| Citation: | LIN Wan-ni, WANG Nuo, GAO Zhong-yin, WU Di. Associated searching and rescuing optimization of salvage vessels and helicopters in remote sea area[J]. Journal of Traffic and Transportation Engineering, 2021, 21(2): 187-199. doi: 10.19818/j.cnki.1671-1637.2021.02.016
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China has vast sea areas and frequent maritime transportation. Due to the impact of natural disasters such as typhoons and tsunamis, maritime accidents occur from time to time. According to incomplete statistics from the International Maritime Organization, there have been a total of 375 maritime accidents in the waters surrounding China since the 21st century, including 197 "particularly serious" maritime accidents and 131 "major" maritime accidents. With the gradual expansion of the current marine economy and development activities to offshore areas, improving the emergency response capability for maritime search and rescue in remote sea areas has become an urgent need in the implementation of the strategy of building a maritime power. For maritime accidents that occur in remote waters far from the mainland, and due to uncertain search and rescue targets and large search areas, search and rescue work is often difficult. Due to the strong timeliness of maritime rescue, the golden rescue time is fleeting. If only ships are used for search and rescue, the efficiency is too low. Combining rescue helicopters for sea air joint search and rescue should be the best way[1-3]For dangerous situations that occur in remote sea areas, it is often necessary to transport rescue helicopters through rescue ships for a certain distance, and then take off from the apron on the deck to the accident site to carry out search and rescue of the distressed target. Therefore, in the context of limited survival time of the distressed personnel and complex and changing marine environment, scientifically formulating a joint sea air search and rescue plan is of great significance for improving the efficiency of maritime accident search and rescue.
In theory, sea air joint search and rescue operations belong to multi-objective optimization problems. In the fields of transportation, emergency logistics, etc., scholars at home and abroad have conducted extensive research on multi-objective transportation optimization problems: Gai Wenmei et al[4]Establish a multi-objective model for the selection of emergency material vehicle transportation routes, and solve the model based on heuristic algorithms; Zhang Lei and others[5]On the premise of ensuring the shortest time limit for emergency rescue, with the optimization goal of maximizing emergency rescue efficiency and minimizing material consumption, a multi-objective assignment model for emergency rescue with the shortest time limit is constructed; Wang Haijun and others[6]A dual objective stochastic programming model was established to solve the location path problem for emergency material distribution using heuristic algorithms; Akbari et al[7]A multi-objective model was established to optimize the allocation of rescue vessels at sea, taking into account factors such as rescue time, fleet operating costs, and the mismatch between vessel workload and operational capabilities. Although the above achievements all involve multi-objective transportation problems in emergency rescue, they only consider one mode of transportation and assume that the driving speed remains constant, which is not suitable for solving the problem in this article.
There are also some achievements related to sea air joint search and rescue that can be used for reference, such as Sun Shibin[8]Analyzed the current situation of China's maritime life rescue and the characteristics of rescue forces, and combined with typical rescue cases, discussed the application of ship engine three-dimensional coordination technology in maritime life rescue; Xie Licheng and others[9]Propose that shipborne rescue helicopters will become a new form of sea air three-dimensional search and rescue; Du Yonghao and others[10]Establish a multi platform maritime joint search path optimization model based on ships, helicopters, and satellites, and conduct search path optimization simulations of different scales; Wang Shuxiao and others[11]A mathematical model was established for the joint maneuvering of rescue helicopters and ships in conducting sea searches under the joint operation of surface vessels. Although the above results consider the transportation mode of sea air joint, they are mostly qualitative analysis or limited to solving single objective optimization problems with the shortest rescue time, without considering the complex coupling relationship between search and rescue time and discovery probability.
There have been attempts to apply Geographic Information Systems (GIS) to the field of maritime emergencies: Jiao Junchao et al[12-13]Predicting the trajectory and diffusion area of oil spills at sea; Su Jingzhi and others[14-15]Simulate the drift trajectory of offshore buoys; Li Xia and others[16]Combining intelligent algorithms for spatial decision optimization. From this, it can be seen that GIS has conducted in-depth research on trajectory prediction in maritime emergencies, but there is still relatively little research on optimizing emergency search and rescue plans.
Although there have been research results on sea air joint search and rescue and GIS, there is still a lack of research on optimizing sea air joint search and rescue for drifting distress targets, and it is even rarer to develop search and rescue optimization plans considering dynamic changes in spatial information. Affected by wind and waves, distressed ships may stall, and the speed of rescue ships is constantly changing. GIS can simulate the changes in ship speed under the influence of wind and waves, but it is rarely combined with optimization calculations. This article combines GIS and intelligent algorithms to fully leverage their advantages and establish an emergency search and rescue decision optimization method for maritime drifting distress targets. The optimization content includes the route of rescue ships, the time to release rescue helicopters, and the search plan of rescue helicopters. The objectives are to minimize search and rescue time and maximize discovery probability, and a sea air joint search and rescue dual objective optimization model is established; Introducing dynamic weights to control the velocity and position of particles, and improving the traditional particle swarm algorithm by using adaptive chaotic search instead of random search; Taking the search and rescue mission in the remote waters of the South China Sea as an example for analysis, corresponding optimization results were obtained, which verified the feasibility and rationality of the proposed model and algorithm in this study.
Maritime rescue is an emergency event. When receiving information of a ship in distress at sea, the maritime search and rescue center at the scene of the incident will formulate a search and rescue plan and deploy search and rescue forces in the shortest possible time. Usually, there are two types of emergency transportation available: rescue ships and rescue helicopters. Rescue ships are the main unit of maritime search and rescue, with the characteristics of long endurance, large passenger capacity, and complete facilities. They can provide operating platforms for diving and rescue helicopters, and also undertake the task of guiding aerial rescue helicopters. However, the disadvantage is slow speed, especially when maritime accidents occur in remote waters, the search efficiency of rescue ships is relatively low. Rescue helicopters have the characteristics of fast flight speed, wide search field of view, and large search and rescue range, which is conducive to quickly discovering maritime targets for rescue. However, the disadvantage is that the endurance time is short. For example, the maximum range of the S-76A search and rescue helicopter is 1092 km, and the idle time is only 3-4 hours. Therefore, for remote sea search and rescue operations, rescue ships usually need to be used as loading platforms for rescue helicopters. After being transported to a certain distance, they are released to fly to the sea area to be searched for rescue. Through the coordination and cooperation of the two, the overall effect can be maximized.
In the process of joint sea air search and rescue of drifting and distressed targets at sea, it is necessary to consider the changes in ship speed under the influence of wind and waves, as well as determine the takeoff time and search plan of the rescue helicopter, in order to achieve the discovery of the searched target with a higher probability in a shorter time. Due to the limited survival time of the distressed individuals, it is crucial to quickly decide when to release the rescue helicopter from the rescue vessel for the search and rescue operation. Although the earlier the release of the rescue helicopter, the earlier it can arrive at the accident area and carry out rescue operations. However, due to the distance between the takeoff point of the rescue helicopter and the search and rescue area, the flight time on the way is longer, leaving less time for the rescue helicopter to arrive at the accident area and carry out search operations, which affects the success rate of the search. If the release time of the rescue helicopter is too late, it will cause the rescue ship carrying the rescue helicopter to sail at sea for a long time. As the speed of the ship is much slower than that of the aircraft, it will prolong the time to rescue the accident area and may miss the golden time for maritime rescue. However, a late release time means that the time available for the rescue helicopter to search is longer, and the search area can be searched more carefully, thereby improving the success rate of search and rescue. Therefore, in the case of limited survival time of the distressed personnel and complex and changing marine environment, considering the dynamic changes of spatial information, real-time prediction of the sea conditions in the accident area can be made to judge the movement trajectory of the distressed ship, adjust the direction of the rescue ship's travel, and assist modern optimization algorithms in determining the route of the rescue ship, The basic problem to be solved in this article is to optimize the timing of releasing rescue helicopters from rescue ships and the search and rescue plan.
