# A Hyper Heuristic Algorithm to Solve the Low-Carbon Location Routing Problem
## 6 Conclusions  
This paper comprehensively studied the impact of HF, simultaneous delivery, customer time windows, and speed regionalization on logistics costs, carbon emissions, and customer satisfaction. It also proposed the RLCLRPTWSPDHF model.  
At the same time, a new hyper-heuristic solving algorithm, named SESMAM-AA, was proposed. This algorithm uses the second exponential smoothing method to predict the recent performance of low-level operators. The operator is adaptively selected according to the performance of the algorithm in the near term (quality operator/inferior operator). Finally, the FRR-MAB method is used to evaluate the operator's credit value, and the roulette probability distribution is used to select the appropriate and accurate low-level operator.  
This paper conducted three types of experiments. The first was to verify the correctness of the model and the accuracy of the algorithm. The second experiment was to verify the efficiency of the algorithm by solving the CLRP/CLRPSPD benchmarks. The purpose of the third experiment was to analyze the influence of customer parameters, depot parameters, and fleet types on logistics costs, carbon emissions, and customer satisfaction. At the same time, the validity of the model was verified. The experimental results show that the RLCLRPTWSPDHF model can effectively reduce distribution costs, reduce carbon emissions, and protect the environment.  
According to the analysis of experimental results, the following conclusions are drawn:  
1. The proposed algorithm has high accuracy in solving small-scale examples;
2. The SESMAM-AA algorithm can obtain high quality solutions in reasonable computing time with high efficiency and robustness;
3. The HF can reduce logistics costs, carbon emissions, and service distances, and can better meet actual distribution requirements;
4. The distribution location of customers and depots has a great influence on each function value;
5. The RLCLRPTWSPDHF model can reduce TC, CO\({}_{2}\), and D better than the traditional model, but there is no guarantee that CWT will always be reduced to improve customer satisfaction.  
In summary, the research in this paper has important practical and theoretical significance for logistics enterprises seeking to reduce logistics costs and protect the ecological environment, and has an important supporting role in sustainable development and energy conservation and emission reduction policies. However, in addition to considering operating costs, customer satisfaction is also a major concern of logistics companies. Therefore, the main task in the next step will be to make customer satisfaction the second optimization goal to build a multi-objective model and, at the same time, to design a multi-objective hyper-heuristic algorithm to obtain the Pareto set. Finally, this paper analyzed customer satisfaction under the premise of soft time windows. To improve customer satisfaction, hard time windows should be researched.  
Conceptualization, Y.Z. and C.Z.; methodology, C.Z.; software, C.Z.; validation, L.L., Y.Z. and C.Z.; formal analysis, Y.Z.; investigation, L.L.; resources, L.L.; data curation, L.L.; writing--original draft preparation, Y.Z.; writing--review and editing, C.Z.; visualization, C.Z.; supervision, C.Z.; project administration, Y.Z.; funding acquisition, Y.Z. and C.Z.  
This research was funded by the National Natural Science Foundation of China grant numbers 61572438, Science Technology plan project of Zhejiang grant number 2017C33224. This support is gratefully acknowledged. Thanks for the reviewers and editors who provided valuable comments and suggestions for revising this paper.  
The authors declare no conflict of interest.