits), and then tested with the benchmark algorithms. Moreover, this comparison was further carried out by testing performance ranking using the standard Friedman rank and Wilcoxon rank-based system. These testing techniques ensure the algorithm’s overall performance in terms of searching the solution space vis-à-vis identifying a superior global optimum solution. Moreover, after establishing and testing any new optimizer, it was then tested over the multidisciplinary optimization challenges. Furthermore, these challenges are most observed in engineering optimization problems, electric power distribution optimization challenges, fuzzy circuits challenges, structural optimization of truss structures, and automobile component optimization [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27].

MHs algorithms solve every optimization problem with high computational accuracy and less time. However, for challenging constrained optimization problems, MH optimizers capture locally optimized solutions and are found inefficient in attaining a balance between the exploration and exploitation phases. Accordingly, to improve performance further, MHs are improved using several techniques. Some of them are not limited to dynamic oppositional-based techniques, dynamic random walk-based techniques, artificial neural network (ANN)-based, Levy flight mechanisms, chaotic maps, and hybridization of multiple algorithms. Moreover, the modifications in the algorithm result in an effective convergence rate, a potential balance between the search and solution phase, and a better success rate [14], [15].

Accordingly, in this article, a novel sled dog optimization algorithm was modified using the dynamic random walk technique and applied to a wide range of disciplinary engineering problems. The sled dog optimizer is a recently obtained optimization algorithm that works based on the various methods observed by the sled dog. For instance, training, sledding, shifting goods, and identifying the path when lost. The performance results were compared with the literature in terms of statistical results.

2 Modified sled dog optimization algorithm (MSDOA)

The sled dog optimizer was a recently developed algorithm based on the techniques of a special category of dogs known as sled dogs. These dogs are found in arctic and semi-arctic regions, where they are trained for sledding, shifting goods from one place to another, special task force, and other well-known techniques. Accordingly, the mathematical foundation of the algorithm is developed based on several methods used by sled dogs.

The algorithm initiates with identifying the particular numbers of sled dogs for the task termed population (N) initialization. As out of the available dogs, particular sled dogs are selected depending on the task of sledding and the required efforts. Hence, the sled dogs are selected for the particular task according to their fitness values. The same can be given by Equation (1) [16].

(1) N 1 = 0.7   N + k 1   2 k 2

with k1 and k2: random numbers selected in the range of 1 to −1 and 1 to 2, respectively. Furthermore, while traveling, sled dogs construct two columns, and leaders in the columns follow the commands of their master. Subsequently, sled dogs behind the leader dogs follow each movement, especially their footprints, and accordingly alter their velocities and path. Apart from these, the dogs at the last in each column pull the heaviest sled straight ahead and follow the preceding dogs. The same can be given by Equations (2)–(4) [16].

(2) V i = ꞷ   V i + c 1 r 1   Dog Gi − Dog i + c 2 r 2   Dog z − Dog i , i = 1 , 2
(3) V i = ꞷ V i + c 1 r 1 Dog i − 2 − Dog i + c 2 r 2 Dog i + 2 − Dog i + 2 l r 3 Dog t − Dog i , i = 3 , N 1 − 2
(4) V i = ꞷ V i + c 1 r 1 Dog i − 2 − Dog i + c 2 r 2 Dog r − Dog i + 2 l r 3 Dog t − Dog i , i = N 1 − 1 , N 1

During travel, sled dogs often encounter obstacles. In such situations, they generally avoid obstacles by shifting their path in accordance with the command from their master and based on their training. The same can be given by Equation (5) [16].

