A flood-avoiding transfer multi-objective optimization analysis method considering road congestion constraints

Abstract

The application discloses a kind of flood-avoiding transfer multi-objective optimization analysis method under the consideration of road congestion constraint, including constructing road network undirected graph;The shortest distance of each node to the settlement area is calculated;Ant colony and road network parameter are initialized, the pheromone concentration and road network congestion degree of last round training are reserved;All ant colonies are traversed, if not traversed, let k=k+1, all ants in ant colony k are traversed again;For each ant, the next node is selected according to the heuristic function, pheromone concentration and congestion degree, until it reaches the settlement area or empty node;Determine whether to meet the training termination condition, if meet, output pheromone concentration, settlement area matching result, and carry out result diagnosis.The application shortens transfer time and reduces transfer batch based on ant colony algorithm framework as optimization target, solves the multi-objective optimization problem of transfer area and settlement area matching and path selection under the constraint of road congestion.

Description

Technical Field

[0001] This invention relates to the field of flood emergency response and disaster avoidance technology, and in particular to a multi-objective optimization analysis method for flood avoidance and relocation considering road congestion constraints. Background Technology

[0002] Flood relocation problems typically involve matching multiple relocation areas to multiple resettlement areas and path analysis. In practice, multiple optimization objectives must be considered, such as minimizing relocation time, reducing the number of relocation batches, and simplifying the relocation plan as much as possible. They also involve various constraints, such as road congestion, road safety during floods, and the capacity of resettlement sites, making it a complex multi-objective optimization problem under complex constraints. Existing flood relocation analysis techniques often break it down into two stages: first, matching relocation areas and resettlement areas; then, finding the shortest route from the relocation area to the resettlement area based on road network connectivity and shortest path algorithms using computer graph theory. These methods rarely consider the reduction in relocation efficiency caused by traffic congestion, or they may set congestion thresholds based on road grade, cutting off roads when traffic exceeds the threshold and forcing subsequent relocations to choose alternative, suboptimal routes. These methods require manually defining the relocation order or conducting dynamic relocation process simulations based on actual vehicle speeds and departure times, resulting in low computational efficiency. Furthermore, in practice, changes in relocation batches and departure times will alter the optimal path, making it difficult to guide practical application.

[0003] From the perspective of practical flood relocation needs, the number of relocation batches should be minimized to reduce the difficulty of organization and coordination. Ideally, the number of resettlement areas corresponding to the same relocation area should be as small as possible, with all relocations ideally occurring in the same resettlement area. On the other hand, congestion must be considered when selecting resettlement areas, as the number of roads leading to these areas is often limited in practice. Once resettlement areas are matched, even considering road congestion, the optimization space is small. These requirements result in a very large search space for solving this problem. Strictly speaking, the optimal solution requires traversing all allocation schemes from each relocation area to each resettlement area, listing all possible path combinations, calculating the congestion degree under various allocation schemes and path combinations, and calculating the relocation time for all possible path combinations and personnel allocation combinations based on the congestion degree. Then, the non-dominated solution for relocation time and batches is selected. To address the issue that existing flood relocation analysis methods mainly consider road connectivity and shortest paths, lacking analysis of road capacity and congestion degree, the path analysis results often deviate from reality. Therefore, a multi-objective optimization analysis method for flood relocation that considers road congestion constraints is needed. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-objective optimization analysis method for flood avoidance and relocation under the constraint of road congestion.

[0005] To achieve the above objectives, the present invention is implemented according to the following technical solution:

[0006] This invention includes the following steps:

[0007] Construct an undirected graph of the road network;

[0008] Calculate the shortest distance from each node to the resettlement area;

[0009] Initialize the ant colony and road network parameters, retaining the pheromone concentration and road network congestion from the previous training round;

[0010] Iterate through all ant colonies. If the colony is not completely traversed, set k = k + 1 and then iterate through all ants in colony k.

[0011] For each ant, the next node is selected based on the heuristic function, pheromone concentration, and crowding, until the ant reaches the resettlement area or an empty node.

[0012] Determine if pathfinding is successful. If successful, record the ant's route, update the pheromone concentration of ant colony k on the route and the congestion of the route; determine if the training termination condition is met. If met, output the pheromone concentration, the matching result of the resettlement area, and perform result diagnosis.