GIS refers to a spatial information system that acquires, stores, edits, processes, analyzes, and displays geographic data, and is widely used for processing and analyzing geographic information. After losing power, the ship drifts due to the influence of offshore wind and waves, and the offshore wind and waves change frequently. GIS can be used to determine the drift direction and speed of the distressed ship in real time based on the offshore wind and wave conditions, providing guidance for the direction of rescue ships' travel[17]The relationship between the relative position changes of rescue ships and distressed ships is as follows:Fig. 1As shown:AThe point is the location where the rescue vessel received the information of the accident;BPoint is the location of the shipwreck;tFor time, ∈ {0, 1, 2, …, n}，tTake 0 as the moment when the rescue vessel receives the distress message,tTake 1 as the time half an hour after the rescue vessel receives the distress message,tTake 2 as the time 1 hour after the rescue vessel receives the distress message,ttakenThe time when the rescue vessel arrives at the distressed vessel. By inputting real-time wind data detected at sea into the GIS system, the drift direction and speed of the distressed vessel can be predicted, and the information can be transmitted to the rescue vessel to help determine the next navigation direction of the rescue vessel, thereby reducing the area to be searched.
This article uses ArcGIS embeddable toolbox Waves 2012 to simulate wind fields and wave heights at sea[18]Including two simulation models of wind zone and waves. By inputting the land/ocean grid, wind direction, and other data of the research area into the wind zone model, the simulation results of the wind zone are obtained. By inputting the simulation results of the wind zone and the seabed topography, wind speed, and other data of the study area into the wave model, the effective wave height, average wave direction, average wave period, and other data can be further calculated.
Regarding the issue of ship speed being affected by wind and waves, He Huiming et al[19-21]Through regression analysis of the model test results of multiple transport ships, an approximate estimation formula was proposed, which can effectively estimate the speed changes of ships in waves, and the obtained results are basically consistent with the model test results. The calculation expression is
| Δvsvs=12(E/W)δQH21/3[0.45(Z/100)2+0.35(Z/100)]Z | (1) |
| δ={−0.05H1/3+0.9Z⩽ |
In the formula: ΔvsChanges in the speed of rescue vessels;vsDesign speed for rescue vessels;ZThe length between the two columns of the ship;EThe width of the rescue vessel;WDraft for ships;QThe characteristic period of waves;δTo adjust the coefficient;H1/3Effective wave height for waves.
Based on the above, the formula for calculating the speed of rescue ships under the influence of wind and waves can be obtained as follows:
| \begin{aligned} v^{\prime}_{\mathrm{s}}=&\left(1-\frac{\Delta v_{\mathrm{s}}}{v_{\mathrm{s}}}\right) v_{\mathrm{s}}=\left\{1-12(E / W) \delta Q H_{1 / 3}^{2} \cdot\right.\\ &\left.\left[\left(0.45(Z / 100)^{2}+0.35(Z / 100)\right) Z\right]^{-1}\right\} v_{\mathrm{s}} \end{aligned} | (2) |
In the formula:v′sThe actual speed of rescue ships under the influence of wind and waves.
When losing power on the sea surface, Li Jinduo and others[22-24]By observing the drift trajectory and wind and sea conditions of the distressed vessel, analyzing and verifying its drift characteristics, it is found that the direction of free drift of the distressed vessel in a wide sea area is controlled by the wind direction, and the drift speed is roughly equivalent to the surface flow velocity, which is about 10% of the wind speed, that is, the wind conductivity coefficient is 0.1. The speed of the distressed vessel under the influence of wind and waves is
| v_{\mathrm{b}}=\lambda v_{\mathrm{w}} | (3) |
In the formula:λWind conductivity coefficient;vwWind speed at the location of the distressed vessel;vbThe speed of ships in distress under the influence of wind and waves.
According to the relevant regulations of China's search and rescue, when it is difficult to accurately determine the location of the distressed vessel and the target is in a wide area, an extended square path is usually used for search. That is, after the rescue helicopter arrives at the search base point, it expands outward from the base point into a square path for search, turning 90 degrees each time. The search path interval isd, such asFig. 2As shown.
When ships and rescue helicopters jointly conduct search and rescue operations, fully utilizing the search and rescue efficiency of rescue helicopters is a key issue. Li Weili[25]The ratio of the effective scanning area of the rescue helicopter to the area of the completed search area is defined as the coverage ratio. When all flight paths are parallel to each other and spaced equally, the coverage ratio is the ratio of the sweeping width of the rescue helicopter to the spacing between the air search flight paths. The relative relationship between the two is shown inFig. 3The expression for calculating coverage ratio is
| \xi=\frac{S^{\prime}}{S}=\frac{g}{d} | (4) |
In the formula:ξFor coverage ratio;SThe area for which the search has been completed;S'is the effective scanning area;gTo sweep the width of the sea.
For rescue helicopters, with a fixed sweeping width, the size of the search route interval directly affects the coverage ratio. The larger the route interval, the smaller the coverage ratio; On the contrary, the smaller the interval between flight routes, the larger the coverage ratio. Therefore, optimizing the interval between search routes for rescue helicopters is the core when formulating search plans. Generally speaking, the larger the coverage ratio, the higher the probability of detection, but the longer the distance flown by rescue helicopters, the more time-consuming it will be; The smaller the coverage ratio, the lower the probability of discovery, but the shorter the flight distance and the less time it takes. The functional relationship between coverage ratio and discovery probability is[26]
| P=1-\mathrm{e}^{-\xi} | (5) |
In the formula:PTo discover probability.
The curve of the relationship between probability and coverage ratio is as follows:Fig. 4As shown, with the increase of coverage ratio, the probability of discovering search and rescue targets increases; But as the coverage ratio continues to increase, the probability of discovering search and rescue targets no longer significantly increases. From this, it can be seen that the probability of discovery and the coverage ratio are mutually constrained, and the search and rescue plan needs to be determined through repeated optimization.
The process of joint sea air search and rescue is as followsFig. 5As shown:CThe point is the position of the rescue vessel at sea when the rescue helicopter takes off from the apron of the rescue vessel;GPoint is the location where the distressed vessel drifts;t*The moment to release the rescue helicopter for the rescue vessel. During the rescue process, the rescue vessel is equipped with a rescue helicopter, and when the rescue vessel travels a certain distance, it arrivesCAt the designated time, the rescue helicopter departs to the search area for further investigation.
