Street Patrol Routing Optimization in Smart City Management Based on Genetic Algorithm: A Case in Zhengzhou, China

Abstract

A series of urban law enforcement events involving city inspectors dispatched by the city management department can reflect some problems in smart city management, such as illegal advertising and unlicensed street operation. In this paper, we propose a model for the allocation of city inspectors and the optimization of patrol paths. The objective is to minimize the average response time and the number of inspectors. We also develop a priority-patrol-and-multiobjective genetic algorithm (DP-MOGA) to classify patrol segments according to the frequency of events and develop an improved genetic algorithm to achieve the aforementioned objective. We conduct numerical experiments using patrol data obtained from city inspectors in Zhengzhou, China, to clearly show that the proposed algorithm generates reasonable routes that reduce the average response time of events and the number of patrol inspectors. Furthermore, we test the algorithm for three different time scenarios (roads with different average numbers of events) and demonstrate the efficiency of the algorithm. The experimental results show that our proposed algorithm is more stable and efficient than other existing algorithms.

1. Introduction

In recent years, smart cities have become a research area and have been used as a strategy to improve quality of life [1,2,3]. Smart city management is a new model of city management that has been developed against the background of smart city construction [4,5,6,7]. The smart city management model has changed the state of management in terms of segmentation, intelligent intersection, extensive management, lack of supervision and inefficiency [8,9]. This model transforms city management from an extensive management state to an intensive, precise and real-time state.

With developing urbanization in China, the limited availability of city jobs has resulted in self-employment, including illegal operations and setting up roadside stalls. These activities present challenges to the construction of smart cities. Chinese government sends urban management law enforcement teams to supervise smart city construction. Urban management law enforcement teams have used patrols to strengthen management of these activities, resulting in a series of urban management law enforcement events [10]. Urban management enforcement inspectors are similar to community police officers, who patrol the roads for problems.

To deal with law enforcement events quickly and strengthen infrastructure maintenance, city inspectors can comprehensively patrol roads. A patrol route should cover all road corners and emphasize key segments. It is very important to provide suitable patrol routes for inspectors.

This paper focuses on the problem of patrol routes in smart city management. A model is proposed that optimizes a patrol route by minimizing the number of city inspectors required and the average response time for events. Then, an algorithm is designed to solve the research problem. The algorithm classifies patrol route segments based on the frequency of urban law enforcement events, and the crossover and mutation operators of the genetic algorithm are improved to obtain an optimized solution.

The remainder of the paper is organized as follows. In Section 2, we review literature related to this research study. In Section 3, the patrol optimization problem of city managers in a grid area is described, and a patrol route optimization model is established. We propose an effective algorithm to solve the research problem based on a genetic algorithm in Section 4. In Section 5, we perform numerical calculations and analysis considering real-world scenarios. We draw conclusions and propose future research directions in Section 6.

2. Literature Review

This section describes the literature review, including processes in smart city management, route optimization in patrols and the application of genetic algorithms.

2.1. Patrol Scheduling in Smart City Management

IBM (International Business Machines Corporation) in the United States first proposed a new management concept for smart cities in 2008 [11,12,13,14]. Smart city management is the use of city information resources and communication technology to analyze and process the events and components of a city [2,3,15]. Information and communication technologies (ICT) featuring artificial intelligence and big data are widely used in the frameworks of smart cities [16].

The patrol scheduling problem is an intersection among ICT, energy and transport. It is the allocation of personnel to patrol the urban transport network [17]. The smart city management department assigns a number of city inspectors to patrol in the street traffic network in order to protect public facilities to solve some problems in the street network such as illegal constructions and road occupancy [18,19].

2.2. Route Optimization in Street Patrol

In real life there are many distributed services on the street. A well-designed route can substantially reduce the cost of a distributed service. Therefore, routing optimization problems are being increasingly studied for both fundamental research and applications [19]. Street patrol is a necessary activity. Patrolling officers prevent emergencies and take action on real-time incidents [20,21,22]. Efficient patrol routes are designed using computerized information systems and more affordable geographic information systems (GISs) [23].

