Earthwork allocation optimization method based on combined problem model framework

Abstract

The invention relates to an earthwork allocation optimization method based on a combined problem model framework. The method comprises the following steps: obtaining construction node information, cost information and vehicle-mounted capacity information of to-be-processed earthwork; constructing a linear programming model based on the construction node information and the cost information by taking the minimum cost as a target, solving through a solver to obtain a static deployment scheme, and storing the static deployment scheme as a multi-way tree; constructing a travel salesman-like problem model based on construction node information, cost information and vehicle-mounted capacity information by taking a shortest path as a target, calling data in the multi-way tree, and solving through an ISABO algorithm to obtain a path allocation scheme; and the static allocation scheme and the path allocation scheme are combined and output, and allocation optimization of the to-be-processed earthwork is completed. According to the earth-rock deployment problem and construction optimization method for solving the complex problem based on the combination problem, the functional composition of the complex mathematical problem model is successfully deconstructed, and the difficulty of mathematical modeling is greatly reduced.

Description

Technical Field

[0001] The invention relates to the fields of computer science, operations research and management science and technology, and in particular to an earthwork allocation optimization method based on a combination problem model framework. Background Art

[0002] Earthwork engineering is a complex system engineering project. Affected by many factors, its construction organization design and management are difficult. Common problems in actual construction include insufficient material sources, insufficient transportation capacity and substandard construction intensity, which lead to construction delays and increased costs. The existing technical route for optimizing earthwork allocation is to establish a mathematical model for the actual engineering problem, use optimization methods to solve the mathematical model, and use it to guide the optimization of the allocation plan. There are two main directions for establishing mathematical models for earthwork allocation with transportation cost as the main optimization target: one is based on the mathematical model of constraint optimization problem; the other is the mathematical model of the transformation type traveling salesman (TSP) problem. The former is mostly a linear programming model, which focuses on the constraints in the actual earthwork allocation optimization problem. For small and medium-sized problems, linear programming has high efficiency and accuracy, but its versatility is poor in large-scale allocation problems. Moreover, this method has great limitations when facing nonlinear factors. The solution results can only display static solutions but not specific construction steps, which is not conducive to engineering personnel organizing and arranging subsequent tasks. The latter focuses on optimizing the construction process of earthwork allocation, can consider nonlinear factors and can display the construction process, transportation volume and transportation direction of the construction plan, but it lacks consideration of factors such as vehicle capacity, vehicle transportation distance limit, traffic conditions, etc. in the actual transportation process, and cannot meet more requirements in the actual construction process.

[0003] Therefore, there is an urgent need for an earthwork allocation optimization method based on a combined problem model framework. Summary of the invention

[0004] The purpose of the present invention is to provide an earthwork allocation optimization method based on a combined problem model framework, solve complex earthwork allocation problems and construction optimization methods based on combined problems, successfully deconstruct the functional composition of complex mathematical problem models, and greatly reduce the difficulty of mathematical modeling. In addition, various models and algorithms can be transplanted in the combined framework, and the expansion capability is excellent, which provides a new idea for engineering practice.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for optimizing earthwork allocation based on a combined problem model framework includes:

[0007] Obtain construction node information, cost information, and vehicle capacity information of the earthwork to be processed;

[0008] Taking the minimum cost as the goal, a linear programming model is constructed based on the construction node information and the cost information, and the model is solved by a solver to obtain a static deployment plan, and the static deployment plan is stored as a multi-branch tree, wherein the root node in the multi-branch tree is the construction area coordinate code, and the leaf node is the construction process code;

[0009] Taking the shortest path as the goal, a traveling salesman problem-like model is constructed based on the construction node information, cost information, and vehicle capacity information, and the data in the multi-branch tree is called to solve the problem through the ISABO algorithm to obtain a path allocation plan;

[0010] The static allocation plan and the path allocation plan are combined and output to complete the allocation optimization of the earth and stone to be processed.

[0011] Optionally, the construction node information includes: construction attributes, amount to be constructed, and distances between construction nodes;

[0012] The cost information includes: unit deployment fees and related costs.

[0013] Optionally, the linear programming model includes an earthwork excavation and filling balance model, an earthwork excavation less than filling model, and an earthwork excavation greater than filling model, wherein the earthwork excavation and filling balance model is:

[0014]

[0015] The earthwork cut less than fill model is:

[0016]

[0017] The earthwork cut greater than fill model is:

[0018]

[0019] Among them, Z is the total transportation cost; c ij is the unit freight from excavation i to filling j; x ij is the amount of transfer from excavation i to filling j; a i is the construction volume of excavation i; b j is the construction volume of fill j; i = 1, 2, ..., m, m is the total number of excavations; j = 1, 2, ..., n, n is the total number of fills.

[0020] Optionally, storing the static deployment scheme as a multi-branch tree comprises:

[0021] Coordinate coding of the excavation construction area and the filling construction area of ​​each construction scheme in the static deployment scheme;

[0022] Calculate the construction process of each construction plan according to the vehicle capacity information and encode them in sequence;

[0023] The coordinate code of each construction plan is stored as the root node of the multi-branch tree, and the construction process code corresponding to the construction plan is stored as the leaf node of the multi-branch tree.

[0024] Optionally, the traveling salesman problem-like model is:

[0025]

[0026] c t =X·C·X T

[0027] st

[0028]

[0029] Among them, E t represents the volume of earthwork transported in step t; c t represents the cost per unit earthwork volume associated with the t-th construction step; is a binary variable (0,1), indicating whether the i node is the starting node of the t-th transport, N is the number of nodes; C is the cost matrix, recording the unit transportation cost between nodes; S i represents the initial earthwork construction volume of node i, S i >0 means that the i-node is a cutting area, otherwise it is a filling area; is the remaining earthwork volume of node i after the t-th construction step, is the input earthwork volume of node i after the t-th construction step, is the output earthwork volume of node i after the t-th construction step, R i represents the designed earthwork volume of node i, is the remaining earthwork volume of node i after s finite steps of construction.

[0030] Optionally, the ISABO algorithm is obtained by improving the initial population generation strategy and update mechanism of the SABO algorithm.

[0031] Optionally, the working process based on the ISABO algorithm is:

[0032] Step 1: Set the population size N and the maximum number of iterations T, generate the initial population based on the chaotic dynamic target strategy, record the initial population as t=0, and calculate the fitness of all individuals in the population;

[0033] Step 2: Let \(i = 1\) and \(t = 1\). Calculate the fitness of the \(i\)-th search agent in the \(t\)-th generation of the current population, and calculate the updated position of the search agent through the exchange learning mechanism. Update the individuals in the \((t - 1)\)-th generation according to the improved Metropolis criterion. If \(i < N\), set \(i\) to \(i + 1\), and continue to iteratively calculate the fitness of the search agent until \(i = N\). Record the best particle position in this iteration.

[0034] Step 3: If \(t < T\), set \(t\) to \(t + 1\) and perform the next round of iteration until \(t = T\), and output the best particle in all iterations.

[0035] Optionally, the process of generating the initial population based on the chaotic dynamic target strategy includes:

[0036] Initialize the alternative pool of process nodes, where the alternative pool contains all unselected leaf nodes of the multi-way tree. Cut the interval into several equal parts according to the total number of root nodes of the multi-way tree, and map all root nodes onto the discretized interval after discretizing the interval.

[0037] Generate a chaotic sequence with a certain number of populations using the Piecewise chaotic mapping, find the corresponding mapped discrete interval of the chaotic sequence, and then find the corresponding root nodes. Use the root nodes corresponding to the chaotic sequence as the initial root nodes of all paths, and select one leaf node from each initial root node as the initial process node of the path. At the same time, remove the initial process node from the alternative pool.

[0038] Each individual in the population starts from the initial process node, selects any leaf node from the root nodes that are closest to the root node where the previous construction node is located in the alternative pool, and then adds the selected leaf node to the path until all leaf nodes in the alternative pool are selected and a path is generated.

[0039] Optionally, the exchange learning mechanism is:

[0040]

[0041] A - v B=-sign(F(A)-F(B))(A - B)

[0042] where is the new search agent, \(X\) i is the search agent, is a vector composed of random numbers in the interval \((0, 1)\), which is the probability set for selecting the exchange operator, represents the current search agent \(X\) iExchange learning is performed on all search agents in the population. -sign(F(A)-F(B)) is the judgment function for comparing the fitness of A and B. A and B refer to two different search agents in the population. v B is an exchange sequence in which A exchanges with B for learning.

[0043] Optionally, the improved Metropolis criterion is:

[0044]

[0045] Among them, t is the current iteration number and T is the maximum iteration number.

[0046] The beneficial effects of the present invention are:

[0047] The present invention solves complex earthwork allocation problems and construction optimization methods based on combination problems, successfully deconstructs the functional composition of complex mathematical problem models, greatly reduces the difficulty of mathematical modeling, and various models and algorithms can be transplanted within the combination framework, with excellent expansion capabilities, providing a new idea for engineering practice; improves the ability of the SABO algorithm to solve discrete optimization problems, integrates the coordinate tree concept and dynamic target generation strategy, and improves the solution performance and expansion capabilities of ISABO. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0049] Figure 1 A flow chart of an earthwork allocation optimization method based on a combined problem model framework according to an embodiment of the present invention;

[0050] Figure 2 A schematic diagram of a multi-branch tree according to an embodiment of the present invention;

[0051] Figure 3 ISABO algorithm flow chart of an embodiment of the present invention;

[0052] Figure 4 A population flow chart is generated for the chaotic dynamic target strategy of an embodiment of the present invention;

[0053] Figure 5 A discrete particle swarm convergence curve diagram of an embodiment of the present invention;

[0054] Figure 6 A construction optimization solution roadmap for an embodiment of the present invention;

[0055] Figure 7 It is a convergence curve diagram of the ISABO algorithm according to an embodiment of the present invention. DETAILED DESCRIPTION

[0056] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0057] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0058] This embodiment provides an earthwork allocation optimization method based on a combined problem model framework. Figure 1 As shown, including:

[0059] S1. Obtaining construction node information, cost information, and vehicle capacity information of the earthwork to be processed;

[0060] The earthwork construction node information includes construction attributes, the amount to be constructed, the distance between construction nodes, etc.; the earthwork construction cost information includes: unit allocation fees and related costs.

[0061] S2. With the goal of minimizing cost, a linear programming model is constructed based on construction node information and cost information, and solved by a solver to obtain a static deployment plan.

[0062] Specifically, enter the constrained optimization problem model framework: According to the information obtained in S1, analyze the construction characteristics of the project and the earthwork allocation process. This embodiment adopts a linear programming model to generate a distance matrix of each construction node and a corresponding unit freight matrix, and constructs a coefficient matrix and a constraint matrix according to the actual material constraints of the project. Substitute the above-constructed matrix into the linear programming solver to output a static allocation plan;

[0063] The basic mathematical model of the constrained optimization framework is as follows

[0064] minmize: z = f(x) (1)

[0065]

[0066] Among them, f(x) is the objective function, g i (x) is an inequality constraint, h i (x) is an equality constraint, l j with u jThe general earthwork allocation problem can be described as a linear programming model. According to the supply relationship between earthwork excavation and filling: excavation-filling balance, excavation less than filling, and excavation greater than filling, linear programming models are constructed respectively, as follows:

[0067] The excavation and filling balance model of earthwork is:

[0068]

[0069] The model of earthwork excavation less than filling is:

[0070]

[0071] The model of earthwork excavation greater than filling is:

[0072]

[0073] Among them, Z is the total transportation cost; c ij is the unit freight from excavation i to filling j; x ij is the amount of transfer from excavation i to filling j; a i is the construction volume of excavation i; b j is the construction volume of fill j; i = 1, 2, ..., m, m is the total number of excavations; j = 1, 2, ..., n, n is the total number of fills.

[0074] Take a specific construction case as an example to illustrate the operation steps:

[0075] Read the data to be processed, as shown in Table 1, and use the linear programming solver to write a linear programming code to organize the data into a matrix form, calculate the relative distance between each cut-and-fill partition, and calculate the unit transportation cost, where the unit transportation cost is adjusted according to the relative distance of transportation.

[0076] Table 1

[0077]

[0078] S3. The static deployment plan is stored as a multi-branch tree, wherein the root node in the multi-branch tree is the construction area coordinate code, and the leaf node is the construction process code.

[0079] According to the static dispatching plan table obtained by S2, the dispatching plans are coded one by one and each plan is decomposed according to the vehicle capacity, and the decomposed steps are numbered one by one in sequence. Figure 2 , in the computer program, the obtained scheme encoding coordinates and the decomposition steps corresponding thereto are stored in a multi-tree data structure.

[0080] Specifically, coordinate coding is performed on the excavation construction area and the filling construction area of ​​each construction plan in the static deployment plan;

[0081] The construction process of each construction plan is calculated based on the vehicle capacity information and coded in sequence;

[0082] The coordinate code of each construction plan is stored as the root node of the multi-branch tree, and the construction process code corresponding to the construction plan is stored as the leaf node of the multi-branch tree.

[0083] S4. With the shortest path as the goal, a traveling salesman problem-like model is constructed based on construction node information, cost information, and vehicle capacity information. The data in the multi-branch tree is called and solved through the ISABO algorithm to obtain the path allocation plan.

[0084] Specifically, we enter the framework of the quasi-traveling salesman problem model: taking the shortest construction dispatch path as the optimization goal, we establish a quasi-traveling salesman problem model and use the ISABO algorithm to solve it: 1. Call the multi-branch tree data and use the chaotic dynamic target chain strategy to generate the population in the population initialization stage; 2. Use the exchange learning update mechanism to optimize and update the population particles; 3. Use the improved Metropolis criterion to accept the inferior solution probabilistically. The algorithm ends and outputs the optimized dispatch path.

[0085] The Traveling Salesman Problem (TSP) is a classic combinatorial optimization problem that describes the shortest path problem in which a traveler needs to visit a series of cities and return to the starting point. Specifically, the problem can be described as follows: Suppose there is a traveling salesman who needs to visit a set of cities, and each city can only be visited once, and finally returns to the starting city. The traveling salesman hopes to find a path that minimizes the total travel distance (or cost) passing through all cities and returning to the starting point. The Traveling Salesman Problem is an NP-hard problem, which means that for large-scale instances, finding an exact solution is very time-consuming. However, for small-scale instances, the optimal solution can be found through brute force search or more efficient algorithms (such as dynamic programming). For large-scale instances, it is usually necessary to use heuristics or approximate algorithms to find an approximate optimal solution.

[0086] Earthwork transportation involves the process of transporting earthwork from an excavation to a backfill, and transportation costs, time, and efficiency need to be considered during this process. This process can be regarded as a deployment activity, except that all deployment activities are composed of several construction processes. A single backfilling scheme from excavation to backfill (as can be seen from the constrained optimization problem model framework) can be decomposed into multiple processes according to the vehicle capacity of the transport vehicle, and these processes can be represented by two-dimensional node coordinates (excavation number, backfill number). For example, the deployment plan from excavation 1 (numbered 1) to backfill 1 (numbered 2) is 210 cubic meters. Assuming that the loading capacity of a loading vehicle is 20 cubic meters, the construction process of the deployment plan can be decomposed into 21 0 / 20=10 (trips), there are 10 cubic meters of earth and stone left in the plan, and an extra loader is needed for transportation, so it means that the (1, 2) node will appear 11 times in all construction processes. Similarly, when the plans and vehicle capacity of all construction areas have been determined, all processes of the entire allocation activity have been determined. The permutations and combinations of all processes represent the possible paths for vehicle transportation, which is also the path in the traveling salesman problem. In this context, we only need to find the shortest vehicle transportation path to assist in completing the earth and stone allocation construction in the shortest time.

[0087] The traveling salesman problem model in this embodiment is:

[0088]

[0089] c t =X·C·X T (7)

[0090] st

[0091]

[0092]

[0093] Among them, E t represents the volume of earthwork transported in step t; c t represents the cost per unit earthwork volume associated with the t-th construction step; is a binary variable (0,1), indicating whether the i node is the starting node of the t-th transport, N is the number of nodes; C is the cost matrix, recording the unit transportation cost between nodes; S i represents the initial earthwork construction volume of node i, S i >0 means that the i-node is a cutting area, otherwise it is a filling area; is the remaining earthwork volume of node i after the t-th construction step, is the input earthwork volume of node i after the t-th construction step, is the output earthwork volume of node i after the t-th construction step, R irepresents the designed earthwork volume of node i, is the remaining earthwork volume of node i after s finite steps of construction.

[0094] Furthermore, the ISABO algorithm is obtained by improving the initial population generation strategy and update mechanism of the SABO algorithm.

[0095] Specifically, the Subtraction-Average-Based Optimizer (SABO) has a simple principle but excellent optimization effect, and has obvious advantages over many meta-heuristic algorithms. It mainly includes two stages: population initialization, search agent search and position update.

[0096] The initialization of this algorithm is consistent with many meta-heuristic algorithms. It requires randomly generating an initial population. At the beginning of the algorithm, it is necessary to set the maximum number of iterations T and the total number of algorithm search agents (population members) N, where the search agent determines the value of the decision variable based on its value in the search space. A search agent containing m decision variables (that is, the dimension of the search agent is m) represents a feasible solution to the optimization problem. The set of all search agents together constitutes the overall algorithm. The initial population of the algorithm can be represented by a matrix.

[0097]

[0098] x i，d =lb d +r i，d ·(ub d -lb d ), i=1,...,N, d=1,...,m, (16)

[0099] Among them, X i represents the i-th search agent in the search population space, x i，d represents the d-th dimension decision variable in the i-th search agent, x i，d The value of the decision variable is determined by the upper limit ub of the dimension d and lower limit lb d Decision, r i，d is a random number in the interval [0, 1]. Each search agent has a fitness function F for evaluating the decision-making solution for the optimization problem. The smaller the value of the fitness function F, the better the quality of the generation's solution. These Fs are stored in the F vector.

[0100] In the agent search and position update phase, the algorithm searches for the optimal solution to the optimization problem through information exchange between search agents. Compared with the particle swarm algorithm, the best quality particles with the best fitness will guide other particles to find the direction of the optimal target. In SABO, the optimization direction of a search agent will be affected by other search agents.

[0101]

[0102] In formula (17), any search agent X i The displacement in the search space is calculated by each search agent X j (j=1,2…)- v The arithmetic mean of the operator is used to calculate, is a vector in the m-dimensional interval [0,1]. Formula (18) introduces the unique definition of this algorithm - v Operators, where A and B are two search agents, is a vector of dimension m, in which the components are random numbers generated from the interval [1,2]. The operation "*" represents the Hadamard product of the two vectors (i.e., all components of the obtained vector are equal to the product of the corresponding components of the two given vectors); F(A) and F(B) are the fitness values ​​of the search agents A and B respectively. sign is a sign function. When the value in the function is less than 0, it returns -1, when it is equal to 0, it returns 0, and when it is greater than 0, it returns 1. It can be concluded from the second formula that A- v B is a signed search displacement, which can be mathematically understood as a vector, so the first formula can be understood as X i The equations of motion for displacement in a specified direction under other agents.

[0103] If the vector is represented by coordinates, it means that the particles in the search space (that is, the search agent) are directedly displaced according to the fitness of all particles in the particle population. If the vector is represented by directed line segments, it can be more intuitive to find that the particles update their positions according to all directed line segments. In the initialization phase, particles are distributed throughout the feasible solution space, with good and bad fitness. Each search particle will comprehensively consider the fitness of the remaining particles and search in the direction of particles with better fitness. If a particle direction with better fitness is found, the position of the original search particle will be updated. After multiple rounds of iterations, all particles will eventually converge to a better position. After the iteration, the particle with the best fitness in the algorithm is regarded as the optimal solution or a better solution to the optimization problem. The execution flow of the entire algorithm is shown in the figure. Figure 3 , specifically including:

[0104] Step 1: Set the population size N and the maximum number of iterations T, generate the initial population based on the chaotic dynamic target strategy, record the initial population as t=0, and calculate the fitness of all individuals in the population;

[0105] Step 2: Let \(i = 1\) and \(t = 1\). Calculate the fitness of the \(i\)-th search agent in the \(t\)-th generation of the current population, and calculate the updated position of the search agent through the exchange learning mechanism. Update the individuals in the \((t - 1)\)-th generation according to the improved Metropolis criterion. If \(i < N\), set \(i\) to \(i + 1\) and continue to iteratively calculate the fitness of the search agent until \(i = N\), and record the best particle position in this iteration.

[0106] Step 3: If \(t < T\), set \(t\) to \(t + 1\) and perform the next round of iteration until \(t = T\), and output the best particle in all iterations.

[0107] In this embodiment, the ISABO algorithm is improved in the following aspects:

[0108] 1. Multi-way tree coding system:

[0109] The original SABO algorithm is mainly applied to continuous optimization problems and is difficult to handle discrete optimization problems. To solve this problem, in this embodiment, a multi-way tree coding system is first designed for the earthwork allocation construction process to represent the structure of the solutions in the algorithm: First, assume there are \(a\) excavation nodes \((1, 2, 3, \cdots, a)\) and \(b\) filling nodes \((a + 1, a + 2, \cdots, a + b)\). According to the allocation plan of the constraint optimization problem model framework, each plan is encoded with coordinates. For example, from the first construction area of excavation (numbered 1) to the fifth construction area of filling (numbered 13), its coordinates are \((1, 13)\), and so on. Then, calculate the construction process of each plan according to the vehicle capacity constraint, sum up the construction processes of all construction plans and encode them in order. The plan coordinates of each plan correspond one by one with its construction process encoding, forming a storage form similar to a multi-way tree structure. The construction encoding of the multi-way tree is its leaf node. It should be noted that when there is only one type of loading vehicle in the problem, for all permutations and combinations of all construction process encodings, it will be more convenient to use the root node of the multi-way tree for encoding (i.e., the construction area coordinates) to solve the TSP problem.

[0110] 2. Chaotic dynamic target chain strategy:

[0111] Since there are many process nodes for finding the construction path, if the random strategy is used to generate the initial population, it is easy to fail to find a better initial solution, resulting in the population falling into the local optimal trap during the algorithm iteration. To accelerate the algorithm convergence speed and help the algorithm find a better initial solution at the beginning, in this embodiment, referring to the node transfer mechanism of the ant colony algorithm, a population generation method based on the chaotic dynamic target chain strategy is designed, as shown in Figure 4 , and the specific method is as follows:

[0112] (1) Initialize the candidate pool of process nodes, which contains all the unselected multitree leaf nodes. Then, according to the total number of multitree root nodes n, cut the interval [0,1] into n equal parts, discretize the interval and map all root nodes to the discretized interval, so that each root node has its corresponding mapped discrete interval.

[0113] (2) Use piecewise chaotic mapping to generate N chaotic sequences of population size, and find the mapping discrete interval corresponding to the chaotic sequence, and then find the corresponding root node. Therefore, the root node corresponding to the chaotic sequence is used as the initial root node of all paths, and then a leaf node is selected from each initial root node as the initial process node of the path. At the same time, these initial process nodes are removed from the candidate pool.

[0114] Piecewise Chaotic Mapping:

[0115]

[0116] (3) Each individual in the population starts from the initial construction node, selects any leaf node from the candidate pool that is closest to the root node where the previous construction node is located (if there are multiple root nodes with the closest external distance in the candidate pool, the root node with the shortest internal distance is selected from them), and then adds the selected leaf node to the path. This process is repeated until all leaf nodes in the candidate pool are selected and a path (initial solution) is generated. Assume that the size of the population is N, of which N / 2 particles are generated using the chaotic dynamic target chain strategy, and the remaining N / 2 particles are generated using the random strategy.

[0117] Root node distance: A two-dimensional coordinate of a construction flow direction represents a root node, where the first coordinate represents the construction area number of the starting point of the construction flow direction, and the second coordinate represents the construction area number of the end point of the construction flow direction. The root node outer distance refers to the distance between the construction area of ​​the end point of the previous root node and the construction area of ​​the starting point of the next root node. The root node inner distance is the distance between the starting point and the end point of a root node. For details, see Figure 4 .

[0118] 3. Update mechanism based on exchange learning:

[0119] Since the TSP problem is a discrete problem, the continuous update method of the SABO algorithm is no longer applicable. Since the SABO particle update mechanism is very similar to the particle swarm algorithm (PSO) update mechanism, this embodiment is inspired by the discrete particle swarm algorithm (DPSO) update formula and the simulated annealing Metropolis criterion to improve the main update mechanism of the SABO algorithm. Before introducing the update formula of the discrete particle swarm, it is necessary to introduce the concepts of the commutator and the exchange sequence: the commutator is defined as s = Swap x (i, j), which means that the commutator s acts on the sequence x to exchange the elements at position i and the elements at position j. For example, if x = (1, 3, 2, 5, 4), add a swap operation s = Swap x (1, 3) to it, and its new sequence is x = (2, 3, 1, 5.4). In the particle swarm algorithm, the commutator can be regarded as the speed of the particle, which can change the position of x. The exchange sequence is defined as a set of commutators with a front-to-back order, that is, ss = [Swap1, Swap2, ...], which means that multiple exchange operations are performed on x in succession. For example, if x = (1, 3, 2, 5, 4), the exchange sequence is ss = [(3, 2)(1, 5)]. After the sequence is transformed by the exchange sequence ss, the new sequence is x = (4, 2, 3, 5, 1). Combining the above two concepts, we can redefine the update mechanism of the particle swarm algorithm for position and speed. The update formula is as follows:

[0120]

[0121] In formula (20), Pbest-x i indicates that there is a swap sequence ss that makes x i After ss transformation, we get Pbest, and similarly Gbest-x i It is also a swap sequence ss; the first symbol from the right is Indicates that two exchange sequences are merged into one exchange sequence, such as The first symbol from the left It means that a sequence is exchanged according to the exchange sequence ss, so formula (21) means After exchanging the sequence After the action, a new sequence is obtained r1 and r2 are random numbers between 0 and 1, indicating the possibility of executing a certain swap sub-operation, which is equivalent to randomly discarding some swap operations. Set the exchange sequence to an empty one, so the velocity update formula of the particle swarm can be simplified to:

[0122]

[0123] Therefore, we refer to the above formula to improve the SABO update mechanism (17) and (18):

[0124]

[0125] A- v B=-sign(F(A)-F(B))(AB) (24)

[0126] First, for formula (18) - v The operator is redefined: A and B are two different search agents in the population, -sign(F(A)-F(B)) is the judgment function for comparing the fitness of A and B. If F(A)-F(B) is less than 0, the function returns 1, and the AB operation is performed to obtain an exchange sequence ss; if F(A)-F(B) is equal to 0, no exchange sequence occurs; if F(A)-F(B) is greater than 0, BA is performed to obtain an exchange sequence ss_ (equivalent to reverse exchange learning for the current particle). For formula (17), Represents the current individual X i Exchange learning is performed on all individuals in the population. All exchange sequences after exchange learning are sorted from large to small according to the fitness of the learning object and form an exchange list. The exchange sequences in the list are added in sequence to obtain a combined exchange sequence. is a list (vector) whose dimension is equal to the total number of exchange sequences in the exchange list M. Each element is a random number between [0,1], which means the current individual X i The probability of taking the mth exchange sequence in the combined exchange sequence is less than the probability of taking exchange learning, otherwise it is not taken. i The number of exchange learning for all individuals in the population is k≤M, and the individual X i After exchange learning, the improved Metropolis criterion is adopted, and there is a certain probability of accepting a worse solution.

[0127]

[0128] Among them, t is the current iteration number and T is the maximum iteration number.

[0129] S5. Arrange output data: combine and output the static allocation scheme obtained by solving the constrained optimization problem model and the path allocation scheme obtained by solving the traveling salesman problem model to complete the allocation optimization of the earth and stone to be processed.

[0130] Verify the ISABO algorithm:

[0131] Taking 31 nodes as an example, after 2000 iterations, the discrete particle swarm converges in nearly 800 iterations, and its convergence curve is shown in Figure 5 , while the optimal distance is 17.1621, taking 17.85s.

[0132] The construction optimization plan route is shown in Figure 6 , the convergence curve of ISABO algorithm can be seen in Figure 7 ,ISABO algorithm can find the optimal solution in almost every generation, and its optimal solution is 16.4129, which takes 15.23s. In terms of comprehensive performance, ISABO algorithm has better optimization performance.

[0133] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for optimizing earthwork allocation based on a combined problem model framework, characterized in that: Including: Obtain the construction node information, cost information, and vehicle load capacity information of the earthwork to be processed; Taking the minimum cost as the goal, construct a linear programming model based on the construction node information and cost information and solve it through a solver to obtain a static allocation plan, and store the static allocation plan as a multi-way tree, where the root node in the multi-way tree is the coordinate code of the construction area, and the leaf node is the construction process code; Taking the shortest path as the goal, construct a traveling salesman problem-like model based on the construction node information, cost information, and vehicle load capacity information, and call the data in the multi-way tree to solve it through the ISABO algorithm to obtain a path allocation plan; Combine and output the static allocation plan and the path allocation plan to complete the allocation optimization of the earthwork to be processed.

2. The earthwork allocation optimization method based on the combined problem model framework according to claim 1 is characterized in that: The construction node information includes: construction attributes, construction volume to be carried out, and distances between construction nodes; The cost information includes: unit allocation cost and related cost expenses.

3. The earthwork allocation optimization method based on the combined problem model framework according to claim 1 is characterized in that: The linear programming model includes an earthwork excavation and filling balance model, an earthwork excavation less than filling model, and an earthwork excavation greater than filling model, where the earthwork excavation and filling balance model is: The earthwork excavation less than filling model is: The earthwork excavation greater than filling model is: Among them, Z is the total transportation cost; c ij is the unit freight from excavation i to filling j; x ij is the amount of transfer from excavation i to filling j; a i is the construction volume of excavation i; b j is the construction volume of fill j; i = 1, 2, ..., m, m is the total number of excavations; j = 1, 2, ..., n, n is the total number of fills.

4. The earthwork allocation optimization method based on the combined problem model framework according to claim 1 is characterized in that: Storing the static allocation plan as a multi-way tree includes: Carry out coordinate coding for the excavation construction area and the filling construction area of each construction plan in the static allocation plan; Calculate the construction process of each construction plan according to the vehicle load capacity information and encode it in sequence; Store the coordinate code of each construction plan as the root node of the multi-way tree, and store the construction process code corresponding to the construction plan as the leaf node of the multi-way tree.

5. The earthwork allocation optimization method based on the combined problem model framework according to claim 1 is characterized in that: The traveling salesman problem-like model is: c t =X·C·X T S, t Among them, E t represents the volume of earthwork transported in step t; c t represents the cost per unit earthwork volume associated with the t-th construction step; is a binary variable (0,1), indicating whether the i node is the starting node of the t-th transport, N is the number of nodes; C is the cost matrix, recording the unit transportation cost between nodes; S i represents the initial earthwork construction volume of node i, S i >0 means that the i-node is a cutting area, otherwise it is a filling area; is the remaining earthwork volume of node i after the t-th construction step, is the input earthwork volume of node i after the t-th construction step, is the output earthwork volume of node i after the t-th construction step, R i represents the designed earthwork volume of node i, is the remaining earthwork volume of node i after s finite steps of construction.

6. The earthwork allocation optimization method based on the combined problem model framework according to claim 1 is characterized in that: The ISABO algorithm is obtained by improving the initial population generation strategy and update mechanism of the SABO algorithm.

7. The earthwork allocation optimization method based on the combined problem model framework according to claim 6 is characterized in that: The working process of the ISABO algorithm is: Step 1: Set the population size N and the maximum number of iterations T, generate an initial population based on the chaotic dynamic target strategy, record the initial generation population t = 0, and calculate the fitness of all individuals in the population; Step 2: Let i = 1, t = 1, calculate the fitness of the i-th search agent in the current population of the t-th generation, and calculate the updated position of the search agent through the exchange learning mechanism, and select and update the individuals of the (t - 1)-th generation through the improved Metropolis criterion; if i < N, then set i to increase by 1 and continue to iteratively calculate the fitness of the search agent until i = N, and record the best particle position of this iteration; Step 3: If t < T, then set t to increase by 1 and perform the next round of iteration until t = T, and output the best particle in all iterations.

8. The earthwork allocation optimization method based on the combined problem model framework according to claim 7 is characterized in that: The process of generating the initial population based on the chaotic dynamic target strategy includes: Initialize the alternative pool of process nodes, where the alternative pool contains all unselected leaf nodes of the multi-way tree; cut the interval into several equal parts according to the total number of root nodes of the multi-way tree, and map all root nodes on the discretized interval after discretizing the interval; A piecewise chaotic map is used to generate a chaotic sequence of several populations, and a mapping discrete interval corresponding to the chaotic sequence is found, and then the corresponding root node is found; the root node corresponding to the chaotic sequence is used as the initial root node of all paths, and then a leaf node is selected from each initial root node as the initial process node of the path, and the initial process node is removed from the candidate pool; Each individual in the population starts from the initial process node, selects any leaf node from the root node closest to the root node where the previous construction node is located from the candidate pool, and then adds the selected leaf node to the path until all leaf nodes in the candidate pool are selected and a path is generated.

9. The earthwork allocation optimization method based on the combined problem model framework according to claim 7 is characterized in that: The exchange learning mechanism is: A- v B=—sign(F(A)-F(B))(A-B) in, For the new search agent, X i For search agents, is a vector of random numbers in the interval (0,1), which is the probability set of selecting the exchange operator. Indicates the current search agent X i Exchange learning is performed on all search agents in the population. -sign(F(A)-F(B)) is the judgment function for comparing the fitness of A and B. A and B refer to two different search agents in the population. v B is an exchange sequence in which A exchanges with B for learning.

10. The earthwork allocation optimization method based on the combined problem model framework according to claim 9 is characterized in that: The improved Metropolis criterion is: Among them, t is the current iteration number and T is the maximum iteration number.

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