Sandy coast back shore ecological restoration multi-objective optimization method based on NSGA-II algorithm

Abstract

The invention relates to a sandy coast back shore ecological restoration multi-objective optimization method based on an NSGA-II algorithm, and the method comprises the following steps: S1, selecting a damaged sandy coast, carrying out the background investigation, and calculating a wave climbing value; s2, determining a vegetation arrangement range of the damaged sandy coast; s3, beach shoulder sand supplement of beach shoulder width is conducted on different areas of the damaged sandy coast, and sand dune sand supplement of an artificial sand dune is conducted; s4, calculating the wind erosion prevention efficiency and the wave erosion prevention efficiency of the dominant vegetation; s5, constructing a sandy coast back shore ecological restoration multi-objective optimization function and constraint conditions; s6, solving the multi-objective optimization function based on an NSGA-II algorithm to obtain an optimal vegetation configuration scheme set; s7, based on actual conditions, selecting an optimal vegetation configuration scheme for planting; and S8, detecting vegetation data after planting, and starting a reseeding program when the survival rate of vegetation is lower than a threshold value. Compared with the prior art, the method has the advantages that the fitness of the multi-power environment is improved, and then the windproof and wave-resistant effects are optimized.

Description

Technical Field

[0001] The present invention relates to the technical field of coastal ecological restoration engineering, and in particular to a multi-objective optimization method for sandy coastal backshore ecological restoration based on an NSGA-II algorithm. Background Art

[0002] The backshore area of ​​a sandy coast, including the beach shoulder and dune system, is an important ecological barrier against storm surge erosion and maintains coastal stability. However, due to the combined impact of high-intensity human activities (such as sand mining and tourism development) and climate change, sandy coasts around the world are facing a systemic crisis of intensified erosion and vegetation degradation. In dune systems, vegetation plays a dual role: deep roots can anchor loose sand and enhance structural stability; the canopy reduces erosion by reducing near-surface wind speed. However, at present, the backshore vegetation coverage rate continues to decline, resulting in an increasingly obvious trend of erosion and degradation of the dune system.

[0003] At present, the integration of sand replenishment and beach maintenance with vegetation reconstruction commonly used in coastal restoration projects has many shortcomings. In terms of vegetation configuration, it is mostly based on experience, and a single pioneer species (such as sand drill sedge) is often used for uniform planting. This single community structure significantly reduces the ability to resist erosion when environmental pressure increases. When considering the type of erosion, the existing method is dominated by wind erosion prevention, ignoring the synergistic effects of multiple forces such as wave erosion and high-frequency storms. A unified configuration scheme is difficult to adapt to the characteristics of a multi-dynamic environment, resulting in insufficient wind and wave protection. At the same time, the extensive mode of vegetation configuration in the restoration project leads to excessively high cost investment. Overall, it not only weakens the dynamic adaptability of the dune system, but also limits the long-term improvement of coastal ecological resilience, making it difficult to meet the requirements of economy and sustainability. Summary of the Invention

[0004] The purpose of the present invention is to provide a multi-objective optimization method for sandy coast backshore ecological restoration based on the NSGA-Ⅱ algorithm in order to balance multiple factors, improve the adaptability of the multi-dynamic environment, and thus optimize the effect of wind and wave protection.

[0005] The purpose of the present invention can be achieved by the following technical solutions:

[0006] A multi-objective optimization method for sandy coastal backshore ecological restoration based on the NSGA-Ⅱ algorithm comprises the following steps:

[0007] S1. Select a damaged sandy coastline and conduct a background survey to calculate the wave run-up value;

[0008] S2. Investigate suitable vegetation and determine the scope of vegetation layout on damaged sandy coasts;

[0009] S3. Replenishing the shoulder width of the beach in different areas of the damaged sandy coast and replenishing the artificial sand dunes, wherein the elevation of the shoulder top during the replenishment is determined based on the wave run-up value;

[0010] S4. Select dominant vegetation and calculate its wind erosion prevention efficiency and wave erosion prevention efficiency;

[0011] S5. Construct a multi-objective optimization function and constraint conditions for sandy coastal backshore ecological restoration based on wind erosion prevention efficiency and wave erosion prevention efficiency;

[0012] S6. Solve the multi-objective optimization function based on the NSGA-II algorithm to obtain the optimal vegetation configuration solution set;

[0013] S7. Based on actual conditions, select the best vegetation configuration scheme from the vegetation configuration scheme set within the vegetation arrangement range for planting;

[0014] S8. Detecting vegetation data after planting, and starting a replanting procedure when the survival rate of the vegetation is lower than a threshold.