Route optimization for street patrol is common, and some research has been done on optimizing patrol paths. Public security officers carry out daily street patrols in order to ensure safety and combat crime [24]. The optimization target for patrol was to allocate personnel and route. Cheng et al. established an optimized, high-performance road patrol task assignment model for multi-Unmanned Aerial Vehicles (multi-UAVs) [25]. The length of patrol routes and the number of UAVs has been optimized to a minimum. Fu et al. solved the problem of smart community security patrol route planning [26]. A community patrol simulation framework is used to determine and evolve a set of routes and find the optimal solution. The multi-agent simulation model is used to set constraints and find the objective value of the route. Xiao et al. investigated patrol personnel and vehicles in the electricity system in order to identify problems in the distribution network [27].

There are some studies that assert that street patrol should focus on hot spots and reflect the impact of cases on patrol paths. The police patrol in areas with high crime hotspots based on geographical crime analysis [28]. Police deployment is optimized by pinpointing hotspot areas [22]. However, there are few studies that focus on route optimization of patrols in hotspots.

2.3. Application of the Genetic Algorithm to the Vehicle Routing Problem

The vehicle routing problem (VRP) was first proposed by Dantzig [29]. Vehicle routing problems are mainly categorized as capacitive VRP [30,31,32,33], distance-constrained VRP [32,34,35,36], VRP with a time window [35,37] and VRP with backhauls [30,31,38].

There has been a lot of research on VRP in recent years. VRP is used in order to optimize the available resources such as green-energy resources and transport such as freight distribution [39,40]. Lin et al. [41] proposed a VRP to solve the time and energy cost routing problem. Musolino et al. [42] solves the problem of VRP on an urban road network. Polimeni et al. [43] presented a VRP in relation to the shipment of dairy products by urban retailers.

The genetic algorithm was first proposed by Holland in 1975 [44,45]. This method is widely used to solve practical routing problems. Street patrol is a common vehicle routing problem (VRP). Jeon et al. proposed a novel hybrid genetic algorithm (HGA) to solve the capacity VRP and the generation of the initial solution in the genetic algorithm has been improved [46]. Berger et al. explored an adaptive genetic algorithm (AGA) to solve the VRP with a time window [47]. The algorithm makes the two populations evolve at the same time by modifying the genetic operators. Zhou et al. presented a multi-objective genetic algorithm (MOGA) by improving the selection operation and the one-point crossover operator and mutation operator to solve the vehicle routing problem [48]. However, there are few studies that focus on the multi-point crossover operators and mutation operators in genetic algorithm.

The shortcomings of the previous studies are as follows: (1) Information collection is an important process in smart city management, but there is a lack of research that focuses on street patrol about city inspectors, (2) For route optimization in street patrol, few studies have considered hot areas and high frequency events and (3) Genetic algorithms consider only one-point crossover and mutation operators, and lack multi-point crossover operators and mutation operators.

3. SPRP Problem in Smart City Management

This section describes the street patrol route problem (SPRP) in smart city management. Specifically, it includes two points: (1) Specific definition of the problem and (2) Objective function and constraints of the model.

3.1. Problem Definition

The street patrol route problem (SPRP) in smart city management can be described as follows: a smart city management department creates patrol areas based on the urban management law enforcement area and dispatches city patrol officers to patrol. City inspectors are assigned patrols according to a prescribed route every day. Inspectors are switched between morning and afternoon and each person works six hours a day. They patrol the main roads along the road network. The number of available vehicles is limited in the department. The patrols drive following a predefined route.

The assumptions are as follows: (1) A city inspector sets out from a starting point, drives through each route and finally returns to the starting point, (2) The patrol routes of inspectors constitute a patrol network. A patrol route is composed of multiple connected road segments. The route is a closed loop and (3) Road segments with a high crime incidence have an increased patrol frequency.

