# Design Optimization of Steering Mechanisms for Articulated Off-Road Vehicles Based on Genetic Algorithms

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## Abstract

**:**

## 1. Introduction

## 2. Problem Description

## 3. Optimization Based on GA

#### 3.1. Determination of Design Variables

#### 3.2. Establishment of Constraints

#### 3.3. Objective Function

#### 3.4. Penalty Function

#### 3.5. Design of Fitness Function

#### 3.6. GA-Based Optimization

- Step 1: Identify design variables and then encode the required variables in the form of a fixed-length binary string. Binary encoding is used because of the following advantages: (a) simple coding and decoding operations; (b) genetic operations such as selection, crossover, and mutation are easy to implement; (c) it complies with the principle of minimum symbol set coding. In this paper, the positions of four hinge points of the two cylinders are taken as the design variables. However, the positions of cylinders will be applied to the actual structure. Given the assembly accuracy, we set the accuracy of the optimization results to four decimal places. Consequently, the length of the binary string is calculated according to Equation (18):$${2}^{i-1}\le ({c}_{m}-{c}_{n})\times {10}^{4}\le {2}^{i}-1,$$$i$: The length of the binary string;${c}_{m},{c}_{n}$: The top and bottom limits of the design variables.
- Step 2: Create a random initial population. The individuals within the population are digitized codes. Set the evolution algebraic counter and the maximum evolution algebra to 0 and T, respectively.
- Step 3: Calculate their corresponding fitness values by means of the Equation (17) for the populations from Step 2 and those newly-bred populations after selection, crossover, and mutation from the next steps. Then, those individuals with relatively high calculated fitness are selected and kept in the procedure, which will be subsequently taken to reproduce a new generation with better adaptability than themselves in Step 5. As can be seen from Equation (17), the greater the fitness value, the smaller the stroke difference and arm difference. As a result, the optimal value is obtained when the fitness value reaches the maximum.
- Step 4: Check whether the iteration termination criterion for the GA has been reached. If the outputs of the GA do not satisfy the termination criteria, the next steps should be implemented.
- Step 5: Create new population through selection, crossover, and mutation. In GA, a method needs to be constructed to generate new species, in order to keep the objective function close to the optimal value. New species are generated via selection, crossover, and mutation. Selection is related to method and criteria, which are used to choose individuals with high fitness. Then, the selected individuals cross-pair with each other to generate new individuals, and these individuals are inserted into the parent population to generate more highly-adaptive populations, which is the offspring created by crossover. In other words, crossover creates new individuals through the recombination between string pairs of the selected individuals in the mating pool. Mutation refers to a new individual that resulted from a change in a gene of an individual’s chromosome.