[0013] Furthermore, when constructing the undirected graph of the road network, the weights of nodes and edges are abstracted based on the actual geographical road network structure to reflect the road traffic attributes. Multiple nodes in the road network are divided into four subsets: a transfer zone, intermediate nodes, and a resettlement zone. The number of people to be transferred in the transfer zone is proportionally represented by the number of ants in the corresponding ant colony, and the remaining capacity in the resettlement zone is represented by the number of ants that can be accommodated. Edge attributes are set, including weight, capacity, length, and congestion level. The road weight represents the pheromone concentration, the road length represents heuristic information, and the road congestion level represents the number of ants that passed through the road in the previous round and the road's traffic capacity.

[0014] Furthermore, Dijkstra's algorithm is used to calculate the shortest distance from each node to the resettlement area, and the minimum distance is stored in the node's attributes for use in calculating the heuristic function. The formula for calculating the pathfinding process of a single ant is as follows:

[0015]

[0016] ρ ij =min_dis(i) / (min_dis(j)+Edge ij )

[0017] In the formula, for any ant, the probability of it moving from node i to its neighboring node j is calculated, where j belongs to the set of nodes the ant has not visited, and P... ijs θ represents the probability that an ant in the s-th transfer zone chooses the i-j route at the i-th node.ijs P represents the pheromone concentration left by the ants after the (t-1)th iteration on this route. ijs As a heuristic function, min_dis(i) represents the shortest distance from the i-th node to the resettlement area, and Edge... ij Represents the distance from node i to j, when P ijs A value greater than 1 indicates that moving from node i to node j will bring the node closer to the resettlement area, and vice versa. This indicates the level of congestion on the road in the previous round, and is equal to the total number of ants (crowd) that should have crossed the road in the previous round divided by the maximum capacity of the road.

[0018] Furthermore, the heuristic function combines the remaining distance from the node to the resettlement area with the road network congestion, making ants tend to choose nodes that are generally closer to the resettlement area.

[0019] Furthermore, the pheromone concentration and road network congestion are dynamically adjusted and updated based on the ant path length and preset update rules. After each round of training, the road network parameters weight and crowd are updated. The weight of each road is a vector of length 5. The formula for updating the pheromone concentration is as follows: weight ij (t)=[εθ ij1 (t-1)+Δθ ij1 ,…,εθ ij5 (t-1)+Δθ ij5 ] T

[0020]

[0021] Where ε is the evaporation rate of the pheromone, set to 0.8, A represents the set of all ants in ant colony s that successfully reach the resettlement area and complete the pathfinding, and La represents the total distance traveled by ant a.

[0022] The training termination condition, after multiple training rounds, is the rate of change in the matching results of the transfer and resettlement areas between the current and previous rounds. The calculation method is shown in the following formula:

[0023]

[0024] Where m0ij represents the number of ants that moved from transfer zone i to resettlement zone j in the previous training round, and m1ij represents the result of this training round. Training can be stopped when the rate of change ΔM is less than 1%.

[0025] The beneficial effects of this invention are:

[0026] This invention is a multi-objective optimization analysis method for flood avoidance and relocation under the constraint of road congestion. Compared with the prior art, this invention has the following technical advantages:

[0027] This invention addresses the multi-objective optimization problem of matching transfer areas and resettlement areas and selecting routes under road congestion constraints by using the ant colony algorithm framework to shorten transfer time and reduce transfer batches as optimization objectives. Attached Figure Description

[0028] Figure 1 This is the overall technical roadmap of the multi-objective optimization analysis method for flood avoidance and relocation under the constraint of road congestion, as described in this invention.

[0029] Figure 2 This is a schematic diagram of the road network in an embodiment of the present invention;

[0030] Nodes 1-5 are transfer units, nodes 13-16 are resettlement units, and the others are intermediate nodes. Road length is in kilometers.

[0031] Figure 3 This is the road weight map of transfer unit 1 in the embodiment of the present invention;

[0032] Figure 4 This is the road weight map of transfer unit 2 in the embodiment of the present invention;

[0033] Figure 5 This is the road weight map of transfer unit 3 in the embodiment of the present invention;

[0034] Figure 6 This is the road weight map of transfer unit 4 in the embodiment of the present invention;

[0035] Figure 7 This is the road weight map of transfer unit 5 in the embodiment of the present invention; Detailed Implementation

[0036] The present invention will be further described below through specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0037] like Figure 1 As shown, in this embodiment, the multi-objective optimization analysis method for flood avoidance and relocation considering road congestion constraints of the present invention includes the following steps:

[0038] Data Preparation: Information such as road network data, road capacity, relocation areas, resettlement areas, population in relocation areas, capacity in resettlement areas, and flood inundation extent are integrated into an undirected graph data structure. The nodes of the graph include relocation areas, resettlement areas, and road intersections. Relocation areas and resettlement areas must each contain the elements of the relocated population and the resettlement capacity, respectively. The edges of the graph represent roads, and each edge contains the basic elements of road length and road capacity. The flood inundation extent map is used to identify roads that are flooded and impassable; these roads are directly removed from the edges of the undirected graph.