Under the hypothetical conditions, an urban management law enforcement department sends several city inspectors to patrol the respective area. The goal is to achieve the best combination of the average incident response time and the number of inspectors. The patrol network model can be represented by the traffic network diagram G = (X, E), where X is a set of nodes and E represents the edge visited in the network.

The binary decision variables are defined as follows:

$$x_{ij}^k=\{\begin{array}{c}1 if inspectors patrol from segment i to j in route k\\ 0 otherwise\end{array}$$

(1)

$$t_{ij}^k=\left\{\begin{array}{c} 1 if inspectors patrol from segment i to j in route k\\ 0 otherwise \end{array}\right.$$

(2)

where $t_{ij}$ and $c_{ij}$ denote the time taken by inspectors to travel from segment i to j and the cases that occurred along segment $i$ to $j$, respectively.

3.2. Objective Function

Table 1. List of mathematical notations used in the proposed model.

Notation	Explanation
$a_i$	the number of cases that have occurred on road segment $i$
$t_{ij}$	the time taken by the inspectors to travel from segment $i$ to $j$
$K$	the number of road segments for all routes
$n$	the number of inspectors
$L_k$	the key patrol section is segment $$
$t_k$	the average patrol time
$v_k$	the number of inspectors patrolling segment $$
$F_1$ $F_2$   $\alpha and \beta$	the average incident response time the number of street inspectors the weights for the average incident response time and the number of inspectors

presents a list of mathematical notations used in SPRP model.

The objective functions on the problem are given as follows:

$$minZ=\alpha F_1+\beta F_2$$

(3)

$$\alpha +\beta =1$$

(4)

$$F_1={\displaystyle \sum }_{i\in E}\frac{a_i}{2\left({{\displaystyle \sum }}_r\frac{{{\displaystyle \sum }}_{j\in E}{x}_{ij}^k}{{{\displaystyle \sum }}_{ij\in E}{t}_{ij}{x}_{ij}^k/L_k}\right)}$$

(5)

$$F_2=\frac{K}{n}$$

(6)

The objective function (3) is a combination of F₁ and F₂, which are two objective functions used to minimize the average incident response time [49] and the number of patrol inspectors. This objective function (4) has two dimensions: the weights $\alpha$ and $\beta$ for the average incident response time and the number of inspectors. The overall objective is 1.

3.3. Constraints

The constraints on the problem are given as follows:

$$\sum v_k\le V$$

(7)

$${\displaystyle \sum }_{\left(i,j\right)\in E}{x}_{ij}^k={\displaystyle \sum }_{\left(j,i\right)\in E}{x}_{ji}^k i\ne j$$

(8)

$${\displaystyle \sum }_{\left(i,1\right)\in E}{x}_{i1}^k=x_0$$

(9)

$${\displaystyle \sum }_{\left(1,i\right)\in E}{x}_{1i}^k=x_0$$

(10)

$${\displaystyle \sum }_{k\in K}{x}_{ij}^k\ge 1 i\ne j$$

(11)

$${\displaystyle \sum }_{\left(i,j\right)\in E}{x}_{ij}^k={\displaystyle \sum }_{\left(j,l\right)}{x}_{jl}^k i\ne j,j\ne l$$

(12)

Constraint (7) ensures that the number of vehicles on patrol does not exceed the total number of vehicles in the department. Equation (8) provides constraints on the number of entrances and exits of each segment. Constraints (9) and (10) ensure that the patrol starts at and eventually returns to the point x₀. Constraint (11) represents passing each segment at least once, and constraint (12) represents an inspector from entering at node j and leaving at node l.

4. Proposed Algorithm for SPRP

In this section, the characteristics of the established model are used to propose a priority patrol and multi-objective genetic algorithm (DP-MOGA) for city inspectors, and the optimal solution for the patrol task is obtained using the following steps.