[0015] Furthermore, the specific steps of calculating the wave run-up value are:

[0016] Analysis of foreshore slope β on damaged sandy coasts f and deep-water wavelength, calculate the Iribarren number ξ, and determine the wave runup value for a 2% exceedance probability based on the Iribarren number ξ.

[0017] Furthermore, the Iribarren number ξ is:

[0018]

[0019] Among them, L0 is the deep water wavelength and H0 is the deep water wave height.

[0020] Furthermore, the wave run-up value is:

[0021]

[0022] Among them, R 2％ The wave height for a 2% exceedance probability.

[0023] Furthermore, the beach shoulder top elevation is:

[0024] H B =R 2％ +H

[0025] Among them, H B is the elevation of the beach shoulder top, and H is the design high water level for the return period.

[0026] Furthermore, the multi-objective optimization function for sandy coast backshore ecological restoration is:

[0027]

[0028] Among them, P is the cost of the vegetation configuration method adopted, Q is the amount of beach shoulder and sand dune erosion under storm and normal wind, Q w0 and Q s0 They represent the benchmark erosion per unit time during normal wind and wave periods and storm periods on bare land, η wi and η si Represent the wind erosion prevention efficiency and wave erosion prevention efficiency respectively, t w and t s are the time weights of wind-dominated and storm-dominated time, A i and S i Respectively represent the area of ​​vegetation planting and the comprehensive cost per unit area, i = 1, 2, 3 represent different types of vegetation, namely grass, shrubs and trees, respectively; A represents the area of ​​the target restoration area;

[0029] The decision variables are the areas A1, A2 and A3 of different types of vegetation configurations.

[0030] Furthermore, the constraints are:

[0031]

[0032] Among them, η wmin and η smin It is the efficiency threshold of overall protection against wind and waves.

[0033] Furthermore, the specific steps of S6 are:

[0034] The population is initialized, and individual genes represent the area proportions of three types of vegetation:

[0035]

[0036] The current population is sorted according to the cost of the vegetation configuration method adopted and the amount of beach shoulder and sand dune erosion under storm and normal wind, and the frontier level is divided and the crowding degree is calculated;

[0037] A new population is obtained by using simulated binary crossover and polynomial mutation;

[0038] Merge the current population and the new population, and select the top N individuals as the next generation population according to the frontier level and crowding degree;

[0039] The non-dominated solution set is obtained by iterative calculation. The non-dominated solution set is a set of optimal vegetation configuration schemes. Each solution in the non-dominated solution set corresponds to a set of vegetation configuration schemes (A1, A2, A3) and an objective function value (P, Q).

[0040] Furthermore, if there are out-of-bounds individuals in the new population, the out-of-bounds individuals are normalized.

[0041] Furthermore, the specific steps of S7 are:

[0042] For strictly protected shore sections, the optimal vegetation configuration scheme with the least erosion of beach shoulders and dunes under storm and normal wind conditions is selected from the vegetation configuration scheme set within the vegetation layout range and planted;

[0043] For general protected bank sections, the vegetation configuration scheme with the lowest cost is selected from the vegetation configuration scheme set within the vegetation layout range and planted as the optimal vegetation configuration scheme.

[0044] (1) Previous studies have mostly focused on either windbreak or wavebreak effectiveness. This paper, however, proposes a multi-objective optimization scheme that comprehensively considers windbreak and wavebreak efficiency and overall cost. By weighing multiple factors, it achieves the synergistic maximization of economic and ecological benefits. This innovative approach provides a new perspective and solution for sandy coastal ecological restoration, improving windbreak and wavebreak effectiveness.

[0045] (2) This paper introduces the advanced NSGA-II multi-objective evolutionary algorithm and successfully calculates the Pareto frontier solution set. This set provides a rich set of ecological restoration options for sandy coasts with different functional requirements and protection levels. Users can flexibly select the most appropriate solution based on specific scenarios, greatly improving the adaptability and flexibility of ecological restoration.

