An Intelligent Decision-Making Approach for Multi-Ship Traffic Conflict Mitigation from the Perspective of Maritime Surveillance

Abstract

Potential multi-ship conflict situations in coastal or near-shore port areas have always been one of the important factors affecting ship navigation safety and a key target of maritime traffic regulatory authorities. In recent years, with the continuous development and integration of various emerging technologies in the maritime field, maritime traffic supervision has also shown a trend of intelligent and autonomous development. The traditional supervision method dominated by human experience is evolving towards data and model-driven practices. In order to solve the problem of ship navigation safety supervision under multi-ship conflict scenarios, it is urgent to build an intelligent conflict mitigation decision-making model. Therefore, this paper designs a novel risk mitigation decision-making model for multi-ship conflict scenarios from the perspective of maritime supervision. The model proposed in this paper first extracts high-density ship clusters based on AIS (Automatic Identification System) data and uses the MCD (Mean Core Density) and PRM (Proportion of Relative Motion) as feature indicators to further mine potential multi-ship conflict scenarios. Finally, a global optimization decision-making model is constructed to effectively mitigate conflict risks. Experimental verification shows that the intelligent decision-making model for the mitigation of maritime traffic conflict proposed in this paper can autonomously identify conflict scenarios and make reasonable decisions in real time. It can effectively ensure the navigation safety of ships in multi-ship conflict scenarios and further improve the supervision level of maritime departments.

1. Introduction

Maritime transport is one of the most important means of international trade, with its low cost, large capacity, environmental friendliness and low unit energy consumption [1]. The continuous development of maritime trade has also led to an increase in the density of ship traffic, which has brought severe challenges to the safety of ships at sea. Maritime traffic accidents have serious consequences, including casualties, property losses and environmental pollution [2]. Multi-ship conflicts are the most common dangerous situations in maritime traffic. If this situation is not handled properly, the possibility of maritime traffic accidents will increase. Therefore, in order to further ensure the safety of ships at sea, it is necessary to continuously enhance the situational awareness and decision-making response capabilities of maritime traffic situations [3].

Maritime traffic supervision is the foundation of maritime traffic operation and the guarantee of sustainable development [4]. The supervision center obtains ship information in the supervised sea area through shore-based radars, AIS base stations, etc. Based on the various types of information obtained, the maritime traffic supervision department can grasp the navigation dynamics of each ship in real time, provide a wide range of information service support to passing ships, and warn and record ships that violate maritime traffic rules. In recent years, with the continuous development and integration of various emerging technologies in the maritime field, such as deep learning, artificial intelligence, cloud computing, the Internet of Things (IoT), blockchain, etc., maritime traffic supervision has also shown a trend of intelligent and autonomous changes, and its management and control methods are undergoing technological updates. Conventional supervision methods dominated by human experience are evolving towards data-driven methods. Using AIS data to achieve situational awareness and decision-making on maritime traffic situations is one of the typical cases [5], but numerous collision risk estimation and control approaches and models have been put forth to mitigate risks and enhance the efficiency of maritime transportation [4]. For instance, AIS data supports the statistics of traffic characteristics in the regulated sea areas, the monitoring of abnormal ship behaviors, the prediction of ship trajectories, the detection of multi-ship conflict situations, the identification of navigation risk areas, etc. [6,7,8,9]. The ever-changing maritime traffic situation and the continuous innovation of information technology have put forward higher requirements for maritime traffic supervision. Maritime traffic supervision is becoming an important means of ensuring the safety of ship navigation under the new model of intelligent shipping [10,11].

At present, the complexity of maritime traffic is increasing. Especially in offshore and coastal port waters, the density of ships is increasing, interactions and negotiations between ships are becoming more frequent, and maritime traffic accidents occur from time to time. Unlike open waters and other waters with sparse traffic flow, the navigation environment in offshore and coastal port waters is complex. There are not only obstructions such as islands, shipwrecks, and reefs, but also the phenomenon of frequent intersections of various types of ships, which makes the maritime traffic situation very complicated [12,13]. At the same time, considering the characteristics of large inertia of ships and delayed response of rudder effect, the ships have poor maneuverability when sailing at sea. Sometimes, there may even be situations where ships alone are unable to resolve the current complex and dangerous maritime traffic situation, and at this time, the importance of maritime traffic supervision becomes more prominent. Not only that, in the new intelligent shipping industry of the future, the mixed traffic environment where intelligent ships and traditional ships coexist will become the “new normal” of maritime traffic [14]. This makes ships in the water present a mixed navigation mode of “manual driving, remote driving, and autonomous navigation”, forming a complex movement scene between ships, which also poses new challenges to the intelligent supervision of maritime traffic.

With the continuous improvement of shipping intelligence and ship autonomy, the maritime traffic environment has become more complex. The problem of how to effectively respond to and deal with multi-ship conflicts in offshore and coastal port waters has become an important challenge for maritime traffic supervision. Currently, for maritime traffic conflict situations, maritime operators still use conventional solutions and technical means, that is, they rely more on the operator’s experience and intuition to make risk-mitigation decisions. However, with the increasing complexity of maritime traffic situations, this traditional manual decision-making method will not only increase the workload of regulators, but also lead to decision-making errors or regulatory omissions caused by human factors. In addition, offshore and coastal port waters and other maritime regulatory areas also show the characteristics of ship clustering; that is, ships at sea are not completely disorderly and chaotically sailing in the given waters. Usually, due to the layout of navigation aids or water channels, the traffic flow in the regulatory waters shows a special clustering phenomenon, which makes the hotspots in the regulatory area more obvious, providing feasibility for risk mitigation and supervision of key conflict areas of maritime traffic from a global perspective.

Based on the above analysis and statements, this paper attempts to propose an intelligent decision-making approach for multi-ship traffic conflict mitigation from the perspective of maritime traffic supervision, so as to further meet the needs of maritime traffic supervision under the new intelligent shipping industry. The main contributions of this paper can be summarized as follows:

(1)

A novel intelligent decision-making approach framework for multi-ship conflict mitigation is proposed. The framework includes three parts: ship density cluster extraction in regulatory waters, multi-ship conflict situation identification, and the global optimization conflict mitigation decision-making method. The model can intelligently and in real-time discover multi-ship conflict scenarios and provide risk-mitigation strategies.

