## 5 Conclusions  
1. With the application of intelligence algorithms, specifically the IRMO algorithm, the design and optimization of HDD trajectories could obviously improve the efficiency and accuracy in this study. All the calculations and optimizations were tested on a 2.30 GHz computer (CPU: Intel i5-6300 HQ), and the total time of fitting and length optimization was stabilized within 60 s, which shows great potential for shortening the manual adjustment time required in actual projects.
2. This study proposed and tested a new method to design the HDD trajectory combining five-segment trajectory with catenary trajectory. With two processes, the five-segment trajectory could be designed with a great similarity to the catenary trajectory, and simultaneously with the shortest length, thereby reducing the associated costs. Both processes were verified through data from the literature or from actual projects. It was proved that the catenary trajectory has great potential to design a traditional drilling path with precise and achievable parameters.
3. Six concise parameters (\(L_{1}\), \(L_{3}\), \(R_{2}\), \(R_{4}\), \(\theta_{1}\), and \(\theta_{2}\)) were concluded herein to design trajectories and be optimized by the IRMO algorithm. According to the analysis of the parameters, it was found that the limits of \(L_{3}\) and \(R_{2}\) have fewer impacts on the optimization results. Therefore, the optimization ranges of the other four parameters should be set carefully during the trajectory design.
4. By improving the structure data of the radial movement optimization, the obtained IRMO algorithm had a great ability to solve the extremum value of the multidimensional nonlinear objective function. Benefitting from the refined parameter matrix and efficient data structure, the authors believe IRMO has further potential in more complex trajectory design such as 3D construction or in avoiding obstacles.
5. It should be emphasized that the importance of the accuracy and viability of the results by algorithm are mostly based on the set of the constraints and validated ranges of input parameters which largely rely on the experience of trained engineers. This method hopes to provide more advice in terms of geometrical parameters and drilling mud pressure for current practice preparations with a large consideration of site and soil property factors. There are more factors, such as geology, rock properties, and drilling rigs that should be discussed in further study to ensure the mechanical design. What is more, the mechanical advantages of the five-segments trajectory similar to the catenary trajectory also need more experimental studies to be verified.  
Figure 23: Comparison of IRMO design and actual design.  
**Author Contributions:** Conceptualization, [PERSON] and [PERSON]; methodology, [PERSON]; software, [PERSON]; validation, [PERSON]; formal analysis, [PERSON]; investigation, [PERSON]; resources, [PERSON]; data curation, [PERSON]; writing--original draft preparation, [PERSON]; writing--review and editing, [PERSON]; visualization, [PERSON]; supervision, [PERSON]; project administration, [PERSON]; funding acquisition, [PERSON] All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research received no external funding.  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The data presented in this study are openly available in published literature, reference number [3; 12].  
**Conflicts of Interest:** The authors declare no conflict of interest.