[0046] (3) The present invention attaches great importance to the sustainability of ecological restoration. Through the organic combination of artificial beach maintenance and vegetation reconstruction, not only the width of the beach shoulder is widened, but also stable artificial sand dunes are constructed, providing a long-term sand source for the coast. In addition, the present invention also introduces a dynamic monitoring mechanism. By regularly monitoring the vegetation survival rate and erosion contribution, the restoration strategy can be adjusted in a timely manner to ensure the long-term stability of the ecological restoration effect and the resilience of the ecosystem, providing a strong guarantee for the sustainable development of the sandy coast. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 is a flow chart of the present invention;

[0048] Figure 2 A schematic diagram of a coast profile of the composite action-dominated optimized configuration of the present invention;

[0049] Figure 3 A top view of an example of a vegetation configuration of the present invention;

[0050] Figure 4 A plan view of a diamond grid according to the present invention;

[0051] Figure 5 It is a structural diagram of the test device of the present invention;

[0052] In the figure, 1. Original profile; 2. Beach shoulder sand replenishment; 3. Sand dune sand replenishment; 4. Herbaceous plant belt; 5. Shrub belt. DETAILED DESCRIPTION

[0053] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0054] Constructing a zone-adapted vegetation configuration system to optimize the matching of plant functional traits with dominant dynamic stresses, strengthen the backshore system's synergistic resistance to multiple erosion factors, and simultaneously balance cost-effectiveness to achieve sustainable economic and environmental development of ecological restoration projects has become a key challenge that urgently needs to be addressed. Therefore, the present invention belongs to the field of coastal ecological restoration technology and specifically proposes a multi-objective optimization method for sandy coastal backshore ecological restoration based on the NSGA-II algorithm. This method obtains historical data and vegetation distribution of the target shore section through remote sensing monitoring and field measurements, and demarcates the vegetation layout boundary by combining sediment grading curves, wave parameters, and meteorological data. Based on the historical data and vegetation distribution, a physical or numerical model is established to determine the wind and wave protection efficiency of the selected vegetation. A multi-objective optimization model is established based on artificial beach construction, widening the beach shoulder, and constructing sand dunes. With the optimization objective of minimizing the amount of backshore erosion under storms and normal winds and the cost of vegetation configuration, the NSGA-II algorithm is used to generate a Pareto frontier solution set, achieving dynamic adaptation of vegetation type, area, and erosion dynamics. This approach combines artificial beach reclamation with widening of the beach shoulder and construction of sand dunes, optimizing restoration results through regular monitoring and dynamic maintenance. This approach addresses the problem of traditional designs that only consider wind action alone and fail to comprehensively account for the synergistic effects of multiple erosion factors. By balancing economic efficiency with protective effectiveness, it significantly enhances the stability, ecological resilience, and long-term protective effectiveness of the backshore system, consolidating the effectiveness of artificial beach reclamation and reducing maintenance costs.

[0055] The method comprises the following steps. Figure 1 As shown:

[0056] S1. Select a damaged sandy coastline and conduct a background survey to calculate the wave run-up value;

[0057] S2. Investigate suitable vegetation and determine the scope of vegetation layout on damaged sandy coasts;

[0058] S3. Replenishing the shoulder width of the beach in different areas of the damaged sandy coast and replenishing the artificial sand dunes, wherein the elevation of the shoulder top during the replenishment is determined based on the wave run-up value;

[0059] S4. Select dominant vegetation and calculate its wind erosion prevention efficiency and wave erosion prevention efficiency;

[0060] S5. Construct a multi-objective optimization function and constraint conditions for sandy coastal backshore ecological restoration based on wind erosion prevention efficiency and wave erosion prevention efficiency;

[0061] S6. Solve the multi-objective optimization function based on the NSGA-II algorithm to obtain the optimal vegetation configuration solution set;

[0062] S7. Based on actual conditions, select the best vegetation configuration scheme from the vegetation configuration scheme set within the vegetation arrangement range for planting;

[0063] S8. Detecting vegetation data after planting, and starting a replanting procedure when the survival rate of the vegetation is lower than a threshold.

[0064] The specific steps are:

[0065] S1. Select a damaged sandy coastline and conduct a baseline survey.

[0066] Damaged sandy coastlines with narrow abutments (<20m wide) and vegetation coverage below 30% were selected as restoration targets. High-precision topographic mapping of the coastline was conducted using drone remote sensing and RTK-GPS. The boundaries of the abutments, dunes, and backshore areas were delineated, and a digital elevation model (DEM) was constructed with a spatial resolution of at least 0.5m x 0.5m.