(2)

An innovative intelligent identification method for multi-ship conflict situations is constructed, which can accurately perceive potential maritime traffic conflicts in a timely manner.

(3)

A multi-ship conflict mitigation decision-making algorithm based on global optimization theory is designed, which can calculate the optimal solution for global risk mitigation from the perspective of maritime traffic supervision, thereby improving the efficiency of maritime traffic conflict mitigation.

The remaining parts of this paper are organized as follows. In Section 2, the literature is reviewed and analyzed, followed by model formulation in Section 3. The model verification and real case study are introduced in Section 4, and the analysis and discussion of the experimental results are also presented in this section. Section 5 concludes this study and provides an outlook on future research.

2. Literature Review

The intelligent decision-making method for multi-ship conflict mitigation from the perspective of maritime traffic supervision mainly involves the following three research areas. Therefore, the literature review of this paper will be discussed according to these three parts, respectively:

• Identification of ship conflict risk.
• Ship intelligent collision avoidance decision-making method.
• Intelligent supervision and decision-making support methods for maritime traffic.

In terms of ship conflict risk identification, at present, the most commonly used method is to calculate the relative motion parameters between ships and use the collision risk index to identify the conflict risk between ships [15]. The inter-ship index factor can intuitively reflect the temporal and spatial relationship between any given ship and a target ship. The two most typical index values are DCPA (Distance of the Closest Point of Approach) and TCPA (Time to the Closest Point of Approach). In addition, these parameters include the distance between ships, ship speed ratio, relative bearing, and changes in the compass bearing of the approaching ship, etc. The calculated results of each parameter are compared with the pre-set safety threshold or a parameter analytical formula is constructed to achieve the classification of ship conflict risk levels [16,17]. In addition to the method based on indicator factors, introducing geometric encounter boundaries to analyze the spatial characteristics of ship navigation waters is also a commonly used method for calculating ship conflict risks, the most typical representative of which is the ship domain [18]. The methods for determining safe encounter boundaries of ships can be divided into two categories. The first is to construct a mathematical model expression to convert the ship domain into an analytical geometry model, including ship domain construction based on quaternions and the dynamic domain construction considering the maneuverability of ships. The second is to determine the boundary range of the domain based on the historical AIS data of the ship’s navigation waters through statistical induction or machine learning. The above methods provide feasible solutions for the identification of ship conflict risks [19].

In terms of intelligent collision avoidance decision-making methods, in recent years, under the background of the development of MASS (Maritime Autonomous Surface Ship), ship collision avoidance decision-making has received continuous attention in the field of maritime research [20,21,22]. From the perspective of decision-making subjects and forms, it can currently be divided into two categories: proactive collision avoidance decision-making methods from the perspective of own ship and collaborative collision avoidance decision-making methods from a global perspective [23]. In the first category of methods, they can be further divided into quantitative analysis methods based on analytic geometry, methods based on physical models, artificial intelligence methods based on deep reinforcement learning, and methods that consider the interactive dynamic behavior of the target ship. In addition, with the improvement of communication levels between ship and shore, it becomes possible for ships to coordinate collision avoidance in the same encounter situation, thereby further improving collision avoidance efficiency [24]. The collaborative collision avoidance decision-making methods from a global perspective can be divided into two subcategories: distributed collaboration and centralized collaboration. The distributed collaborative collision-avoidance method allows multiple ships to calculate their own collision-avoidance strategies at the same time; that is, collaboration does not require centralized coordination, thus improving the robustness of the decision-making system [25,26]. Centralized collaborative collision avoidance means that the collision avoidance decisions of all ships will be centrally allocated from a global perspective. The centralized goal is to find the global optimal solution for the current encounter scenario.

In the areas of intelligent supervision of maritime traffic and decision-making support methods. At present, the supervision method for maritime ships mainly relies on VTS (Vessel Traffic Service), which integrates VHF, satellites, CCTV, meteorological sensors and AIS, providing a convenient supervision platform for maritime regulatory authorities [27,28]. At the same time, in order to improve the level and intelligence of supervision, a number of maritime supervision decision-making support methods based on mathematical models and intelligent algorithms have emerged in the maritime research field in recent years [29], including ship behavior anomaly detection algorithms, port area ship collision risk assessment methods, and maritime traffic model extraction. For example, a ship abnormal behavior detection algorithm combining K-nearest neighbor (KNN) and local outlier factor (LOF) is proposed to achieve fast and efficient ship abnormal behavior detection. An adaptive calibration near-miss risk model based on the AIS is proposed. By using a ship’s heading and speed, the near-miss risk of ships in the port area is assessed to help port management departments to plan and supervise [30,31]. The complex network theory was used to identify key dangerous ships in the regulatory area [32]. Maritime traffic supervision is a process from global waters to the discovery of local dangerous waters [33]. However, there is currently no feasible technical route for the supervision of multi-ship conflict situations, and research on multi-ship conflict mitigation methods from a regulatory perspective needs to be strengthened.

3. Methodology

3.1. The Overall Framework of the Proposed Approach

In response to the challenges faced by maritime traffic supervision under the new intelligent shipping industry, this paper proposes an intelligent risk mitigation decision-making method in the scenario of multi-ship conflict. The basic architecture of this method is shown in Figure 1.

Based on ship information in regulated waters obtained by the navigation aids sensors (mainly based on AIS data in this paper), the Multi-ship Traffic Conflict Mitigation Approach (MTCM) proposed in this paper mainly consists of three parts. Firstly, this paper clusters the density of ships in the regulated waters based on the improved OPTICS method, which can divide the density clusters of ships in the sea area more intelligently and accurately. Secondly, this paper constructs a novel scenario recognition model for potential multi-ship conflict, which further divides the previously obtained ship density clusters based on two indicators: the mean core density of the density clusters and the relative motion trend between ships. Finally, this paper proposes a risk mitigation optimization decision-making model based on NSGA-II, and ultimately generates feasible risk mitigation strategies for different multi-ship conflict scenarios in the regulated waters.