First, the constraints are processed to determine the relative importance of road segments. Second, the relative importance of segments is determined depending on the frequency of cases. Then, the patrol road segments are classified. Third, an improved genetic algorithm is used to generate the optimal patrol path.

4.1. Patrol Segment Classification Algorithm

The classification algorithm categorizes the patrol segments according to their degree of importance. The patrol segments are thus divided into key areas and ordinary areas. The key segments require an increased number and frequency of patrols. The algorithm is based on the number of incidents and patrol time for each road segment.

In this section, we classify road segments, increase the number of patrols for key road segments and obtain data for the grid route, including the number of route segments, the patrol time and the initial parameters for incidents occurring along the segments. Then, for each road segment from $K_1$ to $K_i$, we determine the patrol time and the ratio of incidents to the total number of incidents, which are used to set the threshold of the importance of a road segment. Finally, we compare the path ratio with the set threshold. If the path ratio is greater than the threshold, the road segment is a key patrol segment, and the number of patrols on the key road segment are increased. If the path ratio is less than the threshold, the road segment is considered a normal route segment, and a normal number of patrols are assigned to the road segment. The specific steps are described in Algorithm 1.

Algorithm 1: Patrol Route Classification Algorithm

1: Input: $k_1$$\leftarrow$number of patrols for segment i;  $Ma{x}_k\leftarrow$maximum road segment number;  $t_i\leftarrow$patrol time for road segment i;  $c_i\leftarrow$number of incidents that occurred on road segment i;  $Ma{x}_{t_i}$Max_ti←maximal patrol time for road segment i;  $Mi{n}_{t_i}\leftarrow$minimum patrol time for road segment i;  $Ma{x}_{c_i}\leftarrow$maximal number of incidents that occurred on road segment i;  $Mi{n}_{c_i}\leftarrow$minimum number of incidents that occurred on road segment i;  $n_k\leftarrow$number of patrols for ordinary road segments;   k←number of extra patrols for key segments; 2: Repeat: 3:     $Ma{x}_k\leftarrow$the last segment; 4:   if$K_i\le Ma{x}_k$, then $k_i=k_i+1$ 5:    for each data of the patrol segment do 6:      if $c_i\ge a\left(\frac{Ma{x}_{c_i}}{Mi{n}_{t_i}}-\frac{Mi{n}_{c_i}}{Ma{x}_{c_i}}\right)$ then 7:       set this segment as a key patrol segment route 8:       $n_k=n_k+k$; 9:      else 10:       set this segment as an ordinary patrol segment route; 11:      end if 12:    end for 13:  end if 14:  Until $K_i\ge Ma{x}_K$;

4.2. Genetic Algorithm

The genetic algorithm includes chromosome encoding, population initialization, decoding, implementing a fitness function, selection, crossover, mutation and replacement [50]. It is necessary to design a number of iterations, varying the population size of the iteration, the probability of crossover and the probability of mutation. Different final results are produced using different parameters.

In this section, we design an improved genetic algorithm to ensure the smooth solution of patrol problems for smart city governments. The designed algorithm is added to an elitist strategy [51]. After each operation process, the value of the objective function for the stored data is calculated and used to select the optimal result. The method maintains the initial population diversity and prevents premature convergence of the objective function. The algorithm improves the efficiency of the search process. A flowchart of the improved genetic algorithm is shown in Figure 1.

4.2.1. Encoding Scheme

Chromosome coding is the basis for subsequent operations of crossover and mutation. The matrix is a chromosome, where the number of rows represents the number of paths and the columns represent the road segments in each path. The path code is an integer from 1 to K, and i represents a road segment. A combination of ordered integer and matrix coding is used in the algorithm.

4.2.2. Crossover Operation

The crossover operation of the genetic algorithm consists of selecting a path planning scheme for two parents and determining the number of paths that need to be exchanged. To ensure the connectivity of the patrol path, we design a crossover operator by randomly exchanging the position of the path. The multipoint crossing method is adopted to add and delete patrol route points to connect multiple paths.