[0067] Sampling points were arranged at equal intervals along the cross-shore direction (from the low tide line to the top of the dune). A 0.3m×0.3m square area was defined at each sampling point, and sand samples were collected from the surface layer at a depth of 0.05 to 0.2m. The sediment particle size distribution was determined by sieving or hydrolysis, and the gradation curve was drawn to calculate the median particle size D. 50 (Unit: mm), clarify the particle size characteristics of natural sediment in the target shore section and provide a particle size matching basis for artificial sand replenishment.

[0068] The historical data of the target shore section for the past 30 years were integrated, including meteorological data (annual average wind speed (m / s), prevailing wind direction (°) and extreme wind speed (50-year return period, m / s)), wave parameters (annual average value of significant wave height (m) and 90% and 99% percentile values, deep-water wave height H0 (m) and wave period T0 (s)) and tide data (astronomical tide level (average high tide level, average low tide level) and storm surge value (design high water level H with a 20-year return period, unit: m)).

[0069] Based on the foreshore slope β f (average slope from low tide line to top of beach shoulder) and deep water wavelength (g=9.81m / s 2 ), calculate the Iribarren number ξ:

[0070]

[0071] Determine the wave height R for a 2% exceedance probability based on the ξ value 2％ (Unit: m):

[0072]

[0073] S2. Survey suitable vegetation and determine the range of vegetation placement. Use a combination of line transects and sampling methods to survey native vegetation communities in the backshore area. Line transect layout: Set parallel lines at intervals of ≥100 m perpendicular to the coast, covering the back edge of the beach shoulder to the front edge of the dunes. Sample plot specifications: For trees and large shrubs: 10 m × 10 m plots, record diameter at breast height, crown width, and density; for shrubs and tall herbs: 5 m × 5 m plots, calculate cover and plant height; for short herbs: 1 m × 1 m plots, measure biomass and root depth.

[0074] Simultaneously measure the soil physical and chemical properties (pH value, salt content, organic matter content) and micro-topography parameters (slope, elevation), and screen for wind-resistant, salt-tolerant, and drought-tolerant dominant species (such as Carex serrata, Triticum aestivum, and Amorpha fruticosa). 2％ The location where native vegetation grows is used as the front elevation boundary of vegetation arrangement to prevent wave over-top erosion, that is, native vegetation can grow on dry beaches under normal waves.

[0075] S3. Artificial beach construction builds the foundation for backshore ecological restoration. Figure 2 As shown, including widening the beach shoulder width (L B ) to enhance the coastal buffer capacity and construct artificial sand dunes (L D ) to replenish sand dunes to protect coastal facilities from extreme storms and provide sand sources for the coast. B ) and elevation (H B ) Design parameters. Coastal tourism and leisure area: L B = 20-30m, to meet the needs of tourists for activities and landscape; beach sports and large-scale activity area: L B ≥50m, providing sufficient buffer space. Figure 2 Middle, original profile 1; beach shoulder sand filling 2; dune sand filling 3; herbaceous plant belt 4; shrub 5. Beach shoulder top elevation H B The wave height R of the 2% exceedance probability 2％ Determine by superimposing it with the design high water level H with a return period of 20 years:

[0076] H B =R 2％ +H

[0077] Selection of sand replenishment particle size and median particle size D of natural beach sand 50Similar or slightly coarser sand materials are used to ensure the hydrodynamic compatibility between the sand replenishment body and the original beach shoulder.

[0078] S4. Determine the protective efficiency of dominant vegetation. Based on the results of the preliminary investigation, select plants that are wind-resistant, soil salt-resistant, salt-fog-resistant, drought-resistant, and barren-resistant. Select 1-2 dominant species for each type of vegetation (herbs, shrubs, trees, etc.), and conduct numerical simulations or physical model tests according to the coastal profile designed for the restoration project. The test conditions include typical wind speeds, no vegetation under extreme storms, and coastal profiles with vegetation arranged under two types of power. Measure the amount of beach shoulder and sand dune sediment erosion under each condition, Q w0 and Q s0 They represent the benchmark erosion per unit time during the period of normal wind and waves on bare land and during storms, Q wi and Q si (i = 1, 2, 3 represent grass, shrubs and trees respectively) represents the baseline erosion per unit time of a single vegetation during normal wind and wave periods and during storms. Obtain the wind erosion prevention efficiency η of each type of vegetation wi , and the anti-wave erosion efficiency η si .