(6) Dog i = r 6   Dog i + Dog z 2   + 0.5   C r 7 ζ Dog r − ζ Dog i
(7) Dog i = Dog i + r 8 F r 9 D 1 X 1 + r 10 D 2 X 2 + r 11 D 3 X 3
(5) Dog i = Dog i + 0.5 r 4   Dog z − Dog N + k p 1 2 r 5 Dog Gi − Dog N , if rand  < 0.5 Dog i + 0.5 r 4   Dog z − Dog N + k p 2 r 5 Dog Gi − Dog N , if rand ≥ 0.5

To further improve the effectiveness of the sled dog optimizer, an improved version of the dynamic opposite learning technique is augmented with the algorithm known as dynamic random walk theory. The same can be given by Equation (8).

(8) X DR = X + r 3   X R − X

with XDR: position in the search space as per the dynamic random walk technique; XR: random number enhanced to improve the global optimum efficiency.

Accordingly, the modifications have been carried out to the modified sled dog algorithms, as shown in Figure 1, and applied to the different engineering section problems in the subsequent section.

Figure 1: Approach for development of modified-algorithm.
Figure 1:

Approach for development of modified-algorithm.

3 Optimization of diverse industrial problems using the modified sled dog optimizer

3.1 Optimization of planetary gearbox design

Figure 2 shows the planetary gear study. Nine mixed-choice parameters are included in the mathematical formulation of the optimization problem. These are the planet gears counts (P), the number of gear modules (m1 and m2) that can only take certain discrete values, and the number of teeth in the gears (N1 to N6), which are all integers. The goal function’s detailed description, limitations, and search space design boundaries are below.

Figure 2: Design of planetary gears.
Figure 2:

Design of planetary gears.

The objective is to reduce the vibration noise by minimizing the greatest faults in the gear ratio. The objective function’s mathematical model is provided below:

(9) f y → = max i k − i 0 k , k = 1 , 2 , … , R

with i 1 = N 6 N 4 , i 01 = 3.11 , i 2 = N 6 N 1 × N 3 + N 2 × N 4 N 1 × N 3 N 6 − N 4 , i 02 = 1.84 , i R = N 6 N 4 and i0R = −3.11.

Eleven design restrictions apply to the planetary gear train, including the maximum transmission diameter, the undercutting problem, and the distance between several planets. Interested readers can consult the original article for additional information regarding the optimization formulation of the problem.

As stated in the introduction, MSDOA is compared to the ideal outcomes provided by the crystal structure algorithm (CSA), waterwheel plant algorithm (WPA), light spectrum optimizer (LSO), and spider wasp optimizer (SWO). Tables 1 and 2 compile the comparison results. Both MSDOA and FA achieve the best value for transmission errors in a particular gear train, as shown in Table 2. When compared to what is available in the literature, the findings for the other algorithms that were utilized are found to be competitive and acceptable. As a result, the modified sled dog optimizer outperforms the others in terms of achieving the fitness function’s optimal value of 0.5255886.

Table 1:

Superior results realized by each tested optimizer.

Variables Comparison methods
MSDOA CSA WPA LSO SWO
f min 0.53 0.55 0.56 0.55 0.57
Table 2:

Results comparison in terms of best, mean, worst, and deviations.

Optimization method Best Mean Worst SD
MSDOA 0.53 0.53 0.54 0.01
CSA 0.55 0.56 0.58 0.1
WPA 0.56 0.58 0.61 0.2
LSO 0.55 0.57 0.60 0.3
SWO 0.57 0.59 0.61 0.3

3.2 Design optimization of hydrostatic thrust bearing

In Figure 3, the thrust bearing diagram is shown. The design aims to reduce the power loss when the thrust bearing is operating [18]. Oil viscosity, recess radius R0, oil flow rate Q, and step radius of bearing R are among the design variables.

Figure 3: Design and parameters of thrust bearing.
Figure 3:

Design and parameters of thrust bearing.

The studied MSDOA, crystal structure algorithm (CSA), waterwheel plant algorithm (WPA), light spectrum optimizer (LSO), and spider wasp optimizer (SWO) have all been used to optimize the hydrostatic thrust bearing issue. Table 3 displays the MSDOA statistical findings and compares the earlier methods. The results show that the best mean value and standard deviation are obtained when MSDOA is used. This indicates that the approach performs best in terms of search resilience and convergence rate.