The optimization of joint search and rescue by rescue ships and rescue helicopters can be attributed to the decision problem of the time when the rescue ship releases the rescue helicopter, the number of times the rescue helicopter searches the search area, and the interval between each search route. The goal is to complete the search and rescue as quickly as possible and with the highest probability of discovery. For the convenience of discussion, the following reasonable assumptions can be made: rescue ships immediately rush to the accident area upon receiving distress messages; The rescue ships and helicopters performed well during the search and rescue process. When the rescue ship releases the rescue helicopter, the direction of travel of the rescue ship remains unchanged. The specific model is
| \min f_{1}=t^{*}+\frac{r\left(t^{*}\right)}{v_{\mathrm{h}}}+\frac{\sum\limits_{k=1}^{K} L_{k}}{v_{\mathrm{h}}^{\prime}}+\frac{l}{v_{\mathrm{h}}} | (6) |
| \max f_{2}=P_{k} | (7) |
| \frac{r\left(t^{*}\right)}{v_{\mathrm{h}}}+\frac{\sum\limits_{k=1}^{K} L_{k}}{v_{\mathrm{h}}^{\prime}}+\frac{l}{v_{\mathrm{h}}} \leqslant T_{\mathrm{M}} |
| L_{k}=\sum\limits_{d \in D} x_{k, d} \sum\limits_{i_{d}=1}^{I_{d}} L_{i_{d}} |
| P_{k}=\left\{\begin{array}{ll} x_{1, d}\left(1-\mathrm{e}^{-\frac{g}{d}}\right) & k=1 \\ P_{k-1}+\left(1-P_{k-1}\right) x_{k, d}\left(1-\mathrm{e}^{-\frac{g}{d}}\right) & k \in\{2,3, \cdots, K\} \end{array}\right. |
| L_{i_{d}+2}=L_{i_{d}}+d |
| L_{I_{d}} \geqslant R |
| L_{1}=L_{2}=d |
| \sum\limits_{d \in D} x_{k, d}=1 |
| X_{\mathrm{s}}(t)=X_{\mathrm{s}}(0)+\frac{\sum\limits_{u=0}^{t-1} v_{\mathrm{s}, u}^{\prime} u}{2} |
| X_{\mathrm{b}}(t)=X_{\mathrm{b}}(0)+\frac{\sum\limits_{u=0}^{t-1} v_{\mathrm{b}, u}^{\prime} u}{2} |
| r(t)=\left|X_{\mathrm{s}}(t)-X_{\mathrm{b}}(t)\right| |
In the formula:f1The function of the time it takes for rescue helicopters to complete the search coverage of the search and rescue area;f2A function of the probability of a rescue helicopter discovering a distressed vessel;r(t*）Fort*The distance between the rescue vessel and the predicted location of the distressed vessel at all times;vhFor the normal flight speed of rescue helicopters;v′hThe speed at which rescue helicopters conduct searches;LkComplete the rescue helicopter missionkThe total length of the flight during the second search task,k∈{1, 2, …, K}，KThe total number of searches conducted by rescue helicopters;lThe distance between the rescue helicopter and the rescue vessel after the search is completed;PkAccumulated discovery probability for rescue helicopters;TMThe longest endurance time for rescue helicopters;LidFor rescue helicopters in theidThe flight length on each flight segment,IdFor the interval between flight routesdThe total number of flight segments required to complete the search in the search area;DSet up intervals for flight routes;xk, dIs the rescue helicopter separated by flight routesdCarry out thekSecond search, ifxk, dTake 1, otherwise take 0;RThe side length of the area to be searched;L1, L2The flight lengths of the rescue helicopter on the first and second flight segments respectively;Xs(t）FortThe coordinates of the rescue vessel at all times;udotThe specific value of, ranging from 0 tot-Between 1;v′s, udouUnder the influence of wind and waves, the speed and direction of rescue ships are directed towards the current location of the distressed vessel;Xb(t）FortThe coordinates of the vessel in distress at all times;vb, udouThe speed and direction of the ship in distress under the influence of wind and waves are the same as the wind direction it is in;r(t）FortThe distance between the rescue vessel at all times and the predicted location of the distressed vessel.
Intelligent algorithms are commonly used to solve optimization problems, and GIS can be used to simulate the changes in speed under the influence of wind and waves. Therefore, this article establishes GIS and algorithm modules respectively, and solves the model through data interaction. The specific idea is to use GIS to simulate real-time wind direction and waves on the sea, calculate the speed of rescue ships under the influence of wind and wave factors at any time, the drift speed of distressed ships, and the position of distressed ships. The calculated data will be input into the optimization algorithm module in real time to continuously adjust the route of rescue ships, and then formulate decision plans such as the takeoff time of rescue helicopters, the number of searches in the search area, and the interval between each flight path.
Kennedy and others[27-28]The Particle Swarm Optimization (PSO) algorithm developed is a globally optimized algorithm inspired by nature, which has strong capabilities in solving multi-objective continuous optimization problems. The update of particle swarm position and velocity in traditional PSO algorithm is expressed as
| \begin{aligned} v_{z+1}=& \beta_{1} v_{z}+c_{1} \beta_{2}\left(M_{\mathrm{j}}-M_{z}\right)+\\ & c_{2} \beta_{3}\left(M_{\mathrm{q}}-M_{z}\right) \end{aligned} | (8) |
| M_{z+1}= M_{z}+v_{z+1} | (9) |
In the formula:c1, c2They are self learning factors and social learning factors respectively;β1, β2, β3The weight of the corresponding variable is a random number between (0,1);zFor the current iteration count;MjThe location of the local optimal solution;MzThe position of the current iterative solution;Mz+1The position of the solution for the next iteration;MqThe position of the global optimal solution;vzThe velocity of particles at the current position;vz+1For the velocity of particles at the next position.
The biggest advantage of PSO algorithm is that it requires fewer parameters to be adjusted, and the principle is simple and easy to implement. The disadvantage is that the search performance of the algorithm has a certain dependence on the parameters, and the values of the parameters will directly affect whether the optimization results converge and the accuracy of the solution results. In response to the above issues, this article has made two main improvements to the PSO algorithm.
The traditional PSO algorithm lacks a balance mechanism and can only perform simple random search. During the search process, it is difficult to make correct adjustments when particles deviate from the global optimal position, which can easily lead to getting stuck in local optimal solutions. This article introduces dynamic weights to enable particles to have self-regulation ability. The basic idea is that during the iteration process of the algorithm, if some particles have very high fitness, they are likely to be near the global optimal position. At this time, a larger dynamic weight value should be assigned to make the particles approach the global optimal position; Similarly, if some particles currently have very low fitness, they are likely to have deviated from the global optimal position. In this case, smaller dynamic weight values should be assigned to bring these particles closer to the global optimal position. This article defines dynamic weights as
| a_{z}=\left(\frac{\mathrm{e}^{F_{i} / m}}{1+\mathrm{e}^{-F_{i} / m}}\right)^{z} | (10) |
In the formula:azFor dynamic weighting;FiYes, it isiFitness of individual particles;mFor the average fitness value.
On this basis, equation (9) is updated to
| M_{z+1}=a_{z} M_{z}+\left(1-a_{z}\right) v_{z+1}+\beta_{4} M_{\mathrm{q}} | (11) |
In the formula:β4doMqWeight is a random number between (0,1).
Fig. 6(a)To achieve the effect of dynamic weight changes, represent the relationship between dynamic weights and the current position and speed, and use weight reduction to ensure that the search reaches the global optimal position.