[0039] Initialize the ant colony, road weights, congestion level, and remaining capacity of the resettlement area. Set the number of ant colonies based on the number of transfer areas; each transfer area corresponds to one ant colony. The number of ants in each colony is proportional to the number of people to be transferred in the transfer area. The remaining capacity of each resettlement area equals its maximum capacity. Add a weight attribute to each edge of the undirected graph. This weight attribute is equivalent to the pheromone concentration in the basic ant colony algorithm. The main difference is that the weight of each edge is a vector, and each element in the vector corresponds to an ant colony, representing the pheromone concentration left by that ant colony on that road. A congestion level attribute is added, equivalent to the total number of ants that passed through that road in the previous ant colony pathfinding round. Since this is the initial round, the congestion level of all roads can be initialized to 1, and the weights of all roads can be set to a vector with each element equal to 0.1 (initializing to 0 can easily lead to numerical calculation errors).

[0040] A multi-ant colony algorithm is used for resettlement area matching and path optimization. The optimization process requires multiple rounds of training. At the beginning of each round, the number of ants in each ant colony, the remaining capacity of each resettlement group, and the road congestion level are initialized, but the road weights are not initialized. The road congestion level from the previous round is saved separately for the current round's calculation. During each round of training, each ant colony sends out one ant in turn to perform pathfinding calculations. If an ant colony has no remaining ants, it is skipped. The training round ends only after all ants in all ant colonies have completed their pathfinding calculations. During the pathfinding process, the road weight represents the pheromone concentration, the road length represents heuristic information, and the road congestion index represents the number of ants that passed through the road in the previous round and the road's capacity. The calculation process is detailed in the specific implementation steps. During the pathfinding process, each ant may encounter a closed loop or reach a resettlement area that is already full, resulting in pathfinding failure. All ants that fail to find their way contribute no weight to the road or congestion level, thus accelerating the convergence speed of the solution.

[0041] The training termination condition is that after each training round, a termination index can be set based on the rate of change between the training results of this round and the previous round. For example, the overall rate of change is required to be less than 1%. The rate of change mainly includes two parts: the rate of change of road weight and the rate of change of resettlement area matching results, that is, the rate of change of the number / proportion of ants assigned to each resettlement area in each transfer area.

[0042] After training is completed, the final results need to be evaluated. First, the number of batches is determined based on the allocation ratio of the resettlement area. Then, the ant colony's movement route is determined based on the road weight. Finally, the maximum transfer time and average transfer time are calculated based on the route length and congestion. Finally, three indicators—number of transfer batches, maximum transfer time, and average transfer time—are provided for user reference.

[0043] With attachment Figure 2 An undirected graph representing the characteristics of the road network is created for the example. This network contains 16 nodes and several edges. The nodes are divided into four subsets: transfer zones (nodes 1-5), intermediate nodes (nodes 6-12), and resettlement zones (nodes 13-16). The number of people to be transferred in each transfer zone is divided by 5 to obtain the number of ants in the corresponding ant colony for that transfer zone. Similarly, the remaining capacity of each resettlement zone is divided by 5 to obtain the number of ants that can be accommodated in the ant colony algorithm. This ratio can be adjusted according to the problem size and computational accuracy requirements. Attributes are set for each edge, including weight, capacity, length, and crowding. The weight is a vector of length 5, corresponding to the pheromone concentration of ant colonies from transfer zone 1 to transfer zone 5. The pheromone concentration of the same ant colony only affects the ant colony itself and does not affect other ant colonies. This ensures that ants from the same colony will follow the same routes and reach the same destination as much as possible, thus reducing the number of transfer batches. Capacity represents the maximum passage capacity of a road, and can be given empirical values ​​based on road speed limits and road levels. The closer the number of ants choosing a particular road is to the capacity, the higher the congestion level and the slower the passage speed. Crowd is the total number of ants choosing a particular road in a given training round. This metric is updated with each training session, so the current round can only influence ants' road choices based on past knowledge—that is, the congestion level of the previous round. Length is the actual length of the road.