3.2. Ship Density Cluster Extraction Model

3.2.1. Ship Point Density Clustering Based on OPTICS

Ship density is a basic quantity that represents the actual situation of ship traffic in a certain water area. This paper uses a density clustering method to extract high navigation density areas in regulated waters. In terms of density clustering algorithms, the DBSCAN algorithm is one commonly used method. This algorithm is mainly based on the neighborhood radius eps and the threshold of the number of neighbors with core points Minpts. However, the maritime traffic supervision waters are not always static. The ship density will change with the ship’s navigation process, and eps and Minpts need to be set manually each time, which is obviously not in line with the actual situation. Therefore, this paper attempts to cluster ship density based on the OPTICS algorithm.

In contrast to the DBSCAN algorithm, OPTICS does not produce clusters of clustering results, but instead generates an augmented cluster ranking for cluster analysis. Under this sorting, each object contains two pieces of information: core distance and reachable distance. For ships in the regulated sea area at a certain moment, the ship point set ${\rm P}=\left\{p_1,p_2,\dots ,p_n\right\}$ can be obtained based on its position information. Assume that the neighborhood radius is $\lambda$, and the minimum number of ships in the neighborhood is $MinS$. Then for any ship $p_j$ belonging to the set $P$, its neighborhood can be expressed as:

$$N^{\lambda }\left(p_j\right)=\{p_i\in P:d(p_j,p_i)\le \epsilon \}$$

(1)

In Formula (1), $d(p_j,p_i)$ represents the distance between two ships in the ship point set $P$. The density $\rho \left(p_j\right)$ at ship $p_j$ can be represented by the number of ships $\left|N^{\lambda }\left(p_j\right)\right|$ in the neighborhood. When $\rho \left(p_j\right)\ge MinS$, the core distance $CD\left(p_j\right)$ at ship $p_j$ can be calculated as follows:

$$CD\left(p_j\right)=d(p_j,N_{MinS}^{\lambda }(p_j\left)\right)$$

(2)

In Formula (2), $N_{MinS}^{\lambda }\left(p_j\right)$ represents the ship that is the $MinS$ -th nearest neighbor of ship $p_j$ in the neighborhood set $N^{\lambda }\left(p_j\right)$. When $CD\left(p_j\right)\le \lambda$, the reachable distance $RD\left(p_j\right)$ of $p_j$ can be defined as shown in Formula (3). From the above explanation, it can be seen that ship $p_j$ has the core distance and reachable distance only when $p_j$ is a core ship ($\rho \left(p_j\right)\ge MinS$).

$$RD\left(p_j\right)=\mathit{max}\left\{CD\left(p_j\right),d(p_j,p_i)\right\}$$

(3)

According to the principle of the OPTICS algorithm, after sorting the reachable distance of the data set $P$, the threshold can be determined according to the distribution of the $RD$, and finally the ship density clustering can be realized. However, in order to realize intelligent and automatic traffic conflict mitigation, it is not reasonable for the maritime traffic supervision operator to manually determine the threshold of $RD$ in practice. Therefore, this paper introduces the concept of DoS (Degree of Steep) to realize the efficient division of ship density clusters.

3.2.2. Classification of Ship Clusters Based on DoS

OPTICS clustering can obtain a graph with the number of points as the horizontal axis and the reachable distance as the vertical axis. In this statistical graph, we find that the sample points contained in the peak and valley area of the value $RD$ have a high probability of forming a ship density cluster. Therefore, the Degree of Steep (DoS) parameter $\upsilon$ is introduced, and the upward slope point $UP\left(p_j\right)$ and downward slope point $DP\left(p_j\right)$ under $\upsilon$ can be defined as follows:

$$\begin{gathered} UP\left(p_j\right)\iff RD\left(p_j\right)\le RD\left(p_{j+1}\right)\times (1-\upsilon ) \\ DP\left(p_j\right)\iff RD\left(p_j\right)\times (1-\upsilon )\le RD\left(p_{j+1}\right) \end{gathered}$$

(4)

Based on the calculated $UP\left(p_j\right)$ and $DP\left(p_j\right)$, the upward and downward intervals of the slope can be defined respectively. Set the interval $U=[p_m,p_n]$, if $p_m$ and $p_n$ are both upward slope points, and the $RD$ of any point between $p_m$ and $p_n$ cannot be less than the previous point, and the interval cannot contain more than $MinS$ consecutive non-$\upsilon$ upward slope areas, then the interval $U$ can be regarded as an upward slope interval. Similarly, the downward slope interval $D$ can be defined.

Let any subinterval of the ship point set $P$ after being sorted by $RD$ be $Clus=[s,e]$. At the same time, there are two intervals with upward and downward slopes, $U_c=[s^u,e^u]$ and $D_c=[s^d,e^d]$ respectively. When the starting point of interval $Clus$ is located in interval $D_c$ and the end point is located in interval $U_c$, if both Condition1 and Condition2 are satisfied, then interval $Clus$ can be considered as a ship cluster. Condition1 and Condition2 are expressed by Equations (5) and (6), respectively. Among them, Condition2 represents the three conditions that the starting point and the end point in the ship cluster $Clus$ may satisfy.

$$Condition1\doteq \left\{\begin{array}{c}e-s\ge MinS\\ \forall p_j,s^d<p_j<e^u:(RD\left(p_j\right)\le \mathit{min}(RD\left(s^d\right),RD\left(e^u\right))\times (1-\upsilon \left)\right)\end{array}\right.$$

(5)

$$Condition2\doteq \left\{\begin{array}{c}(\mathit{max}\{p_j\in D|RD\left(p_j\right)>RD(e^u+1)\},e^u),ifRD\left(s^d\right)\times (1-\upsilon )\ge RD(e^u+1)\\ (s^d,\mathit{min}\{p_j\in U|RD\left(p_j\right)<RD\left(s^d\right)\left\}\right),ifr(e^u+1)\times (1-\upsilon )\ge RD\left(s^d\right)\\ (s_D,e_U),\mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right.$$

(6)

3.3. Potential Multi-Ship Conflict Situation Identification Model

According to the improved OPTICS density clustering model in the previous section, we can obtain the density division results of the ship data set in the regulated sea area at any time, i.e., several density clusters. However, these density clusters are not necessarily multi-ship conflict situations. Based on the experience of maritime traffic supervision in offshore or coastal port waters, in general, potential multi-ship conflict situations that require intervention or require sufficient attention from maritime supervision operators must meet at least the following two basic attributes:

• Ship density should be large enough.
• Typical relative motion situations are formed between ships.