Although the random search in traditional PSO algorithms can ensure the breadth of particle search and maintain the diversity of solutions, excessive dispersion between particles may make it difficult for the algorithm to converge. Although chaotic search has characteristics such as traversal, non repeatability, and sensitivity, it can perform traversal search in a shorter time[29]However, in the later stage of chaotic search, it will still maintain a large search range, resulting in waste,Fig. 6(b)The blue line in the middle represents the inertia weight that varies randomly, with values ranging from 0 to 1. This article uses adaptive chaotic search instead of random search to improve the traversal of particles, and the inertia weights that change in a chaotic manner are as follows:Fig. 6(b)As shown by the red line in the middle. The improved algorithm searches in a chaotic manner during the early stages of operation to ensure particle diversity and escape from local optima; As the algorithm runs, the inertia weight values gradually decrease in a chaotic decreasing manner, which helps the particles to quickly converge to the global optimum. Apply the inertia weight in equation (8)β1Adjust to
| {\beta _{1,z}} = \frac{{{\beta _1}(J - z)\sin \left( {{\rm{ \mathsf{ π} }}{\beta _{1,z - 1}}} \right)}}{J}\quad z = 1,2, \cdots ,J | (12) |
In the formula:β1, zFor the thzThe inertia weight value of the second iteration;β1, z-1For the thz-Inertial weight value for one iteration;JFor the maximum number of iterations.
The improved algorithm combining GIS and particle swarm optimization has the following calculation steps, and the corresponding calculation process is as followsFig. 7As shown.
Step 1： Algorithm initialization. Set the basic parameters of the particle swarm algorithm and randomly generate an initial particle swarm based on the set variable range.
Step 2： Read particle data. Obtain the moment when the rescue ship releases the rescue helicopter.
Step 3： Interact with GIS for data exchange. Retrieve from GIStThe position of the rescue vessel at all times, the position of the distressed vessel, and the speed of the rescue vessel under the influence of wind and waves, adjust the direction of travel of the rescue vessel according to the position of the distressed vessel.
Step 4： judgetIs it equal tot*If it is equal, proceed to the next step; Otherwise, it willt+Assign a value to 1tReturn to Step 3.
Step 5： Calculate fitness. Calculate the total search time and discovery probability for each particle in the particle swarm based on the time when the rescue ship releases the rescue helicopter, the number of searches conducted by the rescue helicopter, and the interval between each search.
Step 6： Initial non inferior solution screening. Perform initial non dominated solution screening based on fitness, record all non dominated solutions, and determine the optimal individual and global optimal individual of the initial particle swarm from the non dominated solution set.
Step 7： Particle update. Update the velocity and position of all particles based on equations (8) and (11).
Step 8： Recalculate fitness. Recalculate fitness for all particles obtained after updating.
Step 9： Non inferior solution screening. Based on fitness, screen for non dominated solutions in the current population and record all non dominated solutions; Merge the non dominated solutions obtained from the current population with previously recorded non dominated solutions, re screen for new non dominated solutions, determine a new set of non dominated solutions, and update individual and global optimal records.
Step 10： Inertial weight adjustment. Update the inertia weight according to equation (12).
Step 11： If the calculation result does not meet the predetermined termination condition, return to Step 2; Otherwise, terminate the calculation and output the calculation result.
Step 12： end.
Based on the characteristics of the problem at hand, this article selects the Zitzler Deb Thiele standard test function (hereinafter referred to asZ）Conduct testing.Z1~Z4It is a widely recognized multi-objective testing function, developed by Zitzler et al[30]Calculate its function expression. of whichZ1andZ4The Pareto front is convex,Z2The Pareto front is concave,Z3The Pareto front is discontinuous. Dimension of test function decision variablesZ1~Z3Take 30,Z4Take it as 10. To verify the effectiveness of the improved particle swarm algorithm, a comparison was made between the improved particle swarm algorithm and the traditional particle swarm algorithm. The parameters of the two algorithms were set as follows:c1Take 0.1,c2Take 0.1; Number of particle swarmYTake 100 and iterate 500 times.
The Inverse Generative Distance (IGD) is an indicator that represents the distance between the approximate Pareto optimal solution and the true Pareto optimal solution. The smaller the value of this indicator, the closer the approximate Pareto front is to the true Pareto front, and the better the convergence and diversity of the algorithm[31]The Spacing Metric (SPM) is a performance metric that characterizes the uniformity of the distribution of the optimal solution set. The smaller the value of this metric, the better the uniformity of the Pareto solution set[32]Therefore, this article uses the IGD metric to measure the convergence and diversity of the proposed algorithm, and the SPM metric to measure uniformity. The calculation formula is
| \operatorname{IGD}\left(Q, Q^{*}\right)=\frac{\sum\limits_{x \in Q^{*}, y \in Q} \min d(x, y)}{\left|Q^{*}\right|} | (13) |
| \eta=\sqrt{\frac{\sum\limits_{i=1}^{z}\left(\bar{o}-o_{i}\right)}{N-1}} | (14) |
In the formula: IGD(Q, Q*）To reverse the generation distance function;QThe non dominated solution set obtained by the algorithm;Q*A set of uniformly distributed reference points sampled from the true Pareto solution set;d(x, y）For reference setQ*midpointxTo the non dominated solution setQmidpointyThe Euclidean distance between them;ηFor spacing indicators;oiFor the thiThe Euclidean distance between a non inferior solution and its nearest solution;oThe average distance of Euclidean distances for all non inferior solutions;NThe number of non inferior solutions.
Improved Particle Swarm Optimization and Traditional Particle Swarm Optimization AlgorithmZThe IGD evaluation index and SP evaluation index calculated 10 times using the standard test function are as follows:Tab. 1, 2As shown. causeTab. 1, 2It can be inferred that the improved algorithm is effective for four test functions（Z1~Z4）Good average and minimum values were obtained on both IGD and SPM indicators, indicating that the improved algorithm has strong convergence and uniformity; At the same time, the standard deviation of the improved algorithm is significantly better than that of the compared algorithm, indicating its strong stability and ability to handle multimodal problems well, obtaining a high-quality and highly distributed non dominated solution set.
| 测试函数 | 传统粒子群算法 | 改进粒子群算法 | |||||||
| 计算结果 | 计算结果 | 改进幅度 | |||||||
| 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值改进幅度/% | 最小值改进幅度/% | 标准差改进幅度/% | |
| Z1 | 11.00 | 8.90 | 1.40 | 9.20 | 7.80 | 0.75 | 16.36 | 12.36 | 46.43 |
| Z2 | 8.30 | 7.20 | 0.86 | 7.40 | 6.80 | 0.54 | 10.84 | 5.56 | 37.21 |
| Z3 | 36.00 | 33.00 | 2.40 | 33.00 | 30.00 | 1.50 | 8.33 | 9.09 | 37.50 |
| Z4 | 33.00 | 23.00 | 9.60 | 23.00 | 17.00 | 5.10 | 30.30 | 26.09 | 46.88 |
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| 测试函数 | 传统粒子群算法 | 改进粒子群算法 | |||||||
| 计算结果 | 计算结果 | 改进幅度 | |||||||
| 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值改进幅度/% | 最小值改进幅度/% | 标准差改进幅度/% | |
| Z1 | 24.00 | 21.00 | 2.20 | 20.00 | 18.00 | 1.40 | 16.67 | 14.29 | 36.36 |
| Z2 | 21.00 | 17.00 | 3.10 | 18.00 | 13.00 | 1.80 | 14.29 | 23.53 | 41.94 |
| Z3 | 61.00 | 31.00 | 8.20 | 41.00 | 29.00 | 5.40 | 32.79 | 6.45 | 34.15 |
| Z4 | 43.00 | 50.00 | 24.00 | 29.00 | 14.00 | 17.00 | 32.56 | 72.00 | 29.17 |
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Fig. 8ListedZThe true Pareto front of the standard test function and the Pareto front obtained by the algorithm in this paper indicate that compared to the traditional particle swarm algorithm, the solution calculated by the improved particle swarm algorithm in this paper is closer to the true Pareto front, indicating that the improved particle swarm algorithm has more advantages in solving problems.