Table 3:

Best results and comparison.

Optimizers
CSA WPA LSO SWO MSDOA
f best 1,625.45 1,625.44 1,625.73 1,626.28 1,625.41
f mean 1,645.23 1,642.67 1,636.5 1,698.14 1,625.38
f worst 1,693.12 1,689.65 1,686.54 1,705.68 1,625.56
SD 14.27 16.54 13.17 12.56 0.15

3.3 Industrial robot gripper optimization

Industrial robots are widely used in manufacturing facilities, supply chains, and the automotive sector. These robots are more accurate and efficient in handling than human operators. In order to handle various tasks, the robot gripper’s arm may operate on many axes for picking and placing. However, a robot’s arm is primarily subject to internal and external pressures. The MSDO algorithm is used in this case study to optimize the lag between the lowest and maximum forces operating across the arm. Figures 4 and 5 depict the robot arm’s 3-D model and line diagram, respectively. Seven design factors, including arm length, deflections, and joint angle, are optimized and documented in addition to fitness functions.

Figure 4: Robot gripper design.
Figure 4:

Robot gripper design.

Figure 5: Angular deflections and forces acting over the gripper arm.
Figure 5:

Angular deflections and forces acting over the gripper arm.

The algorithm configuration for this case study includes 50 populations, 2,000 iterations, and 25 runs. As seen in Table 4, the statistical outcomes of four distinct algorithms were compared. Results of crystal structure algorithm (CSA), waterwheel plant algorithm (WPA), light spectrum optimizer (LSO), and spider wasp optimizer (SWO) were compared. As a result, when compared to the other algorithms, MSDOA can achieve the best outcomes for all design variables and the goal function.

Table 4:

Statistical results for robotic arm.

Variables Algorithms
CSA WPA LSO SWO MSDOA
f best 2.552 2.556 2.563 2.564 2.5432
f mean 2.559 2.563 2.569 2.573 2.5435
f worst 2.563 2.569 2.572 2.585 2.5437
SD 0.123 0.134 0.143 0.151 0.0008

3.4 Structural optimization of 10-bar truss

Structural optimization of different truss configurations plays an imperative role in designing a structure in civil engineering. This being said, effective truss structure design depends over two fundamental concerns: as minimum weight of the structure and minimum nodal deflection between the structures. Accordingly, these problems can be solved using the multi-objective versions of the MH algorithms. In the present study, a single objective modified sled dog optimization algorithm is applied over the truss structure containing 10 truss elements and optimized for the least mass as the objective function, as shown in Figure 6.

Figure 6: 10-bar truss structure with acting force.
Figure 6:

10-bar truss structure with acting force.

The MSDO algorithm is used to calculate the optimal weight in this problem, and the simplex index position approach is used for weight optimization. As a result, the system was set up with total populations and iterations of 50 and 250, respectively. The statistical findings include details on the optimization of ten design factors, as well as the mean value, deviation, and minimum weight. The six popular optimizers that are used to compare the statistical data in order to validate the competitive results are crystal structure algorithm (CSA), waterwheel plant algorithm (WPA), light spectrum optimizer (LSO), and spider wasp optimizer (SWO). According to Table 5, MSDO produced the best results for each design variable with the lowest weight of the whole truss construction compared to the other optimizers. Additionally, MSDO sought the fewest potential variances in results.

Table 5:

Structural optimization results for 10-bar truss.

Optimizers
CSA WPA LSO SWO MSDOA
f best 5,492.64 5,492.72 5,491.23 5,490.84 5,490.65

3.5 Automobile component optimization using modified sled dog optimizer

An integral part of any car system is a brake pedal. Brake pedals are, therefore, a crucial component of the brake system. In this portion, the MSDO algorithm optimizes the weight of the brake pedal member. Equations (10) and (11) provide the mathematical equations for the objective function and limitations. Models of the automobile brake pedal with and without constraints are shown in Figures 7 and 8, respectively. Topology optimization results are given in Figure 9.