In other words, if a typical relative motion situation between ships is formed in a higher density of ship clusters, this paper believes that a potential multi-ship conflict situation has been formed. Therefore, based on the above consideration, this section constructs a multi-ship conflict recognition model. The model is mainly based on two parameters, namely the Mean Core Density (MCD) and the Proportion of Relative Motion between ships (PRM).

For ship point set ${\rm P}=\left\{p_1,p_2,\dots ,p_n\right\}$, assuming that $h$ different ship density clusters are obtained after clustering by the improved OPTICS method, for any cluster $Clu{s}_i=[s^i,e^i]$, the MCD calculation formula of the ship point contained in this cluster is shown in Formula (7). According to the definition of MCD, it can be seen that it is a value calculated by the core distance between ships. Therefore, the value of MCD is inversely proportional to the ship density, that is, the smaller the MCD value, the greater the ship density.

$$MCD(Clu{s}_i)={\displaystyle \frac{{\sum }_{p_j=s^i}^{e^i}CD\left(p_j\right)}{e^i-s^i+1}}$$

(7)

PRM refers to the ratio of the number of ship pairs with relative motion trends in a high-density ship cluster to the total number of ship pairs. The relative motion trend of ships determines the potential ship conflict relationship. The ship motion trend is related to the course and speed of two ships and can be represented by the rate of change of the relative distance between ships over time. Assume that any two ships in the density cluster $Clu{s}_i$ are $p_a$ and $p_b$ respectively, let ${\overrightarrow{L}}_{ab}$ represent the relative distance between two ships, and ${\overrightarrow{v}}_{ab}={\overrightarrow{v}}_a-{\overrightarrow{v}}_b$ represent the relative speed, then the discriminant calculation formula for their relative motion trend is shown in Formula (8).

$$\psi ={\displaystyle \frac{d\left|{\overrightarrow{L}}_{ab}\right|}{dt}}={\displaystyle \frac{{\overrightarrow{L}}_{ab}·{\overrightarrow{v}}_{ab}}{\left|{\overrightarrow{L}}_{ab}\right|}}=\left|{\overrightarrow{v}}_{ab}\right|·\mathit{cos}({\overrightarrow{v}}_{ab},{\overrightarrow{L}}_{ab})$$

(8)

For the discrimination parameter $\psi$, when $\psi <0$, it means that the relative distance between $p_a$ and $p_b$ becomes smaller, and two ships are in a converging state; when $\psi \ge 0$, it means that the relative distance between $p_a$ and $p_b$ becomes larger or remains unchanged, and the two ships are in a separating state. The expression of these two relative motion states can be seen in Figure 2. Under the condition of high-density waters, this paper assumes that two ships are forming conflict when they are in a converging state. Therefore, for the ship set $P$, the total number of ships is $n$. If the number of ship pairs with relative motion trend (i.e., $\psi <0$, the converging state) is $\mu$, the parameter $PRM$ can be expressed as Formula (9). This formula means the proportion of ship pairs with relative motion to the total number of ship pairs.

$$PRM={\displaystyle \frac{\mu \times n!}{2\left(n-2\right)!}}\times 100\%$$

(9)

In summary, for each ship density cluster obtained by the improved OPTICS model, a potential multi-ship conflict scenario can be identified based on the MCD and PRM values. Assume that the set of ship clusters after OPTICS division is $CLUS=\left\{Clu{s}_1,Clu{s}_2,\dots ,Clu{s}_n\right\}$. This paper uses the Z-Score normalization method to normalize the characteristic index values of each density cluster $Clu{s}_i$. Among them, MCD is the reverse indicator of the multi-ship conflict area (the larger the indicator value, the lower the ship density), so its normalization formula is shown in Formula (10). Similarly, PRM is a positive indicator of the multi-ship conflict area, and its normalization formula is shown in Formula (11). Among them, $X_i$ represents the standardized result of each indicator value under cluster $Clu{s}_i$, $S_i$ is the characteristic value of the indicator, ${\mu }_i$ is the standard value corresponding to the characteristic value of the indicator, and ${\sigma }_i$ is the standard deviation.

$$X_i^{MCD}={\displaystyle \frac{{\mu }_i^{MCD}-S_i^{MCD}}{{\sigma }_i^{MCD}}}$$

(10)

$$X_i^{PRM}={\displaystyle \frac{S_i^{PRM}-{\mu }_i^{PRM}}{{\sigma }_i^{PRM}}}$$

(11)

The sum of the standardized results of each index value is the corresponding comprehensive evaluation value $K_{Clu{s}_i}$, as shown in Formula (12). Therefore, the value of $K_{Clu{s}_i}$ can be used to determine which are potential multi-ship conflict areas.

$$K_{Clu{s}_i}=X_i^{MCD}+X_i^{PRM}$$

(12)

3.4. Global Optimization Decision-Making Approach for Conflict Mitigation

After identifying a potential multi-ship traffic conflict situation, it is necessary to generate corresponding conflict risk mitigation strategies for each conflict situation. Different from the single-ship mitigation strategy, the mitigation strategy from the perspective of maritime traffic supervision should be aimed at the entire multi-ship conflict situation; that is, from a global perspective, with overall optimization as the goal, by assigning mitigation strategy instructions to each ship. Based on the above consideration, this paper calculates the risk mitigation strategy based on the NSGA-II multi-objective optimization algorithm. This method consists of four parts: decision space calculation and initialization stage, objective function design, iterative optimization stage and multi-ship collaborative decision determination stage.