[0044] Calculate the shortest path length from each node to the nearest settlement area. Use Dijkstra's algorithm to calculate the shortest path length from each node to all settlement areas, and store the minimum distance in the node's attribute min_dis for use in the heuristic function calculation.

[0045] The formula for calculating the pathfinding process of a single ant is:

[0046]

[0047] ρ ij =min_dis(i) / (min_dis(j)+Edge ij )

[0048] In the formula, for any ant, the probability of it moving from node i to its neighboring node j is calculated, where j belongs to the set of nodes that the ant has not visited. Pijs represents the probability that the ant in the s-th transfer zone chooses the i-j route at node i. θijs represents the pheromone concentration left by the ant on the route after the (t-1)-th iteration. ρijs is the heuristic function. min_dis(i) represents the shortest distance from node i to the resettlement zone. Edgeij represents the distance from node i to j. When ρijs is greater than 1, it means that moving from node i to node j will bring the ant closer to the resettlement zone, and vice versa. Cij(t-1) represents the congestion level of the road in the previous round, which is equal to the total number of ants that should have walked on the road in the previous round (crowd) divided by the maximum capacity of the road.

[0049] The denominator represents the sum of probabilities of all possible paths to the i-th node (excluding already visited nodes), used for normalization. α, β, and γ are the three power exponents of the ant colony algorithm's hyperparameters. They characterize the relative importance of pheromone concentration, heuristic function, and road congestion. Based on the above formula and the roulette wheel algorithm, the next node is selected for the ant until it reaches a resettlement area. If the resettlement area has remaining capacity, the ant has successfully found its way, and the calculation terminates. If the resettlement area is full, or the ant's next node is empty, the pathfinding is considered a failure, and the calculation also terminates. Ants that successfully find their way update the pheromone concentration, while ants that fail do not.

[0050] Update the road network parameters (weight and crowd).

[0051] The matching results of the resettlement areas for the sample data are shown in Table 1. The routes from each transfer area to the resettlement area are as follows: Figures 3 to 7 As shown. Figures 3 to 7 The pheromone concentration of each ant colony on each road is given. Roads with a concentration of 0 will not be selected, thus representing a transfer route map. Table 1 shows that transfer unit 3 still has 50 people who have not been transferred. These people will be directly matched to resettlement area 1 based on the shortest path and available resettlement area principles.

[0052] Table 1 Matching Results of Resettlement Areas

[0053]

[0054]

[0055] The ant colony algorithm may provide a locally optimal solution, making it essential to evaluate the reasonableness of the solution using various metrics. During training, the algorithm does not force all ants to reach the resettlement area; instead, it uses a survival-of-the-fittest approach to ensure the majority of ants do reach it. Therefore, the arrival rate can be used as one indicator of solution reasonableness. It is calculated by dividing the number of ants that reach the resettlement area by the total number of ants. Ants that fail to migrate can be resettled in the nearest resettlement area with available space using the shortest path method. Other metrics include migration batches, total migration time, and average migration time. The migration batch is the total number of non-zero items in the migration matrix {m0ij}. The total migration time and average migration time are calculated using the following formulas.

[0056] Total transfer time Tmax = Max(T1,…,T5)

[0057] The average transfer time Tmean = SUM(P1×T1,…,P5×T5) / SUM(P1,…,P5)

[0058] Where P1 represents the total number of people in the first transfer zone, and T1 represents the maximum transfer time in the first transfer zone, which is equal to the maximum time taken for the first transfer zone to reach each resettlement zone. For any road, the transit time is equal to the road length divided by the corresponding road speed, which is adjusted for congestion, as shown in the following formula, where Vmax is the maximum speed of the road.

[0059] Vij = Vmax * (1 - crowd / capacity)

[0060] Compared to the basic ant colony algorithm, this invention mainly introduces three improvements, making it more suitable for flood avoidance and relocation path analysis:

[0061] (1) Set up multiple ant colonies and start order

[0062] The basic ant colony algorithm assumes all ants are equivalent and start simultaneously. However, in the pathfinding problem of flood evacuation, the relocation needs of different communities must be considered. Therefore, ant colonies must be differentiated. Pheromones left by ants belonging to the same colony will affect each other but not ants from other colonies. Furthermore, since the resettlement area has a limited capacity, the order in which ants arrive affects their entry. This invention calculates the pheromones according to the order in which each colony sends out one ant in turn, maximizing fairness among ant colonies.