Taking the search and rescue operations in the South China Sea as an example for analysis. Assuming a ship loses power 200 n miles east of Yongxing Island, the rescue ship immediately departs from Yongxing Island upon receiving the search command, with a speed of 20.000 kn. The speed of the rescue helicopter when flying directly to the search area is 154.968 kn, and the speed when conducting the search is 48.596 kn. The sweeping width is 3 n miles, and the range of route intervals is 0-5 n miles. According to the research scale of this article, the search area is a square with a side length of 20 n miles. Extract land/ocean data from the research area and assign values and rasterize them. Set the resolution of the grid to 0.5 °× 0.5 ° and project it onto the WGS-1984 Web Mercator coordinate system based on the location characteristics of the study area. Obtain level 9 (approximately 22 m · s) through wave modeling-1）The effective wave height distribution under easterly conditions is as followsFig. 9As shown,Tab. 3To measure the sea surface wind and wave data obtained every half hour for rescue ships (data sourced from the GISIS database of the International Maritime Organization:https://gisis.imo.org/Public/Default.aspx）According to section 2.2, the speed and position of rescue and distressed vessels under wind and wave conditions are shown inTab. 4.
| 时间/h | 实测风向/(°) | 实测风速/(m·s-1) | 基于GIS预测的救援船舶位置浪高/m | 基于GIS预测的漂移船舶位置浪高/m |
| 0.0 | 33.1 | 22.4 | 4.1 | 4.2 |
| 0.5 | 41.2 | 21.2 | 5.1 | 4.5 |
| 1.0 | 61.4 | 21.3 | 4.5 | 3.9 |
| 1.5 | 34.1 | 22.3 | 3.7 | 4.3 |
| 2.0 | 40.6 | 21.5 | 4.9 | 5.1 |
| 2.5 | 40.0 | 21.8 | 5.0 | 4.8 |
| 3.0 | 47.2 | 21.5 | 4.0 | 3.7 |
| 3.5 | 45.5 | 21.1 | 4.2 | 4.7 |
| 4.0 | 46.6 | 21.9 | 4.8 | 4.1 |
| 4.5 | 53.6 | 22.5 | 3.6 | 3.6 |
| 5.0 | 58.8 | 21.9 | 5.2 | 4.1 |
| 5.5 | 53.7 | 21.1 | 4.8 | 4.6 |
| 6.0 | 57.6 | 22.6 | 4.5 | 5.0 |
| 6.5 | 40.0 | 21.7 | 3.8 | 3.9 |
| 7.0 | 33.8 | 22.1 | 4.6 | 4.8 |
| 7.5 | 49.4 | 22.6 | 4.8 | 3.6 |
| 8.0 | 52.6 | 21.9 | 4.9 | 4.2 |
| 8.5 | 46.3 | 21.6 | 4.8 | 3.8 |
| 9.0 | 41.0 | 22.6 | 4.9 | 5.0 |
| 9.5 | 61.1 | 21.8 | 5.3 | 4.4 |
| 10.0 | 38.9 | 21.6 | 3.8 | 5.0 |
| 10.5 | 39.5 | 21.9 | 5.1 | 4.2 |
| 11.0 | 38.9 | 21.9 | 5.3 | 5.0 |
| 11.5 | 35.7 | 21.4 | 4.6 | 3.8 |
DownLoad:
CSV
| 时间/h | 风、浪影响下的救援船舶航速/kn | 遇险船舶航速/kn | 遇险船舶航向/(°) | 遇险船舶位置/n mile | 救援船舶位置/n mile |
| 0.0 | 19.967 | 4.342 | 33.1 | (200.00, 0.00) | (0.00, 0.00) |
| 0.5 | 19.969 | 4.647 | 41.2 | (201.85, 1.49) | (9.99, 0.07) |
| 1.0 | 19.968 | 4.522 | 61.4 | (202.94, 2.62) | (19.99, 0.21) |
| 1.5 | 19.966 | 4.446 | 34.1 | (204.10, 4.54) | (29.99, 0.44) |
| 2.0 | 19.969 | 3.414 | 40.6 | (205.23, 5.71) | (39.99, 0.74) |
| 2.5 | 19.969 | 5.023 | 40.0 | (206.66, 7.03) | (49.98, 1.12) |
| 3.0 | 19.967 | 4.940 | 47.2 | (208.45, 8.38) | (59.97, 1.58) |
| 3.5 | 19.967 | 4.672 | 45.5 | (209.62, 9.61) | (69.96, 2.11) |
| 4.0 | 19.969 | 4.369 | 46.6 | (210.94, 11.48) | (79.94, 2.78) |
| 4.5 | 19.966 | 4.355 | 53.6 | (212.18, 12.52) | (89.91, 3.51) |
| 5.0 | 19.970 | 4.465 | 58.8 | (213.91, 14.26) | (99.87, 4.37) |
| 5.5 | 19.969 | 4.436 | 53.7 | (215.82, 15.78) | (109.83, 5.35) |
| 6.0 | 19.968 | 3.897 | 57.6 | (217.63, 17.40) | (119.76, 6.46) |
| 6.5 | 19.966 | 3.352 | 40.0 | (218.99, 18.62) | (129.68, 7.69) |
| 7.0 | 19.968 | 4.722 | 33.8 | (220.34, 20.52) | (139.59, 9.08) |
| 7.5 | 19.969 | 3.528 | 49.4 | (221.91, 22.17) | (149.47, 10.65) |
| 8.0 | 19.969 | 3.541 | 52.6 | (223.84, 23.76) | (159.31, 12.39) |
| 8.5 | 19.969 | 3.773 | 46.3 | (225.08, 25.49) | (169.12, 14.34) |
| 9.0 | 19.969 | 3.870 | 41.0 | (226.54, 27.39) | (178.87, 16.56) |
| 9.5 | 19.970 | 4.371 | 61.1 | (227.83, 28.94) | (188.57, 19.01) |
| 10.0 | 19.966 | 5.112 | 38.9 | (229.82, 30.80) | (198.18, 21.76) |
| 10.5 | 19.969 | 4.663 | 39.5 | (230.85, 31.99) | (207.73, 24.75) |
| 11.0 | 19.970 | 5.028 | 38.9 | (232.54, 33.09) | (217.20, 27.94) |
| 11.5 | 19.968 | 3.630 | 35.7 | (234.30, 34.80) | (226.48, 31.66) |
| 12.0 | (236.20, 36.78) | (235.33, 36.32) |
DownLoad:
CSV
Import the obtained data into the model, use Python programming to interact with ArcGIS software, and run it on a computer with Intel (R) Core (TM) i7-8750H CPU @ 2.21GHz 8GB. Set the number of particle swarm for improving the particle swarm algorithmYTake 100, learning factorc1Take 0.1,c2Taking 0.1 and iterating 500 times, a series of non dominated solutions can be obtained through the improved algorithm proposed in this paper, and the Pareto front composed of these solutions can be obtainedFig. 10As shown, the specific search plan can be found inTab. 5.