3.4.1. Decision Space Calculation and Initialization

Maritime ships have special maneuvering characteristics such as large inertia and cannot be maneuvered as quickly and flexibly as other intelligent agents such as robots. Taking into account the general conflict mitigation strategies of ships and the needs of multi-objective optimization algorithms, this paper sets the ship conflict mitigation strategies decision space and defines this space as the decision steering angle range. By absorbing and summarizing the ideas of other literatures, this paper sets the initial decision space of each ship in the multi-ship conflict scenario from $-40°$ to $40°$. In addition, considering the rationality and effectiveness of the global traffic conflict risk mitigation strategy and the strategic acceptance of ships involved in the conflict, this paper also integrates COLREGS (International Regulations for Preventing Collisions at Sea) in the risk mitigation decision calculation process, mainly focusing on the encounter situation and conflict avoidance responsibility between each conflicting ship pair in Section 3.3. The specific division method can be referred to [1].

For the ship $p_j$ in a multi-ship potential conflict scenario, their decision space can be further limited according to the following three situations: (1) If the responsibility for turning is greater than the responsibility for direct sailing, the optional angle constraint is changed to $-40°$ to $0°$ or $0°$ to $40°$ according to the encounter situation and conflict avoidance responsibility. (2) If the responsibility for direct sailing is greater than the responsibility for turning, the ship is restricted to be more inclined to direct sailing, and the turning constraint is changed to $-20°$ to $20°$. (3) If this ship is not in any ship conflict pair, this ship does not take any turning operation.

At the same time, according to the parameter requirements of the NSGA-II algorithm, it is necessary to first generate an initial population, set the population size and the number of population iterations. This paper sets the population size $pop$ to 100, the number of iterations $gen$ to 200, the number of optimization targets to 2, and the number of variables to the number of ships in the environment. The initial population is generated by a random function, and the objective function fitness value and crowding distance of the initial population are calculated. Generate an initial population and record the current number of iterations as $gen=1$.

3.4.2. Objective Function Construction

In the decision-making process of multi-ship conflict mitigation, the selection of objective function is related to the quality of the mitigation strategy. This paper designs the objective function for the safety of risk mitigation in multi-ship conflict situations and the economy of ship maneuvering (minimizing unnecessary detours, etc.), and takes the decision space specified above as the optimization constraint. In terms of the safety and feasibility of the strategy, this paper draws on the idea of velocity obstacle zone. The closer the relative speed direction between two ships to the velocity obstacle zone, the more dangerous. The farther the relative speed direction from the velocity obstacle zone, the safer. Assume that the sum of the distances from the relative speed direction of all ships to other ships in the environment is taken as the objective function, and the calculation method is shown in Formula (13).

$Q_i$ represents the position vector of ship $i$, $Q_{i+1}$ represents a point in the relative speed direction after ship $i$ takes a new course, which is calculated by the speed and course of ship $i$ and ship $i+1$, $P$ represents the position vector of ship $i+1$, det in this formula represents the determinant of the calculation matrix, ${‖x‖}_2$ represents the L2 norm of vector $x$, that is, the modulus of vector $x$, from which the distance from the position of ship $i+1$ to the straight line generated by the relative speed direction of ship $i$ can be calculated, and $N$ is the total number of ships. Since the NSGA-II algorithm is set to optimize in the direction of minimization, the fitness function $f_1$ takes the opposite number, that is, optimizes in the direction of relative speed away from the velocity obstacle area.

$$f_1=-\sum _{i=1}^{N-1}{\displaystyle \frac{\left|\mathit{det}\left(Q_{i+1}-Q_i,P-Q_i\right)\right|}{{‖Q_{i+1}-Q_i‖}_2}}$$

(13)

In view of the economic efficiency of the risk mitigation strategy, that is, under the premise of ensuring that the risk of conflict situation is controllable and safe, each ship should take the smallest possible turning range to avoid unnecessary detours. Therefore, this paper uses the sum of the turning and yaw angles of all ships as the objective function $f_2$, and the calculation method is shown in Formula (14). Where ${\phi }_i$ represents the turning angle of ship $i$, and $N$ represents the total number of ships. The steering angle is set to be negative when turning left and positive when turning right. The formula calculates the yaw angle of all ships.

$$f_2=\sum _{i=1}^N\left|{\phi }_i\right|$$

(14)

3.4.3. Iterative Optimization Process

The cyclic iteration process is the main process of the NSGA-II algorithm. The parent population generates the child population through selection, crossover, and mutation operations. After the child population is merged with the parent population, a new generation of population is obtained based on the fast non-dominated sorting algorithm and crowding distance calculation. First, the tournament selection process is carried out to select $0.5N$ individuals from the parent population for the subsequent crossover and mutation operations. The selection process is to randomly select $M$ individuals from the parent population each time. The size of the tournament $M$ is set to 2 in this paper. According to the Pareto rank and the crowding distance of each individual, individuals with low Pareto rank or high crowding when the rank is the same are selected to enter the next generation population. The above steps are repeated many times until the new population size reaches $0.5N$, that is, the new generation initial population is generated.

After that, the new generation of initial population obtained through tournament selection is subjected to crossover and mutation operations to obtain the offspring population. Here, the ratio of crossover to mutation is 9:1, that is, there is a 90% probability of performing crossover operations and a 10% probability of performing mutation operations. Since the variable steering angles are all real numbers, SBX is used to simulate binary coding crossover, and the crossover allocation index $\omega$ is set to 20. The calculation method is shown in Formula (15).

$$\begin{gathered} x_{1j}\left(t\right)=0.5\times \left[\left(1+{\gamma }_j\right)x_{1j}\left(t\right)+\left(1-{\gamma }_j\right)x_{2j}\left(t\right)\right] \\ {x}_{2j}\left(t\right)=0.5\times \left[\left(1-{\gamma }_j\right)x_{1j}\left(t\right)+\left(1+{\gamma }_j\right)x_{2j}\left(t\right)\right] \end{gathered}$$

(15)

where ${\gamma }_j$ is calculated from the random number ${\alpha }_j$ and the crossover distribution index $\omega$, as shown in Formula (16). The mutation operation uses the polynomial mutation method, which is calculated from the random number ${\alpha }_j$ and the mutation distribution index $\eta$, as shown in Formula (17). After the crossover and mutation operations, the offspring population can be obtained, and the corresponding fitness value can be calculated according to the objective function.