(10) Fitness function:   Minimum weight of automobile system  F x = mass  x
(11) Stress constraint : σ max ≤ σ permissible
x i l ≤ x i ≤ x i u , i = 1
Figure 7: Provisional design of automobile component.
Figure 7:

Provisional design of automobile component.

Figure 8: Boundary conditions of component.
Figure 8:

Boundary conditions of component.

Figure 9: Material removing after topology optimization.
Figure 9:

Material removing after topology optimization.

Equation (9) gives the allowable stress conditions with four design variables, with allotted ranges tabulated in Table 6. In this problem, four decision parameters are considered to be optimized, each of which has a designated range that is recorded in Table 6. Table 7 also shows a comparison of statistical results obtained by the MSDO algorithm with the existing design and four metaheuristics algorithms. For instance, the crystal structure algorithm (CSA), the waterwheel plant algorithm (WPA), the light spectrum optimizer (LSO), and the spider wasp optimizer (SWO). For a variety of engineering design issues, these methods yield competitive outcomes. Nonetheless, it can be inferred from the data in Table 7 that MSDO offers effective outcomes for optimizing the mass of the component with efficient functional evaluations. Additionally, the marine predator algorithm yields competitive results for the 5291-gram objective function. It’s also noteworthy that, even though MSDO can achieve weight reductions of more than 26.4 %, the stress condition in this situation is higher than in other algorithms. Consequently, Figures 10 and 11, respectively, provide an illustration of the design variables and optimum design.

Table 6:

Design parameters with their ranges.

Design parameters Operating range
X 1 1–9
X 2 1–12
X 3 1–12
X 4 1–9
Table 7:

Results comparison.

Best mass (g) Mean Worst Std Stress (MPa) NFE
Provisional design 72 – – – 40 –
Developed-modified design 68 – – – 58 –
CSA 66 69 71 3 69 100
WPA 64 68 70 2 67 100
LSO 63 67 69 2 69 100
SWO 62 65 67 2 68 100
MSDO 53 54 55 0.5 65 100
Figure 10: Design variables of the redesigned pedal.
Figure 10:

Design variables of the redesigned pedal.

Figure 11: Volume and mass-reduced design.
Figure 11:

Volume and mass-reduced design.

4 Conclusions

The study successfully enhances the sled dog optimizer by integrating adaptive strategies that refine its search capabilities. Performance evaluations indicate significant improvements in convergence rate, accuracy, and robustness over traditional SDO and other optimization techniques. The modified algorithm proves effective in solving both benchmark and real-world optimization problems. Future work may explore hybridization with other metaheuristics and further fine-tuning of adaptive parameters to extend its applicability across diverse domains.

Corresponding author: Dildar Gürses, Department of Electric and Energy, Hybrid and Electric Vehicle Technology, Vocational School of Gemlik Asım Kocabıyık, Bursa Uludağ University, Bursa, 16600, Türkiye, E-mail:

About the authors

Sadiq M. Sait

Dr. Sadiq M. Sait received his Bachelor’s degree in Electronics Engineering from Bangalore University, India, in 1981, and his Master’s and Ph.D. degrees in Electrical Engineering from the King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, in 1983 and 1987, respectively. He is currently a Professor of Computer Engineering and Director of the Center for Communications and IT Research, KFUPM, Dhahran, Saudi Arabia.

Pranav Mehta

Pranav Mehta is an Assistant Professor at the Department of Mechanical Engineering, Dharmsinh Desai University, Nadiad-387001, Gujarat, India. He is currently a Ph.D. research scholar at Dharmsinh Desai University, Nadiad, Gujarat, India. His major research interests include metaheuristics techniques, multiobjective optimization, solar-thermal technologies, and renewable energy.