| 约束概率/% | 起飞时刻/h | 起飞时与遇险船舶之间的距离/n mile | 飞机搜索航线间隔/n mile | 搜寻时间/h | 发现概率/% |
| 85.00 | 3.0 | 145.40 | 1.60 | 6.8 | 85.50 |
| 90.00 | 4.0 | 128.50 | 1.30 | 7.8 | 90.30 |
| 95.00 | 5.5 | 102.60 | 0.96 | 9.3 | 95.50 |
DownLoad:
CSV
causeTab. 5It can be seen that when the constraint probability is 85.00%, the rescue ship will sail for 3.0 hours and release the rescue helicopter 145.40 n miles away from the rescue ship and the distressed ship. After the rescue helicopter arrives at the search area, it will conduct a search at an interval of 1.6 n miles. The total time required for the search and rescue operation is 6.8 hours, and the discovery probability is 85.50%; Under the constraint probability of 90.00%, the rescue vessel releases the rescue helicopter after sailing for 4.0 hours and at a distance of 128.50 n miles from the distressed vessel. After the rescue helicopter arrives at the search area, it conducts a search at intervals of 1.30 n miles. The total time required for the search and rescue operation is 7.8 hours, with a detection probability of 90.30%; Under the constraint probability of 95.00%, the rescue vessel releases the rescue helicopter after sailing for 5.5 hours and is 102.60 n miles away from the distressed vessel. After the rescue helicopter arrives at the search area, it conducts a search at intervals of 0.96 n miles. The total time required for the search and rescue operation is 9.3 hours, and the discovery probability is 95.50%.
The actual situation is that at around 6:46 am on July 11, 2019, the Chinese Hainan fishing boat "Qiongqionghai 01039" was submerged in water about 200 nautical miles south of Yongxing Island and requested rescue. The wind force on site is 5-6 levels, with a wave height of about 1.5 meters. The fishing boat lost contact after the alarm, and the Beidou system signal was lost, with a high possibility of sinking. After receiving the alarm, the China Maritime Search and Rescue Center immediately coordinated the dispatch of professional rescue ships and aircraft to the scene of the incident for search and rescue. Around 11:00, the search aircraft found four small boats carrying passengers near the incident water area, which were preliminarily judged to be "Qiongqionghai 01039" distressed persons. At 16:00, the rescue ship arrived and then carried 32 fishermen back. The entire search and rescue operation lasted about 10.0 hours, which was close to the research results in this article.
To verify the performance of the improved particle swarm algorithm in solving the problem in this paper, the traditional particle swarm algorithm was selected to simultaneously solve the problem in this paper, and the obtained Pareto front is as follows:Fig. 10As shown. In addition, by comparing the calculation results with traditional particle swarm optimization algorithm while satisfying the same discovery probability, the comparison results are listed in the tableTab. 6. ThroughTab. 6It can be seen that under the conditions of discovery probabilities of 85.00%, 90.00%, and 95.00%, the search times obtained by the traditional particle swarm algorithm are 8.3, 9.1, and 10.4 hours, while the search times obtained by our algorithm are 6.8, 7.8, and 9.3 hours, respectively. The improvement ranges are 18.07%, 14.28%, and 10.57%, indicating that our improved algorithm has better performance.
| 约束概率/% | 传统粒子群算法 | 改进粒子群算法 | |||
| 发现概率/% | 搜寻时间/h | 发现概率/% | 搜寻时间/h | 搜寻时间缩减幅度/% | |
| 85.00 | 85.10 | 8.3 | 85.50 | 6.8 | 18.07 |
| 90.00 | 90.20 | 9.1 | 90.30 | 7.8 | 14.28 |
| 95.00 | 95.10 | 10.4 | 95.50 | 9.3 | 10.57 |
DownLoad:
CSV
(1) Due to the urgency of search and rescue operations, it is necessary to consider searching for distressed ships with the highest probability of discovery in the shortest possible time, while also taking into account the impact of wind and waves on the speed and location of rescue ships and distressed ships. Therefore, a specific model needs to be established for joint sea air search and rescue of distressed ships, combined with new technological means for research.
(2) For remote sea rescue missions, a GIS based dual objective optimization model and algorithm for sea air joint search and rescue were established with the optimization content of the rescue ship's travel route, the release time of rescue helicopters, and the search plan of rescue helicopters. The goal was to minimize the search and rescue time and maximize the discovery probability.
(3) Taking the search and rescue mission in the South China Sea as an example for analysis, a relatively ideal optimization effect was obtained, verifying the rationality and effectiveness of the established model and algorithm. By comparing with traditional particle swarm optimization algorithm, the improved algorithm shows good results in various indicators such as calculation speed, optimization results, and calculation stability.
(4) The article only studies the search and rescue operations of a single rescue vessel carrying a single helicopter. However, in reality, when major maritime accidents occur in remote areas, there are often multiple rescue vessels and helicopters working together to carry out search and rescue operations. At this time, the scheduling plan will be more complex. It is recommended to further study this optimization problem in depth.