The detailed procedure is presented in Algorithm 2.

Algorithm 2: Crossover Operator

1: Input: Parent 1←Route 1 selected from the population;  Parent 2←Route 2 different from Parent 1 selected from the population;  $a_n\leftarrow$a road segment selected from Route 1;  $b_n\leftarrow$a road segment selected from Route 2; 2: Select Parent 1 and Parent 2 from the population; 3: Select segment $a_n$ from Parent 1 and path $b_n$ from Parent 2; 4: Select intersection points in the chromosomes; 5: Exchange segment an and segment $b_n$ in Parent 1 and Parent 2; 6: Generate segment an1 and segment bn1 after performing the exchange; 7: for Comparison between the exchanged route and the original route do 8:  for lost segment do 9:    if the road segments are connected along the route, then 10:    Add lost segments; 11:  else Add lost segments after splitting the route into connected sections; 12:  end if 13:   for redundant segment do 14:   if the segment appears in a nonexchange point, then 15:    Delete the redundant road segments at the nonexchange point; 16:    end if 17:    end for 18:  end for 19:  end for 20: Test route internal rationality; 21: Update the original route with $a_{n_1}$ and $b_{n_2}$; 22: Update Parent 1 and Parent 2;

4.2.3. Mutation Operation

We select a parent route planning plan, which can be a multisection mutation, for the mutation operation. In this section, a multipoint mutation method is presented that consists of randomly selecting mutation points.

The mutation process is described here. A route is randomly selected from the route planning plan, and then a road segment is randomly selected. A road segment that has been removed is randomly combined with other road segments. We calculate the value of the objective function for different route planning schemes, adopt the elite strategy and select the optimal fitness function. The objective function is defined as a fitness function in this section.

The detailed procedure is presented in Algorithm 3.

Algorithm 3: Mutation Operator

1: Input: Solution←Route 3 in the population after the crossover operation; $c_n$←a road segment selected from Route 3; mutation points←Select mutation points in the chromosomes; $\mathrm{f}\left(t\right)$←Fitness function; 2: Select road segments from the chromosomes as variant road segments; 3: Select a road segment $c_n$ from the road segments to operate; 4: Select a mutation point in the chromosome; 5: Extract the road segment $c_n$ and combine the segment with other road segments; 6: Repeat 7: for $c_n\leftarrow n$, do 8: Calculate the fitness function under different path plans; 9: Sort the mutated chromosomes according to the fitness function value $\mathrm{f}\left(t\right)$; 10: Select the road segment combination with the maximum value $\mathrm{f}\left(t\right)$; 11: Perform a route internal rationality test; 12: Update the mutation point; 13: Update the population;

5. Experimental Results and Analysis

In this section, actual road network is selected for simulation and the experimental results are analyzed. Firstly, we model a section of a real road network to create three different scenarios. Secondly, the algorithm is evaluated in the three scenarios. Lastly, the algorithm proposed in this paper is compared and analyzed with other algorithm.

5.1. Data and Parameters

Zhengzhou is a provincial city in Henan, China. It is located in central China and is a new modern city. A real network from an area in Zhengzhou is considered in this section. The proposed algorithm is coded in MATLAB 2018a, and experiments are conducted on a computer with an Intel Core i7 processor (3.7 GHz) and 8 GB of RAM.

The area investigated in this study is shown in Figure 1. The road network model is for Erqi District, Zhengzhou. Multiple managers patrol the specified grid area. Each city manager has a fixed patrol route consisting of road segments. This road network is assumed to be patrolled by multiple managers on electric bicycles. The road network for the study area is shown on Figure 2. The figure shows a section of the road network near Xizhan Road in Erqi District. A road network model is established for roads in the patrol area on the map. The width of the road is shown in the figure according to the actual situation. Figure 3 is a mathematical abstract model of the road network model, which can be abstracted as an undirected graph. This network includes 23 nodes and 66 directed road segments.