The parent population is then merged with the offspring population generated after selection, crossover, and mutation operations, and the new population is subjected to a fast non-dominated sorting operation. In a multi-objective minimization optimization problem, if there is a decision variable that no other decision variable can dominate, then the decision variable is called a non-dominated solution. In a set of solutions, the Pareto rank of a non-dominated solution is defined as 1. After deleting the non-dominated solution from the solution set, the Pareto rank of the remaining non-dominated solution is 2. Similarly, the Pareto rank of all solutions in the solution set can be obtained. This process is called fast non-dominated sorting.

$${\gamma }_j=\left\{\begin{array}{c}{\left(2\times {\alpha }_j\right)}^{{\displaystyle \frac{1}{\left(\omega +1\right)}}}{\alpha }_j<0.5\\ {\left({\displaystyle \frac{1}{\left(2\times \left(1-{\alpha }_j\right)\right)}}\right)}^{{\displaystyle \frac{1}{\left(\omega +1\right)}}}else\end{array}\right.$$

(16)

$$\begin{array}{c}{x}_{1j}\left(t\right)=x_{1j}\left(t\right)+{\Delta }_j\\ {\Delta }_j=\left\{\begin{array}{c}{\left(2\times {\alpha }_j\right)}^{{\displaystyle \frac{1}{\eta +1}}}-1{\alpha }_j<0.5\\ 1-{\left(2\times \left(1-{\alpha }_j\right)\right)}^{{\displaystyle \frac{1}{\eta +1}}}else\end{array}\right.\end{array}$$

(17)

In order to maintain the diversity of the solution set, the NSGA-II algorithm introduces the concept of crowding. After fast non-dominated sorting, the crowding of the two boundary individuals in the current sorting is set to be infinite, that is, $o_d=I_d=\infty$. Let $f_j^{max}$ be the maximum value of the individual objective function $f_j$, $f_j^{min}$ be the minimum value of the individual objective function $f_j$, $m$ represents the number of objective functions, $i_d$ represents the congestion degree of point $i$, $f_j^{i+1}$ represents the function value of the $j$-th target at point $i+1$, $f_j^{i-1}$ represents the function value of the $j$-th target at point $i-1$, and calculation method of the congestion degree $i_d$ is as shown in Formula (18). The congestion degree value is calculated by adding the congestion degree distance of each target, and the congestion degree of each target will be normalized.

$$i_d=\sum _{j=1}^m{\displaystyle \frac{\left|f_j^{i+1}-f_j^{i-1}\right|}{\left(f_j^{max}-f_j^{min}\right)}}$$

(18)

Finally, the population selects suitable individuals to enter the next generation population $R_i$ through the elite retention strategy. Then, sort the Pareto levels from high to low, and put the whole layer of population $C_i$ into the next generation of population $R_i$. When $R_i<N$ and $R_i+C_{i+1}>N$, sort the individuals in the $i+1$-th layer from large to small according to the crowding degree, and put the individuals with larger crowding degree into the next generation of population $R_i$, so as to increase the diversity of the solution set to a greater extent, until $R_i=pop$ fills the population. Then check whether the number of iterations $Gen$ reaches the threshold. If it does not reach the threshold, continue the loop iteration operation. If it reaches the threshold, the final non-dominated sorting solution set is obtained.

3.4.4. Determination of the Collaborative Decisions

After iterative optimization and solving through the improved NSGA-II algorithm, the final non-inferior solution set will be obtained, and the solutions in this set are evenly distributed on the Pareto frontier. However, some solutions in the Pareto-optimal solution set obtained by the multi-objective optimization algorithm will be biased towards a certain goal, and it is necessary to find a suitable optimal solution based on the actual problem to be solved.

In the multi-ship conflict mitigation problem, some solutions in the Pareto optimal solution set will make the objective function infinitely close to 0, that is, the ship avoidance angle is close to 0. In terms of optimization, it is too inclined to navigation economy and ignores navigation safety, and it is impossible to achieve safe avoidance. Therefore, when determining the decision of multi-ship collaborative conflict mitigation, it is necessary to draw on the knowledge of the ship domain to ensure navigation safety, that is, the relative speed direction of the ship must not fall within the scope of the ship domain. If the relative speed direction relative to another ship in the environment is within the ship domain, the navigation angle cannot guarantee navigation safety. The ship domain used in this paper is a modified version from Goodwin, as listed in Formula (19). Among them, $d_s$ represents the safe passing distance between ships, $B$ is the true bearing of the target ship relative to own ship. Therefore, when determining the final decision, the solution set is first sorted according to the conflict avoidance angle, and then the unsafe solutions are filtered out according to whether the relative speed direction of the ship falls within the ship domain. Finally, the solution with the smallest avoidance angle under the premise of ensuring navigation safety is selected as the multi-ship collaborative conflict mitigation strategies.

$$d_s=\left\{\begin{array}{c}\begin{array}{cc}1.1-{\displaystyle \frac{B}{\pi }}\times 0.2& 0\le B<{\displaystyle \frac{5\pi }{8}}\end{array}\\ \begin{array}{c}\begin{array}{cc}1.0-{\displaystyle \frac{B}{\pi }}\times 0.4& {\displaystyle \frac{5\pi }{8}}\le B<\pi \end{array}\\ \begin{array}{c}\begin{array}{cc}1.0-{\displaystyle \frac{2\pi -B}{\pi }}\times 0.2& \pi \le B<{\displaystyle \frac{11\pi }{8}}\end{array}\\ \begin{array}{cc}1.1-{\displaystyle \frac{B}{\pi }}\times 0.2& {\displaystyle \frac{11\pi }{8}}\le B<2\pi \end{array}\end{array}\end{array}\end{array}\right.$$

(19)

4. Applications and Case Study Results

4.1. Extraction of Potential Multi-Hip Conflict Areas

In order to verify the MTCM model proposed in this paper, this paper conducted tests based on AIS data in the southeastern coastal area of China. The location description of this area and the AIS data in this area are shown in Figure 3a and the trajectories of all ships in this area within a period of one month are shown in Figure 3b. The specific area selected in this paper is located off the coast of Ningbo Port, China. It belongs to the offshore area outside the port and is one of the important regulatory areas of the maritime authorities. There are multiple dense traffic flows in this area, including inbound and outbound routes and the busiest north-south routes on the southeast coast. In addition to ships on the main routes, there are also other ships in this water, such as irregularly sailing fishing vessels. Such a complex maritime traffic environment often leads to typical multi-ship conflict situations, which brings many challenges to maritime traffic supervision.

