# A Hyper Heuristic Algorithm to Solve the Low-Carbon Location Routing Problem
## 2 Review  
LRP integrates two classic NP-hard problems: the location allocation problem (LAP) and the vehicle routing problem (VRP) [3]. At present, LRP has become one of the most important tools and research hotspots for operations management and cargo transportation [4; 5]. LCLRP is an LRP problem that aims to reduce greenhouse gases, such as carbon emissions generated in logistics and distribution. It also combines two types of NP-hard problems: LAP and the pollution routing problem (PRP) or green VRP (GVRP). PRP and GVRP focus on the social and environmental impacts of carbon emissions from cargo transportation. To establish a reasonable model, a model for assessing vehicle carbon emissions is essential. Table 1 lists 14 different fuel consumption/carbon emission models, covering the model classification and source and providing the carbon emission impact factors involved in the model. In the above table, the meanings of the abbreviation are as follows:  
MEET: Methodology for calculating transportation emissions and energy consumption; NTM Network for transport and environment; COPERT: Computer program to calculate emissions from road transportation; ECOTRANSIT: Ecological transport information tool; NAEI: National atmospheric emissions inventory; MOVES: Motor Vehicle Emission Simulator; IVE: The international vehicle emissions model; IFCM: An instantaneous fuel consumption model; FMEFCM: A four-mode elemental fuel consumption model; RSFCM: A running speed fuel consumption model; ASFCM: Average speed fuel consumption model; VSP: Vehicle specific power; OFDM: The Oguchi fuel consumption model; CMEM is the abbreviation of Comprehensive Modal Emissions Modeling. And, VP is the vehicle parameter, FT is the fuel type, RG is the road gradient, E is the environmental factor, S is the speed, and AS is the acceleration. The above 14 models involved factors affecting carbon emissions: environmental conditions, vehicle parameters, traffic conditions, and driver factors. In urban logistics, the use of a heterogeneous fleet (HF) is one of the key factors in reducing logistics costs and carbon emissions and improving logistics distribution efficiency [17; 18; 19; 20]. [PERSON] et al. [17; 21] \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Macro Model** & **VP** & **FT** & **RG** & **E** & **S** & **AS** & **Micro Model** & **VP** & **FT** & **RG** & **E** & **S** & **AS** \\ \hline MEET [6] & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & & IFCM [7] & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ NTM [2] & \(\surd\) & \(\surd\) & & & & & \(\quad\) & FMEFCM [8] & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ COPERT [9] & \(\surd\) & \(\surd\) & & & \(\surd\) & & RSFCM [8] & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \\ ECOTRANSIT [10] & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & & \\ NAEI [12] & \(\surd\) & \(\surd\) & & \(\surd\) & & \(\quad\) & VSP [13] & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ MOVES [14] & \(\surd\) & \(\surd\) & & \(\surd\) & & \(\quad\) & OFCM [15] & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ IVE [16] & \(\surd\) & \(\surd\) & & & \(\quad\) & \(\quad\) & CMEM [17] & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) & \(\surd\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fuel consumption/carbon emission model. analyzed the impact of fleet size and composition on costs and carbon emissions. The conclusions showed the advantages of a heterogeneous fleet compared to single-model logistics distribution networks. [PERSON] et al. (2018) constructed a heterogeneous fleet, low-carbon VRP model with a fixed number of vehicles. The data showed that using HF can improve vehicle capacity utilization and reduce energy consumption and carbon emissions. The number of vehicles can also meet the requirements of actual distribution applications. [PERSON] et al.