[0079]

[0080] S5. Determine the multi-objective optimization function and constraints for sandy coast backshore ecological restoration. The objective function is the goal to be achieved for sandy coast ecological restoration, including minimizing the amount of beach shoulder and dune erosion Q under storm and normal wind conditions, and minimizing the cost P of the vegetation configuration method adopted:

[0081]

[0082] Among them, A i and S i They represent the area of ​​vegetation planting (i=1, 2, 3 represent grass, shrubs and trees respectively) and the comprehensive cost per unit area (including planting cost, labor cost and multi-year maintenance cost, unit: m 2 );t w and t s They are the time weights dominated by normal winds and storms, respectively. The normal wind time weight is determined by the wind speed over many years and the starting wind speed of the corresponding particle size (for general beaches, the starting wind speed at a height of 2m is greater than 6m / s), specifically the proportion of wind speeds greater than the starting wind speed during the measurement time; the storm time weight is determined by the proportion of the total duration of storms over many years to the selected total time.

[0083] Decision variables are used to form different optimization schemes, including the area of ​​different types of vegetation configurations. Based on the feasibility of the project and ecological needs, the following constraints are set: the total planting area is equal to the target restoration area area A, and the area of ​​each type of vegetation is non-negative. The overall wind and wave protection efficiency of the vegetation is not less than the minimum threshold η.wmin and η smin As a constraint, to obtain an engineering feasible solution:

[0084]

[0085] S6. Multi-objective optimization solution based on NSGA-II algorithm. NSGA-II algorithm (non-dominated sorting genetic algorithm) is used for multi-objective optimization to obtain the Pareto frontier solution set. The general solution process is as follows:

[0086] Population initialization. Set the number of individuals in the population N, and the decision variables are vegetation areas A1, A2, and A3; use real number coding, and individual genes represent the area proportions of the three types of vegetation.

[0087] Non-dominated sorting and crowding calculation. Based on the dual objective values ​​(total cost P and total erosion Q), the population is quickly non-dominated sorted, the frontier is graded, and the crowding distance is calculated to assess the distribution density of solutions on the frontier, avoiding local aggregation and ensuring solution diversity.

[0088] Genetic operation design. Using simulated binary crossover, with probability p c and distribution index η c , perform gene recombination on the parent individuals to retain the dominant characteristics. Apply polynomial mutation, mutation probability p m , introduce the disturbance amplitude η m To enhance population diversity. Normalize the individuals that cross the boundary to ensure ∑A i =A;

[0089] Elite retention and iteration termination. The parent and offspring populations (a total of 2N individuals) are merged, and the top N individuals are selected for the next generation based on frontier level and crowding, maintaining a constant population size. Termination conditions are set as either a maximum number of iterations T or an improvement rate of <1% for the optimal solution over 10 consecutive generations. A set of non-dominated solutions is output, each corresponding to a set of vegetation configurations (A1, A2, A3) and an objective function value (P, Q).

[0090] S7. Vegetation configuration scheme decision and zoning adaptation. Based on the Pareto front solution set generated by the NSGA-II algorithm, the vegetation configuration parameters (herb area A1, shrub area A2, tree area A3) and the objective function value (total cost P, erosion amount Q) corresponding to the non-dominated solution are extracted to form a multi-objective optimization solution library. According to the protection level and use requirements of the target bank section, the adaptation scheme is selected from the solution set: for the strictly protected bank section (such as the core ecological zone and the front of important infrastructure), the erosion minimization scheme (Q min ); For general protected shore sections (such as tourist and leisure areas): Under the premise of meeting the protection efficiency threshold, select the lowest cost solution (Pmin );

[0091] According to the micro-topographic features (slope, elevation) of the repair area, vegetation is laid out using a diamond grid method (see Figure 4 ) : the back edge of the berm and the front edge of the dune: mainly herbaceous, supplemented by shrubs, forming a wave dissipation buffer zone;

[0092] The top of the dune: using a mixture of grass and shrubs to enhance root anchoring and canopy wind interception synergy;

[0093] If the back of the dune faces the road, a protective forest of trees can be planted.

[0094] S8. Construction layout and planting operation.