This paper selected AIS data of some areas in this water at a certain moment (including 42 ships in total) to verify the model proposed in this paper. According to the MTCM processing flow, we set the $MinS$ equal to 4, and the slope threshold equal to 5%. The ship density clustering result after OPTICS processing is shown in Figure 4a. The ships are divided into 4 clusters and marked with different colors (pink-0, green-1, blue-2, and orange-3). The remaining ships that are not classified into any category (such as gray points in the figure) are regarded as noise points. Among these four categories, the densest cluster (i.e., the one with the largest average core density) according to the definition of the OPTICS algorithm is “Orange-3”, as shown in Figure 4b. During the clustering process, the statistical results of the reachable distance calculation of different ship points are shown in Figure 5. It is necessary to explain here that the reachable distance in Figure 5 is an indicator of the distance between ships calculated based on multiple ship coordinates. This indicator is only used to reflect the distance relationship between ships and does not have a practical distance unit.

After achieving density clustering in the selected waters, it is necessary to calculate the two index values of MCD and PRM respectively to further identify the potential multi-ship conflict area. Therefore, for the four clusters obtained by clustering with the improved OPTICS algorithm, the MCD, PRM, standardized value and Comprehensive Evaluation Value (CEV) of each cluster can be seen in

Table 1. Calculation results of indicator values for various clusters.

ID	0	1	2	3
MCD	0.0206	0.0280	0.0362	0.0364
PRM	0.3	0.5	0.6	0.5
MCD (norm)	1.4809	0.3530	−0.9010	−0.9329
PRM (norm)	−1.5686	0.1766	1.2154	0.1766
CEV	−0.0877	0.5296	0.3144	−0.7563

. In this paper, clusters with a comprehensive evaluation value exceeding 0.3 are identified as potential multi-ship conflict areas, namely, two clusters numbered 1 and 2. Therefore, the identification results of potential multi-ship conflict areas in the current maritime traffic environment (a total of 42 ships) are shown in Figure 6. Among them, cluster 1 contains a total of 4 ships, and cluster 2 contains a total of 7 ships, which are referred to by ID-1 and ID-2 respectively.

4.2. The Strategies and Results for Multi-Ship Conflict Mitigation

According to the two current potential multi-ship conflict situations ID-1 and ID-2 extracted in the previous section, based on the multi-objective optimization algorithm designed in this paper, this section attempts to provide risk mitigation strategies for the two conflict situations and verify the rationality of the algorithm in a simulation environment. According to the AIS data, the information of each ship in the two conflict situations can be obtained, as shown in

Table 2. Ship information of Cluster ID-1.

No.	Latitude	Longitude	Course (Degree)	Speed (kn)	Coordinate
1	29.6863	122.6267	205	8.5	(10.8, 10)
2	29.6629	122.6134	95.3	10.3	(10, 8.4)
3	29.6713	122.6139	287.7	11.8	(10, 9)
4	29.6445	122.5867	300	9	(8.4, 7.1)

and

Table 3. Ship information of Cluster ID-2.

No.	Latitude	Longitude	Course (Degree)	Speed (kn)	Coordinate
1	29.58348	122.59542	213.3	8.6	(8.9, 12.9)
2	29.5689	122.5960	208.9	12.3	(8.9, 11.9)
3	29.5475	122.5906	211.0	9.1	(8.6, 10.4)
4	29.5548	122.6227	27.2	9.3	(10.6, 10.9)
5	29.5273	122.6155	31.5	13.7	(10.1, 9.0)
6	29.5063	122.5842	26.8	8.3	(8.3, 7.6)
7	29.4703	122.5888	29.5	7.4	(8.5, 5.1)

respectively. It should be noted that the ship position coordinates in the AIS data are expressed in longitude and latitude, while the mitigation decision made in the model is based on a Cartesian coordinate system with nautical miles as the unit. Therefore, this paper first converts the longitude and latitude coordinates into Mercator coordinates respectively, and then converts them into nautical miles and calculates the relative coordinates in the Cartesian coordinate system.

According to the MTCM model, the conflict mitigation strategy set for scenarios ID-1 and ID-2 can be obtained, as shown in Formula (20). The strategy set corresponds to the order of the ships in Table 2 and Table 3.

$$\begin{gathered} De{c}_{ID-1}:\left\{\mathrm{0,32,24,11}\right\} \\ De{c}_{ID-2}:\left\{-\mathrm{2,12,3},-\mathrm{17,23,5},-1\right\} \end{gathered}$$

(20)

According to the mitigation strategy of each multi-ship conflict scenario, this paper verifies the effectiveness and rationality of the strategy in a simulation environment. In the specific simulation process, this paper sets the starting position of each ship at the position coordinates in Table 2 and Table 3, which are 600 s forward, and the end position is set at the position coordinates 3000 s backward. After all ships reach the position coordinates, the mitigation strategy set in Formula (20) is triggered.