Dildar Gürses

Dr. Dildar Gürses is a lecturer at Bursa Uludağ University, Bursa, Turkey. She completed her BSc, MSc and Ph.D. degrees at Uludağ University, Bursa, Turkey. Her research interests are thermodynamics, electric vehicles, meta-heuristic optimization algorithms, and applications to industrial problems.

Ali Riza Yildiz

Dr. Ali Riza Yildiz is a Professor in the Department of Mechanical Engineering, Bursa Uludağ University, Bursa, Turkey. His research interests are the finite element analysis of structural components, lightweight design, vehicle design, vehicle crashworthiness, shape and topology optimization of vehicle components, meta-heuristic optimization techniques, and additive manufacturing.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors state no conflict of interest.

  6. Research funding: None declared.

  7. Data availability: Not applicable.

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Published Online: 2025-10-01
Published in Print: 2025-11-25

© 2025 the author(s), published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

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  10. Metaporous acoustic metamaterials with Helmholtz resonators for enhanced NVH performance in battery electric vehicles
  11. Improving the energy absorption capabilities of carbon fiber/epoxy composites by embedding steel wire meshes
  12. Energy absorption and deformation characteristics of eight SLS-manufactured PA12 lattice structures under an intermediate compressive load rate
  13. Effect of basalt and kenaf fiber hybridization on the physical, mechanical, and thermal properties of polymer composites
  14. Wear behavior of different SiC and WC reinforced high entropy alloys deposited by the spark emmission procedure on a AISI 1010 steel
  15. Microstructure and mechanical properties of matching and non-matching resistance spot welds of DP450 and DP800 steels
  16. Stress concentration factors for bending with symmetric opposite notches in thin beam evaluated by FEM and ANN
  17. Numerical and experimental investigation of impact performances of cast and stretched polymethyl methacrylate panels
https://doi.org/10.1515/mt-2025-0172
Schlagwörter für diesen Artikel
sled dog optimization algorithm; engineering optimization problem; nature-inspired algorithms; structural optimization; brake pedal
Creative Commons
BY 4.0

Artikel in diesem Heft

  1. Frontmatter
  2. Microstructural evolution and mechanical properties of shear-spun 5052 aluminum alloy components under feed rate regulation
  3. Effect of hot extrusion on mechanical properties of Al2O3/Al composite prepared by spark plasma sintering
  4. A novel approach for modeling liner interface debonding in solid rocket motors
  5. Surface defect detection of curved mosaic ceramics based on improved coupling denoising algorithm
  6. Increasing the range of EVs: a TRIZ-inspired approach
  7. Electrochemical behavior of welded joints of 10MnNiCr marine steel under stress in seawater
  8. Dynamic random walk-based sled dog optimization algorithm and artificial neural network for optimizing design engineering problems
  9. Using design thinking methodology for developing innovative auto-injection systems
  10. Metaporous acoustic metamaterials with Helmholtz resonators for enhanced NVH performance in battery electric vehicles
  11. Improving the energy absorption capabilities of carbon fiber/epoxy composites by embedding steel wire meshes
  12. Energy absorption and deformation characteristics of eight SLS-manufactured PA12 lattice structures under an intermediate compressive load rate
  13. Effect of basalt and kenaf fiber hybridization on the physical, mechanical, and thermal properties of polymer composites
  14. Wear behavior of different SiC and WC reinforced high entropy alloys deposited by the spark emmission procedure on a AISI 1010 steel
  15. Microstructure and mechanical properties of matching and non-matching resistance spot welds of DP450 and DP800 steels
  16. Stress concentration factors for bending with symmetric opposite notches in thin beam evaluated by FEM and ANN
  17. Numerical and experimental investigation of impact performances of cast and stretched polymethyl methacrylate panels
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Heruntergeladen am 24.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/mt-2025-0172/html
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