[0095] Material transportation: use closed constant-temperature trucks to transport grass seeds and seedlings to avoid mechanical damage and physiological dehydration; remove berm debris (stones, garbage), and level the dune slope to the designed slope.

[0096] Line positioning: use RTK-GPS to lay out according to the design drawing, and pull nylon ropes to mark the planting grid;

[0097] Herbaceous planting: evenly spread the grass seeds after soil loosening, cover the soil and pour water thoroughly;

[0098] Shrub planting: dig transplanting holes, plant shrub seedlings, backfill and compact the soil, and pour root-fixing water.

[0099] Tree planting: dig planting holes, lay geotextile at the bottom, pad the soil, fill the soil, and pour root-fixing water.

[0100] S9. Post-monitoring and dynamic maintenance.

[0101] Vegetation monitoring: 3 months, 6 months, and 12 months after planting, sample units of 1m x 1m (herbaceous), 5m x 5m (shrubs), and 10m x 10m (trees) are counted; collect data such as plant height, diameter at breast height, and vegetation coverage.

[0102] Landform monitoring: use RTK-GPS to measure the vertical length of the bank.

[0103] Regularly observe the vegetation survival rate and the stability of the dune. If the survival rate is less than 80% or the dune is continuously damaged, the reseeding program is started.

[0104] The overhead view of the vegetation configuration example of the present application is shown in Figure 3 .

[0105] Compared with the prior art, the present application has the following beneficial effects:

[0106] (1) This paper quantitatively analyzes the wind and wave protection efficiency of typical dominant vegetation by combining physical experiments and numerical simulations. This scientific, empirical approach effectively overcomes the uncertainty inherent in previous empirical determinations, provides a solid and reliable theoretical basis for the development of ecological restoration plans, and significantly improves the scientific nature and accuracy of these plans.

[0107] (2) Previous studies have mostly focused on either windbreak (e.g., patent CN 111967145 A) or wavebreak (e.g., patent CN 119096834 A). This paper, however, proposes for the first time a multi-objective optimization scheme that comprehensively considers windbreak and wavebreak efficiency and overall cost. By weighing multiple factors, it achieves the synergistic maximization of economic and ecological benefits. This innovative approach provides a new perspective and solution for sandy coast ecological restoration.

[0108] (3) This paper introduces the advanced NSGA-II multi-objective evolutionary algorithm and successfully calculates the Pareto frontier solution set. This set provides a rich set of ecological restoration options for sandy coasts with different functional requirements and protection levels. Users can flexibly select the most appropriate solution based on specific scenarios, greatly improving the adaptability and flexibility of ecological restoration.

[0109] (4) The present invention attaches great importance to the sustainability of ecological restoration. Through the organic combination of artificial beach maintenance and vegetation reconstruction, not only the width of the beach shoulder is widened, but also stable artificial sand dunes are constructed, providing a long-term sand source for the coast. In addition, the present invention also introduces a dynamic monitoring mechanism. By regularly monitoring the vegetation survival rate and erosion contribution, the restoration strategy can be adjusted in a timely manner to ensure the long-term stability of the ecological restoration effect and the resilience of the ecosystem, providing a strong guarantee for the sustainable development of the sandy coast.

[0110] The protective effects of different grass-shrub ratios were simulated through wave flume tests to verify the effectiveness of the vegetation configuration scheme in the Pareto solution generated by the NSGA-II algorithm, providing empirical data for the optimization model.

[0111] A typical beach-dune system was established in a wave tank, and herbs and shrubs of different proportions were arranged on the windward slope and top of the dunes to evaluate the protective effect of different backshore vegetation configurations on the dunes under extreme storm surges. The experiment used a normal scale model with a geometric scale of 1:10. The herbaceous plant (marine wheat) was simulated using plastic material and tied to a flexible cylinder with a diameter of 3mm. The length exposed above the ground was 5cm and the bottom was buried 25cm deep to simulate the underground root system. The cylinder was fixed on an acrylic board and planted at a density of 1000 plants / m 2The shrubs (Amorpha fruticosa) are plastic simulated plants, including branches and leaves, fixed in a hollow rigid acrylic tube with an outer diameter of 10mm. The tube is also fixed on an acrylic board with a height of 15cm above the ground. The density is 500 plants / m 2 , with a spacing of 6 cm. The test arrangement is as follows Figure 5 The test results are shown in Table 1.