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Figures(10) / Tables(6)
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LIN Wan-ni, WANG Nuo, GAO Zhong-yin, WU Di. Associated searching and rescuing optimization of salvage vessels and helicopters in remote sea area[J]. Journal of Traffic and Transportation Engineering, 2021, 21(2): 187-199. doi: 10.19818/j.cnki.1671-1637.2021.02.016
| 测试函数 | 传统粒子群算法 | 改进粒子群算法 | |||||||
| 计算结果 | 计算结果 | 改进幅度 | |||||||
| 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值改进幅度/% | 最小值改进幅度/% | 标准差改进幅度/% | |
| Z1 | 11.00 | 8.90 | 1.40 | 9.20 | 7.80 | 0.75 | 16.36 | 12.36 | 46.43 |
| Z2 | 8.30 | 7.20 | 0.86 | 7.40 | 6.80 | 0.54 | 10.84 | 5.56 | 37.21 |
| Z3 | 36.00 | 33.00 | 2.40 | 33.00 | 30.00 | 1.50 | 8.33 | 9.09 | 37.50 |
| Z4 | 33.00 | 23.00 | 9.60 | 23.00 | 17.00 | 5.10 | 30.30 | 26.09 | 46.88 |
DownLoad:
CSV
| 测试函数 | 传统粒子群算法 | 改进粒子群算法 | |||||||
| 计算结果 | 计算结果 | 改进幅度 | |||||||
| 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值改进幅度/% | 最小值改进幅度/% | 标准差改进幅度/% | |
| Z1 | 24.00 | 21.00 | 2.20 | 20.00 | 18.00 | 1.40 | 16.67 | 14.29 | 36.36 |
| Z2 | 21.00 | 17.00 | 3.10 | 18.00 | 13.00 | 1.80 | 14.29 | 23.53 | 41.94 |
| Z3 | 61.00 | 31.00 | 8.20 | 41.00 | 29.00 | 5.40 | 32.79 | 6.45 | 34.15 |
| Z4 | 43.00 | 50.00 | 24.00 | 29.00 | 14.00 | 17.00 | 32.56 | 72.00 | 29.17 |
DownLoad:
CSV
| 时间/h | 实测风向/(°) | 实测风速/(m·s-1) | 基于GIS预测的救援船舶位置浪高/m | 基于GIS预测的漂移船舶位置浪高/m |
| 0.0 | 33.1 | 22.4 | 4.1 | 4.2 |
| 0.5 | 41.2 | 21.2 | 5.1 | 4.5 |
| 1.0 | 61.4 | 21.3 | 4.5 | 3.9 |
| 1.5 | 34.1 | 22.3 | 3.7 | 4.3 |
| 2.0 | 40.6 | 21.5 | 4.9 | 5.1 |
| 2.5 | 40.0 | 21.8 | 5.0 | 4.8 |
| 3.0 | 47.2 | 21.5 | 4.0 | 3.7 |
| 3.5 | 45.5 | 21.1 | 4.2 | 4.7 |
| 4.0 | 46.6 | 21.9 | 4.8 | 4.1 |
| 4.5 | 53.6 | 22.5 | 3.6 | 3.6 |
| 5.0 | 58.8 | 21.9 | 5.2 | 4.1 |
| 5.5 | 53.7 | 21.1 | 4.8 | 4.6 |
| 6.0 | 57.6 | 22.6 | 4.5 | 5.0 |
| 6.5 | 40.0 | 21.7 | 3.8 | 3.9 |
| 7.0 | 33.8 | 22.1 | 4.6 | 4.8 |
| 7.5 | 49.4 | 22.6 | 4.8 | 3.6 |
| 8.0 | 52.6 | 21.9 | 4.9 | 4.2 |
| 8.5 | 46.3 | 21.6 | 4.8 | 3.8 |
| 9.0 | 41.0 | 22.6 | 4.9 | 5.0 |
| 9.5 | 61.1 | 21.8 | 5.3 | 4.4 |
| 10.0 | 38.9 | 21.6 | 3.8 | 5.0 |
| 10.5 | 39.5 | 21.9 | 5.1 | 4.2 |
| 11.0 | 38.9 | 21.9 | 5.3 | 5.0 |
| 11.5 | 35.7 | 21.4 | 4.6 | 3.8 |
DownLoad:
CSV
| 时间/h | 风、浪影响下的救援船舶航速/kn | 遇险船舶航速/kn | 遇险船舶航向/(°) | 遇险船舶位置/n mile | 救援船舶位置/n mile |
| 0.0 | 19.967 | 4.342 | 33.1 | (200.00, 0.00) | (0.00, 0.00) |
| 0.5 | 19.969 | 4.647 | 41.2 | (201.85, 1.49) | (9.99, 0.07) |
| 1.0 | 19.968 | 4.522 | 61.4 | (202.94, 2.62) | (19.99, 0.21) |
| 1.5 | 19.966 | 4.446 | 34.1 | (204.10, 4.54) | (29.99, 0.44) |
| 2.0 | 19.969 | 3.414 | 40.6 | (205.23, 5.71) | (39.99, 0.74) |
| 2.5 | 19.969 | 5.023 | 40.0 | (206.66, 7.03) | (49.98, 1.12) |
| 3.0 | 19.967 | 4.940 | 47.2 | (208.45, 8.38) | (59.97, 1.58) |
| 3.5 | 19.967 | 4.672 | 45.5 | (209.62, 9.61) | (69.96, 2.11) |
| 4.0 | 19.969 | 4.369 | 46.6 | (210.94, 11.48) | (79.94, 2.78) |
| 4.5 | 19.966 | 4.355 | 53.6 | (212.18, 12.52) | (89.91, 3.51) |
| 5.0 | 19.970 | 4.465 | 58.8 | (213.91, 14.26) | (99.87, 4.37) |
| 5.5 | 19.969 | 4.436 | 53.7 | (215.82, 15.78) | (109.83, 5.35) |
| 6.0 | 19.968 | 3.897 | 57.6 | (217.63, 17.40) | (119.76, 6.46) |
| 6.5 | 19.966 | 3.352 | 40.0 | (218.99, 18.62) | (129.68, 7.69) |
| 7.0 | 19.968 | 4.722 | 33.8 | (220.34, 20.52) | (139.59, 9.08) |
| 7.5 | 19.969 | 3.528 | 49.4 | (221.91, 22.17) | (149.47, 10.65) |
| 8.0 | 19.969 | 3.541 | 52.6 | (223.84, 23.76) | (159.31, 12.39) |
| 8.5 | 19.969 | 3.773 | 46.3 | (225.08, 25.49) | (169.12, 14.34) |
| 9.0 | 19.969 | 3.870 | 41.0 | (226.54, 27.39) | (178.87, 16.56) |
| 9.5 | 19.970 | 4.371 | 61.1 | (227.83, 28.94) | (188.57, 19.01) |
| 10.0 | 19.966 | 5.112 | 38.9 | (229.82, 30.80) | (198.18, 21.76) |
| 10.5 | 19.969 | 4.663 | 39.5 | (230.85, 31.99) | (207.73, 24.75) |
| 11.0 | 19.970 | 5.028 | 38.9 | (232.54, 33.09) | (217.20, 27.94) |
| 11.5 | 19.968 | 3.630 | 35.7 | (234.30, 34.80) | (226.48, 31.66) |
| 12.0 | (236.20, 36.78) | (235.33, 36.32) |
DownLoad:
CSV
| 约束概率/% | 起飞时刻/h | 起飞时与遇险船舶之间的距离/n mile | 飞机搜索航线间隔/n mile | 搜寻时间/h | 发现概率/% |
| 85.00 | 3.0 | 145.40 | 1.60 | 6.8 | 85.50 |
| 90.00 | 4.0 | 128.50 | 1.30 | 7.8 | 90.30 |
| 95.00 | 5.5 | 102.60 | 0.96 | 9.3 | 95.50 |
DownLoad:
CSV
| 约束概率/% | 传统粒子群算法 | 改进粒子群算法 | |||