## 4. Case Study

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Fang, J.; Wang, F. Optimum design of hydraulic power steering system for wheel loader. Constr. Mach.
**1989**, 11, 8–10. [Google Scholar] - Tan, Z.; Ye, B. Parameter optimization for the engineering machinery double oil cylinder steering mechanism. Constr. Mach.
**2005**, 4, 76–77. [Google Scholar] - Zhou, L. Optimal design for pivot position of articulating steering mechanism on loaders. Constr. Mach. Equip.
**2007**, 38, 25–28. [Google Scholar] - Wei, Q.; Zhu, B.; Jing, B.; Liu, H.; Liu, M. Optimization design of loader steering mechanism based on MATLAB. In Proceedings of the IEEE 10th International Conference on Computer-Aided Industrial Design & Conceptual Design, Wenzhou, China, 26–29 November 2009; pp. 751–754. [Google Scholar]
- Du, L.; Deng, K.; Gong, Y. The optimum design for pivot points of steering mechanism on HT25J wheel loader. In Proceedings of the International Conference on Consumer Electronics, Communications and Networks (CECNet), XianNing, China, 16–18 April 2011; pp. 2760–2763. [Google Scholar]
- Wang, H.; Li, W. Layout Design Analysis of Double Cylinder Steering Mechanism of Articulated Loader. Chin. J. Constr. Mach.
**2012**, 68–71. [Google Scholar] - Zhang, L.; Raut, R.; Jiang, Y.; Kleine, U. Two-stage placement for VLSI analogue layout designs. IEE Proc. Circuits Devices Syst.
**2006**, 153, 274–280. [Google Scholar] [CrossRef] - Munetomi, M.; Takai, Y.; Sato, Y. StGA: An application of a genetic algorithm to stochastic learning automata. Syst. Comput. Jpn.
**1996**, 27, 68–78. [Google Scholar] [CrossRef] - Nabavi, S.; Zhang, L. Design and Optimization of Piezoelectric MEMS Vibration Energy Harvesters Based on Genetic Algorithm. IEEE Sens. J.
**2017**, 17, 7372–7382. [Google Scholar] [CrossRef] - Senthilkumar, B.; Kannan, T.; Madesh, R. Optimization of flux-cored arc welding process parameters by using genetic algorithm. Int. J. Adv. Manuf. Technol.
**2017**, 93, 35–41. [Google Scholar] [CrossRef] - Zhang, H.; Hua, M.; Dong, G. Optimization of texture shape based on Genetic Algorithm under unidirectional sliding. Tribol. Int.
**2017**, 115, 222–232. [Google Scholar] [CrossRef] - Ferdyn-Grygierek, J.; Grygierek, K. Multi-Variable Optimization of Building Thermal Design Using Genetic Algorithms. Energies
**2017**, 10, 1570. [Google Scholar] [CrossRef] - Meng, J.; Hu, J.; Xia, H.; Lv, M. Hierarchical optimization of the composite blade of a stratospheric airship propeller based on genetic algorithm. Struct. Multidiscip. Optim.
**2017**, 56, 1341–1352. [Google Scholar] [CrossRef] - Panthangi, R.K.; Naduvinamani, V. Optimization of surface roughness in cylindrical grinding Process. Int. J. Appl. Eng. Res.
**2017**, 12, 7350–7354. [Google Scholar] - Mallik, S.; Mallik, K.; Barman, A. Efficiency and cost Ooptimized design of an induction motor using genetic algorithm. IEEE Trans. Ind. Electron.
**2017**, 64, 9854–9863. [Google Scholar] [CrossRef] - Almeida, J.H.S.; Ribeiro, M.L. Stacking sequence optimization in composite tubes under internal pressure based on genetic algorithm accounting for progressive damage. Compos. Struct.
**2017**, 178, 20–26. [Google Scholar] [CrossRef] - Knust, J.; Podszus, F.; Stonis, M. Preform optimization for hot forging processes using genetic algorithms. Int. J. Adv. Manuf. Technol.
**2017**, 89, 1623–1634. [Google Scholar] [CrossRef] - Xu, Y.; Wang, J.; Wu, Q. Distributed learning of equilibria with incomplete, dynamic, and uncertain information in wireless communication networks. In Game Theory Framework Applied to Wireless Communication Networks; IGI Global: Hershey, PA, USA, 2016; pp. 63–86. [Google Scholar]
- Tsiropoulou, E.E.; Mitsis, G.; Papavassiliou, S. Interest-aware energy collection & resource management in machine to machine communications. Ad Hoc Netw.
**2017**, 68, 48–57. [Google Scholar] - Blasco, P.; Gunduz, D.; Dohler, M. A learning theoretic approach to energy harvesting communication system optimization. IEEE Trans. Wirel. Commun.
**2012**, 12, 1872–1882. [Google Scholar] [CrossRef] - Razavi, R.; Klein, S.; Claussen, H. Self-optimization of capacity and coverage in LTE networks using a fuzzy reinforcement learning approach. In Proceedings of the 21st Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Istanbul, Turkey, 26–30 September 2010; pp. 1865–1870. [Google Scholar]
- Wang, J. Mechanical Principle; Huazhong University of Science and Technology Press: Wuhan, China, 2017. [Google Scholar]
- Zhou, F. Design and Calculation of Soil-Spade Transportation Machinery; China Water Power Press: Beijing, China, 1984. [Google Scholar]
- Li, L. Mechanical-Hydraulic Co-Simulation of Full Hydraulic Steering System and Optimal Design of Mining LHD. Master’s Thesis, Taiyuan University of Technology, Taiyuan, China, May 2016. [Google Scholar]
- Andrew, A.M. MOBILE ROBOTICS: A PRACTICAL INTRODUCTION (APPLIED COMPUTING SERIES), by Ulrich Nehmzow, Springer, London, 2000, ISBN 1852331739, xii+243 pp. (Pbk, £24.50). Robotica
**2000**, 18, 219–223. [Google Scholar] [CrossRef]

**Figure 7.**The pre-optimization steering model of FW50GL in ADAMS (automatic dynamic analysis of mechanical systems).

Variables | Values |
---|---|

AP | 150 mm |

CQ | 360 mm |

PO | 1017 mm |

QO | 13 mm |

L | 3300 mm |

b | 40° |

${l}_{\mathrm{max}}$ | 1040 mm |

$s$ | 800 mm |

G | 3.8 t |

$\epsilon $ | 8 mm |

Variables | Values |
---|---|

Population | 1000 |

Mutation ratio | 0.02 |

Crossover ratio | 0.5 |

T (Genetic algebra) | 100 |

Variables | AP | CQ | PO | QO |
---|---|---|---|---|

Pre-Opt | 150 mm | 360 mm | 1017 mm | 13 mm |

After-GA-Opt | 258 mm | 300 mm | 1158 mm | 0.25 mm |

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**MDPI and ACS Style**

Zhou, C.; Liu, X.; Xu, F.
Design Optimization of Steering Mechanisms for Articulated Off-Road Vehicles Based on Genetic Algorithms. *Algorithms* **2018**, *11*, 22.
https://doi.org/10.3390/a11020022

**AMA Style**

Zhou C, Liu X, Xu F.
Design Optimization of Steering Mechanisms for Articulated Off-Road Vehicles Based on Genetic Algorithms. *Algorithms*. 2018; 11(2):22.
https://doi.org/10.3390/a11020022

**Chicago/Turabian Style**

Zhou, Chen, Xinhui Liu, and Feixiang Xu.
2018. "Design Optimization of Steering Mechanisms for Articulated Off-Road Vehicles Based on Genetic Algorithms" *Algorithms* 11, no. 2: 22.
https://doi.org/10.3390/a11020022