[0063] (2) Constructing a new heuristic function and crowding index

[0064] Traditional ant colony algorithms typically use a heuristic function that is the reciprocal of the path length, meaning ants tend to choose the next node that is closer. The heuristic function designed in this invention encourages ants to choose nodes that are generally closer to the resettlement area, rather than the node closest to the current node. A congestion index guides ants to choose less congested paths based on past experience, thus better meeting the needs of flood avoidance and relocation practices.

[0065] (3) Pheromone concentration update based on survival of the fittest strategy

[0066] Considering the complexity of the road network and the fact that ants do not take backtracking routes, if an ant fails to reach the correct (unsaturated) resettlement area, or fails to reach the resettlement area within a reasonable number of steps, it will not leave pheromones. This method can reduce the time spent by a single ant in pathfinding and prevent the ant colony from discovering some extremely long and unreasonable routes. Traditional algorithms often make adjustments to prevent ants from entering "infinite loops," such as using "backtracking" to ensure that ants avoid repeating routes, which often involves a large amount of computation.

[0067] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A flood transfer multi-objective optimization analysis method considering road congestion constraints, characterized in that, The method comprises the following steps: constructing a road network undirected graph; calculating the shortest distance from each node to the settlement area; initializing the ant colony and road network parameters, and retaining the pheromone concentration and road network congestion degree of the last round of training; traversing all the ant colonies, if not all the ant colonies are traversed, setting k=k+1, and then traversing all the ants in the ant colony k; for each ant, selecting the next node according to the heuristic function, the pheromone concentration and the congestion degree, until the settlement area or the empty node is reached; judging whether the path finding is successful, if yes, recording the route of the ant, updating the pheromone concentration of the ant colony k on the route and the road network congestion degree, judging whether the training termination condition is met, if yes, outputting the pheromone concentration and the matching result of the settlement area, and performing result diagnosis; According to the ant path length and a preset updating rule, the pheromone concentration and the road network congestion degree are dynamically adjusted and updated. After each round of training, the road network parameters weight ij and crowd ij are updated, wherein the weight of each road is a vector with a length of K, K represents the number of ants, and the updated pheromone concentration formula is as follows: where ε is the evaporation rate of pheromone, set to 0.8, where A k denotes the set of all ants in colony k that successfully reached the nest site and completed the path, and La denotes the total distance traveled by ant a; the training termination condition, after multiple rounds of training, the change rate of the transfer area and the settlement area matching result in the current round and the last round is calculated, and the calculation method is shown in the following formula: where m0 kh represents the number of ants of the ant colony k that moved to the settlement area h in the previous round of training, m1 kh represents the result of the current round of training, and the training is stopped when the change rate AM is less than 1%. 2.The flood transfer multi-objective optimization analysis method considering road congestion constraints according to claim 1, wherein, when constructing the road network undirected graph, the weights of the nodes and edges are abstracted based on the actual geographical road network structure to reflect the road passing properties, multiple nodes of the road network are divided into three subsets of the transfer area, the intermediate node and the settlement area, the number of ants in the transfer area is proportional to the number of ants in the corresponding ant colony, the remaining capacity of the settlement area is proportional to the number of ants that can be accommodated, the edge attribute is set, the edge attribute includes the weight, the capacity, the length and the congestion degree, the weight of the road represents the pheromone concentration, the length of the road represents the heuristic information, and the road network congestion degree represents the number of ants passing through the road and the road passing capacity in the last round. 3.The method of claim 1, wherein The shortest distance from each node to the settlement area is calculated by using the Dijkstra algorithm, and the minimum distance is stored in the attribute of the node for the calculation of the heuristic function, and the calculation formula of the path finding process of a single ant is: In the formula, for any one ant, the probability of its transition from node i to its adjacent node j is calculated, where j belongs to the set of nodes G adjacent to i and not passed through by the ant, represents the probability of the ant of the kth ant colony selecting the road i—j at the ith node, represents the pheromone concentration left by the ant colony k after the t-1th iteration on the route, is a heuristic function, represents the shortest distance from the ith node to the settlement area, represents the distance from node i to j, when is greater than 1, it indicates that the transition from the i node to the j node will be closer to the settlement area, and vice versa, represents the road network congestion degree of the road in the last round, which is equal to the total number of ants passing through the road in the last round crowd divided by the maximum capacity of the road, α, β, and γ are three power indexes of the ant colony algorithm, which are used to represent the relative importance of the pheromone concentration, the heuristic function, and the road congestion degree, and the greater the power index value, the higher the importance. 4.The method of claim 1, wherein, The heuristic function combines the residual distance from the node to the settlement area and the road network congestion degree to make the ant tend to select the node that is closer to the settlement area as a whole.

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