5.2. Algorithm Evaluation

City inspectors conduct patrols during three different time periods in the morning, noon and evening. As the frequency of cases is different for the three time periods, patrol inspectors focus on different road segments during each period. There are two main parameters for the segments: the travel time and the average number of events. The shorter the driving time is, the smoother the road segment is. The shorter the driving time is, the smoother the road segment is. The longer the driving time is, the more congested the road segment is. Considering the aforementioned parameters, the following three different time scenarios are proposed.

Scenario 1: There is a high average number of events for specific road segments, and the road state of the entire grid is unbalanced. Patrols need to focus on these high-incidence road segments.

Scenario 2: The travel time and average number of incidents tend to be similar for all road segments, and there are no major differences among road segments. The road state of the entire grid is balanced.

Scenario 3: Some road sections have longer driving times, and the road state of the entire grid is unbalanced.

These three scenarios reflect actual patrol situations. We perform a variety of analyses using these scenarios.

It is useful to analyze the test results using mathematical statistics and identify the degree of influence of various factors on the results. We use variance to evaluate the algorithm efficiency.

We evaluate the quality of a solution using various D, which is defined as follows:

$$\mathrm{D}=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^n{\left(x_i-\overline{x}\right)}^2}{n}}$$

(13)

where $x_i$ is the number of segments for a route, n is the total number of routes, and $\overline{x}$ is the average number of road segments. The solution generated by the patrol algorithm based on key areas is used to determine the variance. An algorithm with a lower D value is more efficient.

A lower bound gap (LBG) can be used to evaluate the performance of the algorithm, which is defined as follows:

$$\mathrm{LBG}=\frac{L_{max}\left(R\right)-L_{min}\left(R\right)}{L_{max\left(R\right)}}$$

(14)

where $L_{max}\left(R\right)$ is the length of the longest road segment and $L_{min}\left(R\right)$ is the length of the shortest road segment. An algorithm with a higher LBG value is more efficient.

Table 2. Computational results for S1, S2 and S3.

Scenario	Objective Value	LBG	D
S1	0.7276	0.8571	1.7670
S2	0.5112	0.9091	3.0443
S3	0.7071	0.8000	1.1595

shows the objective value, D and LBG, in three different scenarios. The values of the algorithm do not change much in the three scenarios. The results illustrate that DP-MOGA algorithm has a stable performance.

5.3. Comparative Analysis

Multi-objective genetic algorithm (MOGA) is used to solve multi-objective optimization problems by improving genetic algorithms [52]. We use the priority patrol and multi-objective genetic algorithm (DP-MOGA) compared with MOGA and a very large-scale neighborhood searching (VLNS) algorithm [49].

The obtained results are shown in

Table 3. Comparisons of experimental results.

Algorithm	Objective Value	Event Response Time	Convergence	Running Time
DP-MOGA	0.5112	2539.5	30 iterations	14
MOGA	0.5114	2545.3	35 iterations	17.77
VLNS	0.5147	2552	45 iterations	1

. The objective value, event response time and convergence in DP-MOGA are the smallest values. The results demonstrate that the DP-MOGA algorithm is more effective than the MOGA and VLNS algorithms.

In real-life, city inspectors are assigned patrol tasks by a smart city management department based on scenario 1. City inspectors design routes for patrols based on actual experience. Figure 4 shows the path patrol scheme for real-life scenario.

The proposed algorithm increases the number of patrols based on the high-frequency of events in segments. The improvement in the crossover operator and mutation operator of the genetic algorithm results in the shortest average response time to incidents and the fewest patrol inspectors. The proposed algorithm is used to optimize the route for the study area.

Table 4. Number of road network incidents and road patrol time.