| 发现概率/% | 搜寻时间/h | 发现概率/% | 搜寻时间/h | 搜寻时间缩减幅度/% | |
| 85.00 | 85.10 | 8.3 | 85.50 | 6.8 | 18.07 |
| 90.00 | 90.20 | 9.1 | 90.30 | 7.8 | 14.28 |
| 95.00 | 95.10 | 10.4 | 95.50 | 9.3 | 10.57 |
DownLoad:
CSV
| 测试函数 | 传统粒子群算法 | 改进粒子群算法 | |||||||
| 计算结果 | 计算结果 | 改进幅度 | |||||||
| 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值改进幅度/% | 最小值改进幅度/% | 标准差改进幅度/% | |
| Z1 | 11.00 | 8.90 | 1.40 | 9.20 | 7.80 | 0.75 | 16.36 | 12.36 | 46.43 |
| Z2 | 8.30 | 7.20 | 0.86 | 7.40 | 6.80 | 0.54 | 10.84 | 5.56 | 37.21 |
| Z3 | 36.00 | 33.00 | 2.40 | 33.00 | 30.00 | 1.50 | 8.33 | 9.09 | 37.50 |
| Z4 | 33.00 | 23.00 | 9.60 | 23.00 | 17.00 | 5.10 | 30.30 | 26.09 | 46.88 |
| 测试函数 | 传统粒子群算法 | 改进粒子群算法 | |||||||
| 计算结果 | 计算结果 | 改进幅度 | |||||||
| 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值/10-4 | 最小值/10-4 | 标准差/10-4 | 平均值改进幅度/% | 最小值改进幅度/% | 标准差改进幅度/% | |
| Z1 | 24.00 | 21.00 | 2.20 | 20.00 | 18.00 | 1.40 | 16.67 | 14.29 | 36.36 |
| Z2 | 21.00 | 17.00 | 3.10 | 18.00 | 13.00 | 1.80 | 14.29 | 23.53 | 41.94 |
| Z3 | 61.00 | 31.00 | 8.20 | 41.00 | 29.00 | 5.40 | 32.79 | 6.45 | 34.15 |
| Z4 | 43.00 | 50.00 | 24.00 | 29.00 | 14.00 | 17.00 | 32.56 | 72.00 | 29.17 |
| 时间/h | 实测风向/(°) | 实测风速/(m·s-1) | 基于GIS预测的救援船舶位置浪高/m | 基于GIS预测的漂移船舶位置浪高/m |
| 0.0 | 33.1 | 22.4 | 4.1 | 4.2 |
| 0.5 | 41.2 | 21.2 | 5.1 | 4.5 |
| 1.0 | 61.4 | 21.3 | 4.5 | 3.9 |
| 1.5 | 34.1 | 22.3 | 3.7 | 4.3 |
| 2.0 | 40.6 | 21.5 | 4.9 | 5.1 |
| 2.5 | 40.0 | 21.8 | 5.0 | 4.8 |
| 3.0 | 47.2 | 21.5 | 4.0 | 3.7 |
| 3.5 | 45.5 | 21.1 | 4.2 | 4.7 |
| 4.0 | 46.6 | 21.9 | 4.8 | 4.1 |
| 4.5 | 53.6 | 22.5 | 3.6 | 3.6 |
| 5.0 | 58.8 | 21.9 | 5.2 | 4.1 |
| 5.5 | 53.7 | 21.1 | 4.8 | 4.6 |
| 6.0 | 57.6 | 22.6 | 4.5 | 5.0 |
| 6.5 | 40.0 | 21.7 | 3.8 | 3.9 |
| 7.0 | 33.8 | 22.1 | 4.6 | 4.8 |
| 7.5 | 49.4 | 22.6 | 4.8 | 3.6 |
| 8.0 | 52.6 | 21.9 | 4.9 | 4.2 |
| 8.5 | 46.3 | 21.6 | 4.8 | 3.8 |
| 9.0 | 41.0 | 22.6 | 4.9 | 5.0 |
| 9.5 | 61.1 | 21.8 | 5.3 | 4.4 |
| 10.0 | 38.9 | 21.6 | 3.8 | 5.0 |
| 10.5 | 39.5 | 21.9 | 5.1 | 4.2 |
| 11.0 | 38.9 | 21.9 | 5.3 | 5.0 |
| 11.5 | 35.7 | 21.4 | 4.6 | 3.8 |
| 时间/h | 风、浪影响下的救援船舶航速/kn | 遇险船舶航速/kn | 遇险船舶航向/(°) | 遇险船舶位置/n mile | 救援船舶位置/n mile |
| 0.0 | 19.967 | 4.342 | 33.1 | (200.00, 0.00) | (0.00, 0.00) |
| 0.5 | 19.969 | 4.647 | 41.2 | (201.85, 1.49) | (9.99, 0.07) |
| 1.0 | 19.968 | 4.522 | 61.4 | (202.94, 2.62) | (19.99, 0.21) |
| 1.5 | 19.966 | 4.446 | 34.1 | (204.10, 4.54) | (29.99, 0.44) |
| 2.0 | 19.969 | 3.414 | 40.6 | (205.23, 5.71) | (39.99, 0.74) |
| 2.5 | 19.969 | 5.023 | 40.0 | (206.66, 7.03) | (49.98, 1.12) |
| 3.0 | 19.967 | 4.940 | 47.2 | (208.45, 8.38) | (59.97, 1.58) |
| 3.5 | 19.967 | 4.672 | 45.5 | (209.62, 9.61) | (69.96, 2.11) |
| 4.0 | 19.969 | 4.369 | 46.6 | (210.94, 11.48) | (79.94, 2.78) |
| 4.5 | 19.966 | 4.355 | 53.6 | (212.18, 12.52) | (89.91, 3.51) |
| 5.0 | 19.970 | 4.465 | 58.8 | (213.91, 14.26) | (99.87, 4.37) |
| 5.5 | 19.969 | 4.436 | 53.7 | (215.82, 15.78) | (109.83, 5.35) |
| 6.0 | 19.968 | 3.897 | 57.6 | (217.63, 17.40) | (119.76, 6.46) |
| 6.5 | 19.966 | 3.352 | 40.0 | (218.99, 18.62) | (129.68, 7.69) |
| 7.0 | 19.968 | 4.722 | 33.8 | (220.34, 20.52) | (139.59, 9.08) |
| 7.5 | 19.969 | 3.528 | 49.4 | (221.91, 22.17) | (149.47, 10.65) |
| 8.0 | 19.969 | 3.541 | 52.6 | (223.84, 23.76) | (159.31, 12.39) |
| 8.5 | 19.969 | 3.773 | 46.3 | (225.08, 25.49) | (169.12, 14.34) |
| 9.0 | 19.969 | 3.870 | 41.0 | (226.54, 27.39) | (178.87, 16.56) |
| 9.5 | 19.970 | 4.371 | 61.1 | (227.83, 28.94) | (188.57, 19.01) |
| 10.0 | 19.966 | 5.112 | 38.9 | (229.82, 30.80) | (198.18, 21.76) |
| 10.5 | 19.969 | 4.663 | 39.5 | (230.85, 31.99) | (207.73, 24.75) |
| 11.0 | 19.970 | 5.028 | 38.9 | (232.54, 33.09) | (217.20, 27.94) |
| 11.5 | 19.968 | 3.630 | 35.7 | (234.30, 34.80) | (226.48, 31.66) |
| 12.0 | (236.20, 36.78) | (235.33, 36.32) |
| 约束概率/% | 起飞时刻/h | 起飞时与遇险船舶之间的距离/n mile | 飞机搜索航线间隔/n mile | 搜寻时间/h | 发现概率/% |
| 85.00 | 3.0 | 145.40 | 1.60 | 6.8 | 85.50 |
| 90.00 | 4.0 | 128.50 | 1.30 | 7.8 | 90.30 |
| 95.00 | 5.5 | 102.60 | 0.96 | 9.3 | 95.50 |
| 约束概率/% | 传统粒子群算法 | 改进粒子群算法 | |||
| 发现概率/% | 搜寻时间/h | 发现概率/% | 搜寻时间/h | 搜寻时间缩减幅度/% | |
| 85.00 | 85.10 | 8.3 | 85.50 | 6.8 | 18.07 |
| 90.00 | 90.20 | 9.1 | 90.30 | 7.8 | 14.28 |
| 95.00 | 95.10 | 10.4 | 95.50 | 9.3 | 10.57 |
DownLoad:
DownLoad:
