Flood avoidance transfer multi-objective optimization analysis method considering road congestion constraint

Abstract

The invention discloses a flood avoidance transfer multi-objective optimization analysis method considering road congestion constraints. The method comprises the following steps: constructing a road network undirected graph; calculating the shortest distance from each node to the placement area; initializing ant colony and road network parameters, and retaining pheromone concentration and road network congestion degree of the last round of training; traversing all ant colonies, if traversing is not completed, letting k = k + 1, and traversing all ants in the ant colony k; for each ant, selecting a next node according to a heuristic function, pheromone concentration and crowding degree until the ant reaches a resettlement area or an empty node; and judging whether a training termination condition is met or not, if so, outputting a pheromone concentration and placement area matching result, and performing result diagnosis. According to the invention, based on the ant colony algorithm framework, transfer time shortening and transfer batch reduction are taken as optimization objectives, and the problem of multi-objective optimization of transfer area and placement area matching and path selection under the constraint of road congestion is solved.

Description

Technical Field

[0001] The present invention relates to the technical field of flood emergency risk avoidance, and particularly to a multi-objective optimization analysis method for flood avoidance transfer considering road congestion constraints. Background Art

[0002] The flood avoidance transfer problem usually involves the matching problem and path analysis from multiple transfer areas to multiple resettlement areas. In actual operation, multiple optimization objectives often need to be considered, such as the shortest transfer time, the fewest transfer batches, and the simplest transfer plan as possible. At the same time, various constraint conditions are involved, such as road congestion conditions, road safety during floods, the number of people that can be accommodated at resettlement points, etc. It is a multi-objective optimization problem under complex constraint conditions. Existing flood avoidance transfer analysis technologies often consider it in two separate steps. First is the matching of transfer areas and resettlement areas, and then based on road network connectivity and computer graph theory shortest path related algorithms to find the shortest route from the transfer area to the resettlement area. Little consideration is given to the decrease in transfer efficiency caused by traffic congestion, or by setting a congestion threshold according to road grades. When the traffic flow exceeds the threshold, the road is truncated, forcing subsequent transfer populations to choose other sub-optimal paths. Such methods require artificially specifying the order of transfer, or carrying out dynamic simulation of the transfer process based on the actual vehicle driving speed and departure time, with relatively low computational efficiency. And in practice, once the transfer batches and departure time change, the optimal path will change, making it difficult to guide practice.

[0003] From the practical requirements of flood avoidance transfer, the number of transfer batches should be as few as possible to reduce the difficulty of organization and coordination. Mainly, the fewer resettlement areas corresponding to the same transfer area, the better, and it is best to transfer all to the same resettlement area. On the other hand, congestion problems need to be considered when choosing a resettlement area because the number of roads that can lead to the resettlement area is often limited in practice. Once the resettlement area matching is completed, even if road congestion is considered, the room for optimization is small. The above requirements lead to a very large search space for solving this problem. Strictly speaking, the optimal solution requires traversing all allocation schemes from each transfer area to each resettlement area, listing all possible path combinations on this basis, calculating the congestion degree under various allocation schemes and path combinations, and calculating the transfer time of all possible path combinations and personnel allocation combinations according to the congestion degree, and then selecting the non-dominated solutions of transfer time and transfer batches. To solve the problem that existing flood avoidance transfer analysis methods mainly consider road connectivity and shortest paths, lacking analysis of road traffic capacity and congestion degree, the path analysis results often deviate from the actual situation. Therefore, a multi-objective optimization analysis method for flood avoidance transfer considering road congestion constraints is needed. Summary of the Invention

[0004] The object of the present invention is to provide a multi-objective optimization analysis method for flood avoidance transfer considering road congestion constraints.

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

[0006] The present 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, and retain the pheromone concentration and road network congestion degree of the previous round of training;

[0010] Traverse all ant colonies. If not all are traversed, let k = k + 1, and then traverse all ants in ant colony k;

[0011] For each ant, select the next node according to the heuristic function, pheromone concentration, and congestion degree until reaching the resettlement area or an empty node;

[0012] Judge whether the path finding is successful. If successful, record the route passed by the ant, update the pheromone concentration of ant colony k on the passed road and the congestion degree of the passed road; judge whether the training termination condition is met. If met, output the pheromone concentration, resettlement area matching result, and perform result diagnosis.

[0013] Furthermore, when constructing the undirected graph of the road network, based on the actual geographical road network structure, abstract the weights of nodes and edges to reflect the road traffic attributes. Divide the multiple nodes of the road network into four subsets: transfer area, intermediate nodes, and resettlement area. The number of people to be transferred in the transfer area is used as the number of ants in the corresponding ant colony according to the proportion, and the remaining capacity of the resettlement area is used as the number of ants that can be accommodated. Set the edge attributes, and the edge attributes include weight, capacity, length, and congestion degree. The weight of the road represents the pheromone concentration, the road length represents the heuristic information, and the road congestion degree index represents the number of ants passing through the road in the previous round and the road traffic capacity.

[0014] Furthermore, the Dijkstra algorithm is used to calculate the shortest distance from each node to the resettlement area, and the minimum distance is stored in the attributes of the nodes for the calculation of the heuristic function. The calculation formula for the path finding process of a single ant is:

[0015]

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

[0017] In the formula, for any ant, calculate the probability of its transfer from node i to its adjacent node j, where j belongs to the set of nodes not passed by the ant. Among them, P ijs represents the probability that the ant in the s-th transfer area selects the route i - j at the i-th node, and θijs It represents the pheromone concentration left by ants after the (t - 1)-th round of iteration on this route, P ijs is the heuristic function, and min_dis(i) represents the shortest distance from the i-th node to the resettlement area, Edge ij represents the distance from node i to j. When P ijs is greater than 1, it means that transferring from node i to node j will be closer to the resettlement area, otherwise it will be farther away. It represents the congestion degree of this road in the previous round, which is equal to the total number of ants crowd that passed through this 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 and the road network congestion degree to make ants tend to choose nodes that are generally closer to the resettlement area.

[0019] Furthermore, according to the ant path length and the preset update 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 and crowd are updated once. Among them, the weight of each road is a vector of length 5. The updated pheromone concentration formula is as follows, weight ij (t) = [εθ ij1 (t - 1) + Δθ ij1 , …, εθ ij5 (t - 1) + Δθ ij5 T

[0020]

[0021] Among them, ε is the pheromone evaporation rate, set to 0.8. Among them, A represents the set of all ants in the ant colony s that have successfully reached the resettlement area and completed the path finding, and La represents the total distance traveled by ant a;

[0022] The training termination condition. After multiple rounds of training, the change rate of the matching results between the transfer area and the resettlement area in this round and the previous round is calculated as shown in the following formula:

[0023]

[0024] Among them, m0ij represents the number of ants transferred from transfer area i to resettlement area j in the previous round of training, and m1ij represents the result of this round of training. When the change rate ΔM is less than 1%, the training can be stopped.

[0025] The beneficial effects of the present invention are:

[0026] The present invention is a multi-objective optimization analysis method for flood avoidance transfer considering road congestion constraints. Compared with the prior art, the present invention has the following technical effects:​

[0027] Based on the ant colony algorithm framework, the present invention aims to shorten the transfer time and reduce the number of transfer batches, and solve the multi-objective optimization problem of matching the transfer area and the resettlement area and path selection under the constraint of road congestion. Description of the Drawings

[0028] Figure 1 is the overall technical roadmap of the multi-objective optimization analysis method for flood avoidance transfer considering road congestion constraints in the present invention

[0029] Figure 2 is the road network schematic diagram in the implementation case of the present invention;

[0030] Nodes 1-5 are transfer units, nodes 13-16 are resettlement units, and the others are intermediate nodes. The unit of road length is kilometer

[0031] Figure 3 is the road weight diagram of transfer unit 1 in the implementation case of the present invention;

[0032] Figure 4 is the road weight diagram of transfer unit 2 in the implementation case of the present invention;

[0033] Figure 5 is the road weight diagram of transfer unit 3 in the implementation case of the present invention;

[0034] Figure 6 is the road weight diagram of transfer unit 4 in the implementation case of the present invention;

[0035] Figure 7 is the road weight diagram of transfer unit 5 in the implementation case of the present invention; Detailed Implementation Manner

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

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

[0038] Data Preparation: Integrate information such as road network data, road traffic capacity, transfer area, resettlement area, transfer area population, resettlement area accommodation capacity, and flood inundation range into an undirected graph data structure. The nodes of the graph include transfer areas, resettlement areas, and road intersections. Among them, the transfer area and the resettlement area should respectively include two elements: the number of people in the transfer area and the accommodation capacity of the resettlement area. The edges of the graph are roads, and each edge includes two basic elements: road length and road traffic capacity. The flood inundation range map is used to judge the roads that are flooded and impassable, and these roads are directly removed from the edges of the undirected graph.

[0039] Initialize the ant colony, road weights, congestion levels, and the remaining capacity of the resettlement areas. Set the number of ant colonies according to the number of transfer areas, with each transfer area corresponding to an ant colony. The number of ants in each ant colony is proportional to the number of people to be transferred in the transfer area. The remaining capacity of the resettlement area is equal to 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 the ants of that ant colony on this road. Add a congestion attribute, which is equivalent to the total number of ants passing through this road during the ant colony pathfinding process in the previous round. Since this is the initial round, during initialization, the congestion levels of all roads can be initialized to 1, and the weights of all roads can be set to a vector with all elements being 0.1 (initializing to 0 is likely to cause numerical calculation errors).

[0040] Based on the multi - ant colony algorithm, perform resettlement area matching and path optimization. The optimization process requires multiple rounds of training to complete. At the start of each round of training, the number of ants in each ant colony, the remaining capacity of each resettlement area, and the congestion levels of the roads are initialized, but the weights of the roads are not initialized. And the congestion levels of the roads in the previous round are separately saved for use in this round of calculation. During each round of training, each ant colony takes turns sending out one ant in sequence for pathfinding calculation. If an ant colony has no remaining ants, that ant colony is skipped until all the ants from all ant colonies have completed pathfinding calculation, and then this round of training ends. During the pathfinding process of each ant, the weight of the road represents the pheromone concentration, the length of the road represents the heuristic information, and the road congestion index represents the number of ants passing through this road in the previous round and the road traffic capacity. The calculation process is detailed in the specific implementation steps. During the pathfinding process of each ant, a closed - loop path may occur, or the ant may reach a resettlement area that is already full, resulting in the failure of the pathfinding process. All ants with failed pathfinding will not contribute to the weights and congestion levels of the roads, thus accelerating the convergence speed of the solution.

[0041] The training termination condition is that after each round of training, termination indicators can be set according to the change rate between the results of this round of training and the previous round of training. For example, it is required that the overall change rate is less than 1%. The change rate mainly includes two parts. One is the change rate of the road weights, and the other is the change rate of the resettlement area matching results, that is, the change rate of the number / ratio of ants assigned to each resettlement area for each transfer area.

[0042] After the training terminates, the final results need to be evaluated. First, determine the number of batches according to the allocation ratio of the resettlement areas. Then, determine the travel routes of the ant colonies according to the road weights. Finally, calculate the maximum transfer time and the average transfer time based on the route length and congestion levels. Finally, provide three indicators: the number of transfer batches, the maximum transfer duration, and the average transfer duration for the user's reference.

[0043] Taking Figure 2 as an example, an undirected graph representing the characteristics of the road network is created. The road network contains 16 nodes and several edges. The nodes are divided into four subsets: transfer areas (nodes 1 - 5), intermediate nodes (nodes 6 - 12), and resettlement areas (nodes 13 - 16). The number of people to be transferred in each transfer area is divided by 5 to obtain the number of ants in the ant colony corresponding to that transfer area. Correspondingly, the remaining capacity of each resettlement area 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 scale and calculation accuracy requirements. Attributes are set for each edge, including weight, capacity, length, and crowding degree. Among them, the weight is a vector of length 5, corresponding to the pheromone concentrations of the ant colonies in transfer areas 1 to 5 respectively. The pheromone concentration of the same ant colony only acts within the ant colony and does not affect other ant colonies. This can ensure that the ants in the same ant colony will try to follow the same route and reach the same destination, thus reducing the number of transfer batches. The capacity represents the maximum traffic capacity of the road, and an empirical value can be given according to the road speed limit and road level. The closer the number of ants choosing a certain road is to the capacity, the higher the crowding degree and the slower the traffic speed. The crowding degree is the total number of ants choosing this road during a certain round of training. This indicator is updated during each training, so the current round can only affect the ants' choice of road based on past knowledge - that is, the crowding degree of the previous round. The length is the actual length of the road.

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

[0045] The calculation formula for the path - finding 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, calculate the probability that it transfers from node i to its adjacent node j, where j belongs to the set of nodes that the ant has not passed through. Here, Pijs represents the probability that the ant in the s-th transfer area selects the route i-j at the i-th node, θijs represents the pheromone concentration left by the ant after the (t-1)-th iteration on this route, ρijs is the heuristic function, min_dis(i) represents the shortest distance from the i-th node to the resettlement area, Edgeij represents the distance from node i to j. When ρijs is greater than 1, it means that transferring from node i to node j will be closer to the resettlement area, otherwise it is farther away. Cij(t-1) represents the congestion degree of this road in the previous round, which is equal to the total number of ants crowd that passed through this road in the previous round divided by the maximum capacity capacity of the road.

[0049] The denominator represents the sum of the probabilities of all possible paths (excluding the nodes that have already been passed through) that can be taken from the i-th node, and is used for normalization. The three power exponents α, β, and γ are hyperparameters of the ant colony algorithm, and are used to characterize the relative importance of the pheromone concentration, the heuristic function, and the road congestion degree. Based on the above formula and the roulette algorithm, select the next node for the ant until the ant reaches a resettlement area. If there is remaining capacity in the resettlement area, the ant's path finding is successful and the calculation terminates. If the resettlement area is full, or the next node of the ant is an empty set, it is considered that the path finding fails and the calculation also terminates. The ants that succeed in path finding will update the pheromone concentration, while the ants that fail in path finding will not update the pheromone concentration.

[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, and the routes from each transfer area to the resettlement area are as Figures 3 to 7 shown. Figures 3 to 7 The pheromone concentrations of each ant colony on each road are given. The roads with a concentration of 0 will not be selected, so it is equivalent to the transfer route map. From Table 1, there are still 50 people in transfer unit 3 who have not been transferred, and this part of the population will be directly matched to resettlement area 1 according to the principle of the shortest path and the available resettlement area.

[0052] Table 1 Matching Results of Resettlement Areas

[0053]

[0054]

[0055] The results given by the ant colony algorithm may be local optimal solutions. It is very necessary to evaluate the rationality of the solution results through some indicators. During the training process of this algorithm, it is not mandatory for all ants to reach the resettlement area. Instead, through the survival of the fittest, most ants reach the resettlement area. Therefore, the arrival rate can be used as one of the rationality indicators of the solution. The calculation method is to divide the number of ants reaching the resettlement area by the total number of ants. Ants that fail to transfer successfully can be placed nearby in the resettlement area with remaining accommodation space by using the shortest path method. Secondly, there are the number of transfer batches, the total transfer duration, and the average duration. The number of transfer batches is the total number of non-zero terms in the transfer matrix {m0ij}. The total transfer duration and the average duration are calculated according to the following formulas.

[0056] The total transfer duration Tmax = Max(T1,…,T5)

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

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

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

[0060] Compared with the basic ant colony algorithm, the present invention mainly introduces three aspects of improvements, which are more suitable for flood avoidance transfer path analysis:

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

[0062] The basic ant colony algorithm believes that all ants are equivalent and start at the same time. In the path - finding problem of flood avoidance transfer, the transfer requirements of different communities need to be considered. Therefore, the ant colonies need to be distinguished. The pheromones left by ants belonging to the same ant colony will act on each other, but not on ants of other ant colonies. On the other hand, due to the limited accommodation capacity of the resettlement area, the order of arrival of ants will affect whether they can enter the resettlement area. The present invention calculates in the order of sending one ant from each ant colony in turn to ensure fairness among ant colonies to the greatest extent.

[0063] (2) Construct a new heuristic function and congestion index

[0064] The heuristic function of the traditional ant colony algorithm is usually the reciprocal of the road length, that is, ants tend to choose the next node with a shorter distance. The heuristic function designed in the present invention enables ants to tend to choose nodes that are generally closer to the resettlement area rather than the node closest to the current node. The congestion index is used to guide ants to choose relatively uncongested roads based on past experience, thus better meeting the needs of flood avoidance and transfer practice.

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

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

[0067] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A multi-objective optimization analysis method for flood avoidance transfer under road congestion constraints, characterized in that: The following steps are involved: Construct an undirected graph of road network; Calculate the shortest distance from each node to the resettlement area; Initialize the ant colony and road network parameters, and retain the pheromone concentration and road network congestion of the previous round of training; Traverse all ant colonies. If the traversal is not complete, set k = k + 1 and then traverse all ants in ant colony k; For each ant, the next node is selected according to the heuristic function, pheromone concentration, and crowding degree until it reaches the resettlement area or an empty node; Determine whether the pathfinding is successful. If successful, record the ant route and update the pheromone concentration of ant colony k on the route and the congestion of the route. Determine whether the training termination conditions are met. If so, output the pheromone concentration and resettlement area matching results, and perform result diagnosis.

2. The multi-objective optimization analysis method for flood avoidance transfer under road congestion constraints according to claim 1 is characterized in that: When constructing an undirected road network graph, the weights of abstract nodes and edges based on the actual geographical road network structure reflect the road traffic attributes. The multiple nodes of the road network are divided into four subsets: transfer area, intermediate node, and resettlement area. The number of people to be transferred in the transfer area is used as the number of ants in the corresponding ant colony in proportion, and the remaining number of ants in the resettlement area is used as the number of ants that can be accommodated. The edge attributes are set, including weight, capacity, length and congestion. The weight of the road represents the pheromone concentration, the road length represents the heuristic information, and the road congestion index represents the number of ants passing through the road in the previous round and the road traffic capacity.

3. The multi-objective optimization analysis method for flood avoidance transfer under road congestion constraints according to claim 1 is characterized in that: The Dijkstra 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 the calculation of the heuristic function. The calculation formula for the pathfinding process of a single ant is: ρ ij =min_haze(i) / (min_haze(j)+Edge ij ) In the formula, for any ant, the probability of its transfer from node i to its adjacent node j is calculated, where j belongs to the set of nodes that the ant has not passed through, where P ijs represents the probability that the ant in the sth transfer area chooses the route i-j at the i-th node, θ ijs represents the pheromone concentration left by ants after the t-1th iteration on the route, P ijs is the heuristic function, min_dis(i) represents the shortest distance from the i-th node to the resettlement area, Edge ij represents the distance from node i to j. When P ijs When it is greater than 1, it means that the transfer from node i to node j will be closer to the resettlement area, and vice versa. It indicates the degree of congestion of the road in the previous round, which is equal to the total number of ants crowd that should have walked on the road in the previous round divided by the maximum capacity of the road.

4. The multi-objective optimization analysis method for flood avoidance transfer under road congestion constraints according to claim 1 is characterized in that: The heuristic function combines the remaining distance from the node to the resettlement area with the road network congestion to make ants tend to choose nodes that are generally closer to the resettlement area.

5. The multi-objective optimization analysis method for flood avoidance transfer under road congestion constraints according to claim 1 is characterized in that: The pheromone concentration and road network congestion are dynamically adjusted and updated according to the ant path length and the 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 updated pheromone concentration formula is as follows: weight ij (t)=[θ ij1 (t-1)+Δθ ij1 ,…,th ij5 (t-1)+Δθ ij5 ] T Where ε is the volatilization rate of pheromone, which is set to 0.8, A represents the set of all ants in ant colony s that successfully reach the resettlement area and complete pathfinding, and La represents the total distance traveled by ant a; Training termination conditions, after multiple rounds of training, the change rate of the matching results of the transfer area and the resettlement area between the current round and the previous round, is calculated as shown in the following formula: Where m0 ij represents the number of ants transferred from transfer area i to resettlement area j in the previous round of training, and m1 ij represents the result of this round of training. When the change rate ΔM is less than 1%, the training can be stopped.

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