[0112] The three working conditions represent that the top of the hill is entirely covered with herbaceous plants, the width ratio of herbaceous plants to shrubs is about 2:1, and 1:1, the water depth is 0.53m, the incident wave height is 0.19m, the duration is 1600s, and the situation of continuous storm waves is simulated. The waves propagate to the right from the position of the wave maker, the slope below the still water level of the coast is 1:10, the vertical length of the beach shoulder is 0.8m, the dune slope is set to 1:3, the hilltop elevation is 0.7m, its vertical length is 1.2m, and the back of the dune is supported by a stainless steel plate. The vegetation layout range is as follows Figure 5 The shoreline position is the intersection of the still water level and the coast, with an initial position of 6 m. That is, the eroded shoreline = the shoreline after wave action – the initial shoreline, and the vegetation effect = (vegetation eroded shoreline – bare beach eroded shoreline) / bare beach eroded shoreline × 100%.

[0113] Table 1 Test results under different test conditions

[0114]

[0115] Table 1 shows that different grass-shrub ratios significantly affect the coastal protection effects. Both pure grass (Condition 1) and a 2:1 grass-shrub ratio (Condition 2) effectively mitigated shoreline erosion, with protection efficiencies of 20.5% and 24.5%, respectively. Condition 3 (1:1 grass-shrub ratio) resulted in the same amount of shoreline erosion as the bare beach, but the duration of protection was extended from less than 800 seconds in the bare beach to over 1200 seconds, a 50% increase. A 2:1 grass-shrub ratio achieved optimal protection, maintaining the dense, wave-dissipating properties of the herb layer while enhancing structural stability through the shrub root system. A 1:1 grass-shrub ratio, while weakening storm resistance, prolonged the protection period and enhanced the aboveground canopy.

[0116] Table 2 Simulation results of windbreak performance under different grass-shrub width ratios

[0117]

[0118] To evaluate the effectiveness of different grass-shrub belt width ratios in improving the backshore wind environment, a numerical backshore wind model was developed. The herb height in the model was set at 0.5 m, the shrub height was 1.5 m, and a porous media model was used to simulate the vegetation belt. The wind protection performance of each operating condition was evaluated by defining the sheltered area enclosed by the contour line where the inlet velocity was reduced to 70%. The percentage increase in sheltered area compared to a single herb belt was calculated as: (sheltered area under the operating condition – sheltered area under a single herb belt) / sheltered area under a single herb belt × 100%. The results are shown in Table 2.

[0119] The results showed that the sheltered area increased gradually with the increase of shrub ratio. When the grass-shrub ratio was 1:2, the sheltered area was the largest (99.68m 2 Increasing the proportion of shrubs significantly improves the windbreak performance of the backshore, especially in sections of the shoreline prone to wind erosion. A grass-shrub ratio of 1:2 is recommended.

[0120] This invention significantly improves coastal protection effectiveness by optimizing the grass-shrub width ratio. A grass-shrub ratio of 2:1 provides optimal wave protection, while a grass-shrub ratio of 1:2 provides optimal wind protection. Coastal restoration projects should comprehensively consider the design of vegetation community structures, balancing immediate wave-breaking capacity with system resilience to impact, to achieve a synergistic improvement in ecological function and project benefits.

[0121] The above describes in detail the preferred embodiments of the present invention. It should be understood that those skilled in the art can make numerous modifications and variations based on the concepts of the present invention without inventive effort. Therefore, any technical solutions that can be derived by those skilled in the art through logical analysis, reasoning, or limited experimentation based on the concepts of the present invention and the prior art should be within the scope of protection defined by the claims.

Claims

1. A multi-objective optimization method for sandy coastal backshore ecological restoration based on the NSGA-Ⅱ algorithm, characterized in that: The method comprises the following steps: S1. Select a damaged sandy coastline and conduct a background survey to calculate the wave run-up value; S2. Investigate suitable vegetation and determine the scope of vegetation layout on damaged sandy coasts; S3. Replenishing the shoulder width of the beach in different areas of the damaged sandy coast and replenishing the artificial sand dunes, wherein the elevation of the shoulder top during the replenishment is determined based on the wave run-up value; S4. Select dominant vegetation and calculate its wind erosion prevention efficiency and wave erosion prevention efficiency; S5. Construct a multi-objective optimization function and constraint conditions for sandy coastal backshore ecological restoration based on wind erosion prevention efficiency and wave erosion prevention efficiency; S6. Solve the multi-objective optimization function based on the NSGA-II algorithm to obtain the optimal vegetation configuration solution set; S7. Based on actual conditions, select the best vegetation configuration scheme from the vegetation configuration scheme set within the vegetation arrangement range for planting; S8. Detecting vegetation data after planting, and starting a replanting procedure when the survival rate of the vegetation is lower than a threshold.