Segment	Patrol Time	Incidents	Segment	Patrol Time	Incidents
1	9.5	7	18	9.5	7
2	10.5	8	19	10.5	9
3	10	9	20	9.5	7
4	9.5	7	21	11	9
5	10.5	8	22	9.5	6
6	10	9	23	10.5	7
7	9.5	7	24	10	8
8	10.5	8	25	10	8
9	10	9	26	9.5	9
10	9.5	7	27	10.5	7
11	10.5	8	28	9.5	9
12	10	9	29	10	8
13	9.5	7	30	10	8
14	11	8	31	10.5	7
15	10.5	8	32	9.5	9
16	10	9	33	10	8
17	9.5	7

shows the number of road network incidents and road patrol time in real-life scenario.

Table 5. Path patrol scheme in real scenario.

Route	Segment Covered	Number of City Inspectors
1	23–18–15–22–16–9–4	4
2	4–7–3–1	2
3	10–11	1
4	6–13–12–8–21	3
5	2–5	1
6	31–30–33–29–32–26	3
7	25–28–24	2
8	17–19–20–27	2

shows the route patrol scheme based on actual experience. The optimized route patrol scheme is shown in

Table 6. The path patrol scheme of the improved algorithm.

Route	Segment Covered	Number of City Inspectors
1	32–9–31	2
2	33–30	1
3	22–23–28–16–19–26–24	4
4	20–25–27–12–21–18	3
5	6–13	1
6	1–3–5–7–2–4–8	4
7	10–11–17	2
8	14–15	1

. The actual patrol routes before and after optimization are shown in Figure 4 and Figure 5.

Table 7. Comparison of the solution before and after optimization.

Real Scenario	Objective Value after Optimization	Objective Value before Optimization	City Inspectors before Optimization	City Inspectors after Optimization
	0.5112	0.5159	26	18

shows that the objective function value of the optimized scheme is 0.5112, compared to a value of 0.5159 for the unoptimized scheme. Compared with the existing patrol route for city inspectors, the optimized path patrol scheme reduces the average response time and the number of personnel for real cases. Applying this optimization method to actual daily patrols can improve the efficiency of the patrols. This method allows city inspectors to be arranged and urban law enforcement events to be handled better.

6. Conclusions and Future Work

In this study, we propose a model for street patrol by city inspectors. The number of inspectors deployed for patrol is allocated, and the patrol route is optimized. The objective is to minimize the average response time and the number of inspectors. Then, we propose a priority patrol and multi-objective genetic algorithm (DP-MOGA) to solve the optimization problem. The proposed algorithm increases the frequency and number of patrols in key areas with a high incidence of events. We improve the crossover operator and mutation operator of the genetic algorithm. An elite selection strategy is added to maintain population diversity and prevent premature convergence. Finally, a series of experiments are carried out using a case study in Zhengzhou, China. The goal is to minimize the overall average incident response time and the number of patrol personnel. The proposed algorithm is applied to real-life scenarios.

Three scenarios (S1, S2 and S3) are defined to analyze the model of this paper. Scenarios are classified according to the travel time and average number of events on the road segments. Through experimental analysis, we can draw some conclusions as follows:

• Algorithm evaluation through the calculation of variance values reveals that DP-MOGA has a stable performance in three scenarios.
• The algorithm DP-MOGA performs better than the algorithm MOGA and algorithm VLNS.
• In real life, the model proposed in this paper optimizes personnel allocation and the patrol routes of city inspectors. The model improves patrol efficiency for inspectors.

In addition, our model has a wide application to smart city management. Our future research studies will focus on aspects that have not been considered in this study: The algorithm can take into account many influencing factors, such as the duration of random events and other statistical characteristics of the road and the time changes in the frequency of city management incidents and dynamic changes in the patrol trajectory of patrol vehicles. We can design dynamic patrol routes based on time characteristics and the trajectory of patrol vehicles. In future studies, these factors will be considered to make the research problem more practical.