For conflict scenario ID-1, the conflict mitigation process is shown in Figure 7, and 6 moments are selected in chronological order. During the risk mitigation process, the relative distance change record between the ships is shown in Figure 8. According to the relative distance change, it can be seen that the conflict mitigation strategy can effectively ensure that each ship safely passes through the conflict risk area. Similarly, for conflict scenario ID-2, the conflict mitigation process and results can be seen in Figure 9, and the relative distance change record between ships can be referred to Figure 10. There are 7 ships in scene ID-2, which can be roughly divided into left and right sides according to their location distribution, that is, three ships sailing downward and four ships sailing upward. However, due to the excessive density of ships at different speeds, there are obvious ship navigation conflicts in this area. The conflict mitigation strategies generated by the model in this paper can effectively handle the ship navigation conflicts in this situation and ensure that each ship passes safely.

The MTCM model proposed in this paper is verified based on these two cases. According to the calculation process, it can be seen that the model can intelligently extract dangerous conflict situations in the environment and give corresponding risk mitigation strategies. However, it should be noted that the model proposed in this paper and its verification link still have limitations. First, this paper is to mitigate the risk of multi-ship conflict situations at sea from the perspective of maritime traffic surveillance. For maritime surveillance, there are several channels for obtaining information on ships in the waters, including but not limited to AIS, shore-based radar, infrared thermal imager, satellite, etc., and the coordinated identification of various targets in the waters is achieved by integrating multiple sensing devices. For example, for ships that are not equipped with or normally turned on AIS, target information can be obtained through shore-based radar. In this paper, we mainly obtain ship information in the supervised waters based on AIS data. The main purpose is to explain the calculation process of the model and verify its effectiveness. In the actual application of the model, a variety of different methods can be used to obtain ship information. Second, the MTCM proposed in this paper does not further consider other key parameters such as the type and size of the ship and the characteristics of the water environment. In the calculation process of the conflict resolution strategy, we set the safe passing distance of all ships to the same range, but in fact the range should vary according to the type of ship, motion state, ship maneuverability and ship size, which requires further optimization of the MTCM model in the future. In addition, the environmental characteristics of the regulated waters should also be factors that the MTCM model needs to carefully consider. The characteristics and density of traffic flow in the waters will also determine whether the resolution strategy is appropriate. Considering the limitations of the research work in this article, these factors will be further studied in the future.

It should be noted that, compared with other ship-to-ship conflict risk mitigation methods, the MTCM model proposed in this paper does not calculate the mitigation strategy that best suits individual interests based on the ship itself, but proposes a risk mitigation strategy for global optimization from the perspective of maritime traffic surveillance. When the MTCM model determines that there is a potential multi-ship conflict area in the current waters, it can give a globally optimal risk mitigation set based on the motion state and parameters of the ships in the waters, and issue instructions to each ship through supervision and scheduling. The MTCM model designed based on this idea can achieve the result of global mitigation in one decision, greatly improving the efficiency of ship-to-ship conflict mitigation. At the same time, this mitigation mode under supervision also provides a new idea for the problem of traffic mitigation in future waters mixed with intelligent ships.

5. Conclusions and Future Research

Maritime multi-ship conflict is one of the important factors affecting the safety of ship navigation. In particular, with the continuous improvement of the intelligence level of ships in recent years, the current maritime navigation scene is in the transition stage towards a fully autonomous level. During this transition stage, the maritime navigation scene will be in a situation where multiple ships with different intelligence or autonomy levels coexist for a long time, which will derive new navigation risks. Maritime multi-ship traffic conflict areas often occur near the coast or coastal ports, such as areas where commercial and fishing ships densely converge, intersections of major shipping routes, and waterways in and out of ports. Due to the dense ship traffic and geographical restrictions in these waters, it is more difficult for a ship to make navigation decisions alone. In addition, more complex navigation decisions may occur due to uncoordinated decisions between ships, especially for special mixed navigation scenarios. This poses greater challenges to the navigation decision-making task under multi-ship conflict situations.

In general, for ship navigation in offshore or coastal port areas, local maritime regulatory departments are often responsible for control and guidance to ensure the safety of ship navigation in key waters. At the same time, the role of ship-shore information exchange in ensuring ship navigation safety is becoming increasingly prominent. Rich shore-based support information will enable ships to obtain more comprehensive navigation information, thereby making ship navigation decisions more reasonable and effective. Especially for intelligent ships, shore-based information will play a greater role in the navigation decision-making process. Besides, for special navigation waters mixed with intelligent ships, this puts forward new requirements for the maritime regulatory capabilities of the maritime department. The information service content, monitoring means and methods of maritime supervision should also be upgraded with the level of ship intelligence. Therefore, for the maritime multi-ship conflict area, especially the navigation scenarios mixed with intelligent ships, risk mitigation decision-making for complex conflict scenarios from maritime surveillance perspective will help improve ship navigation efficiency and strongly ensure the safety of maritime navigation.

Therefore, the Multi-ship Traffic Conflict Mitigation Approach (MTCM) was proposed in this paper. This model can autonomously perceive potential multi-ship conflict areas at sea and generate globally optimal conflict mitigation strategies in real time, thereby achieving intelligent mitigation of maritime traffic conflict scenarios. This model explores high-density ship navigation areas and constructs potential conflict identification indicators between ships. It uses global deviation costs and navigation safety as constraints to assign conflict mitigation scheduling instructions to each ship in the conflict scenario, thereby achieving efficient conflict mitigation that meets the global optimization. This model can further improve the ability of maritime regulatory authorities to deal with complex multi-ship conflict scenarios and reduce problems such as untimely supervision due to operator errors. At the same time, it can effectively enhance the shore-based information support capabilities of maritime regulatory authorities and provide strong support for the safety supervision of future intelligent shipping.

In addition, maritime traffic conflict areas and their mitigation strategies should further meet actual maritime supervision needs. In the next step of research, the model parameters should be adaptively adjusted according to the specific characteristics of the regulated waters, and a more comprehensive consideration should be given in the global decision-making optimization process, including additional cost functions such as the behavioral characteristics of ships, so that the mitigation strategy can better meet the actual regulatory scenarios. Besides, there are also special navigation rules in certain regulated waters, and the model can be further optimized in a targeted manner based on these rules, so as to continuously improve the maritime supervision capabilities of multi-ship conflict scenarios and intelligent ships.