2. The multi-objective optimization method for sandy coast backshore ecological restoration based on the NSGA-II algorithm according to claim 1, characterized in that: The specific steps of calculating the wave run-up value are: Analysis of foreshore slope β on damaged sandy coasts f and deep-water wavelength, calculate the Iribarren number ξ, and determine the wave runup value for a 2% exceedance probability based on the Iribarren number ξ.

3. The multi-objective optimization method for sandy coast backshore ecological restoration based on the NSGA-II algorithm according to claim 2 is characterized in that: The Iribarren number ξ is: Among them, L0 is the deep water wavelength and H0 is the deep water wave height.

4. The multi-objective optimization method for sandy coast backshore ecological restoration based on NSGA-II algorithm according to claim 3 is characterized in that: The wave run-up values ​​are: Among them, R 2％ The wave height for a 2% exceedance probability.

5. The multi-objective optimization method for sandy coast backshore ecological restoration based on NSGA-II algorithm according to claim 4 is characterized in that: The beach shoulder top elevation is: H B =R 2％ +H Among them, H B is the elevation of the beach shoulder top, and H is the design high water level for the return period.

6. The multi-objective optimization method for sandy coast backshore ecological restoration based on NSGA-II algorithm according to claim 1, characterized in that: The multi-objective optimization function for sandy coast backshore ecological restoration is: Among them, P is the cost of the vegetation configuration method adopted, Q is the amount of beach shoulder and sand dune erosion under storm and normal wind, Q w0 and Q s0 They represent the benchmark erosion per unit time during normal wind and wave periods and storm periods on bare land, η wi and η si Represent the wind erosion prevention efficiency and wave erosion prevention efficiency respectively, t w and t s are the time weights of wind-dominated and storm-dominated time, A i and S i Respectively represent the area of ​​vegetation planting and the comprehensive cost per unit area, i = 1, 2, 3 represent different types of vegetation, namely grass, shrubs and trees, respectively; A represents the area of ​​the target restoration area; The decision variables are the areas A1, A2 and A3 of different types of vegetation configurations.

7. The multi-objective optimization method for sandy coast backshore ecological restoration based on NSGA-II algorithm according to claim 6, characterized in that: The constraints are: Among them, η wmin and η smin It is the efficiency threshold of overall protection against wind and waves.

8. The multi-objective optimization method for sandy coast backshore ecological restoration based on NSGA-II algorithm according to claim 7, characterized in that: The specific steps of S6 are: The population is initialized, and individual genes represent the area proportions of three types of vegetation: The current population is sorted according to the cost of the vegetation configuration method adopted and the amount of beach shoulder and sand dune erosion under storm and normal wind, and the frontier level is divided and the crowding degree is calculated; A new population is obtained by using simulated binary crossover and polynomial mutation; Merge the current population and the new population, and select the top N individuals as the next generation population according to the frontier level and crowding degree; The non-dominated solution set is obtained by iterative calculation. The non-dominated solution set is a set of optimal vegetation configuration schemes. Each solution in the non-dominated solution set corresponds to a set of vegetation configuration schemes (A1, A2, A3) and an objective function value (P, Q).

9. The multi-objective optimization method for sandy coast backshore ecological restoration based on NSGA-II algorithm according to claim 8, characterized in that: If there are out-of-bounds individuals in the new population, the out-of-bounds individuals will be normalized.

10. The multi-objective optimization method for sandy coast backshore ecological restoration based on NSGA-II algorithm according to claim 9, characterized in that: The specific steps of S7 are: For strictly protected shore sections, the optimal vegetation configuration scheme with the least erosion of beach shoulders and dunes under storm and normal wind conditions is selected from the vegetation configuration scheme set within the vegetation layout range and planted; For general protected bank sections, the vegetation configuration scheme with the lowest cost is selected from the vegetation configuration scheme set within the vegetation layout range and planted as the optimal vegetation configuration scheme.

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