Earth and stone allocation optimization method and system based on discrete marine predator algorithm

Abstract

The invention provides an earth-rock allocation optimization method and system based on a discrete ocean predator algorithm. The method comprises the following steps: initialization: encoding an earth-rock allocation scheme in a triple form; in a high speed ratio stage, a population grouping strategy is adopted for the initialized deployment scheme; at the same speed ratio stage, half of the prey moves in a small range in a Levy flight mode, and the other half of the prey updates the position through large-range movement of the predator; in the low speed ratio stage, the prey moves in a small range according to the position of the predator; and in consideration of a fish aggregation effect caused by environmental change, performing large neighborhood jump according to probability in an iteration process so as to avoid falling into a local optimal solution. The discrete ocean predator algorithm based on a population exchange and update mechanism of a triple coding mode is superior to a traditional ant colony algorithm in solving performance and solving precision, and a brand-new design thought is provided for converting a continuous optimization algorithm into a discrete optimization algorithm to solve an earth-rock deployment optimization problem.

Description

Technical Field

[0001] The present invention relates to the technical field of earthwork allocation, and in particular to an earthwork allocation optimization method and system based on a discrete ocean predator algorithm. 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 and improper human resource organization, which lead to construction delays and increased costs. The main technical route currently used to optimize earthwork allocation is to establish a discrete mathematical model of combinatorial optimization problems for actual engineering problems and use optimization methods to solve them. Due to the high efficiency and accuracy of linear programming solutions, the mathematical model of earthwork allocation in engineering is often simplified to a linear programming model, mainly considering the material constraints in the actual earthwork allocation optimization problem. However, in large-scale allocation and complex problems involving multiple factors, the linear programming method has poor versatility and has great limitations in the face of nonlinear factors. The solution results can only show the overall static plan, but cannot reflect the specific construction steps, which is not conducive to the organization and arrangement of subsequent tasks by engineering personnel.

[0003] In recent years, discrete metaheuristic algorithms represented by genetic algorithms and ant colony optimization (ACO) have shown good versatility in practical problems in various engineering fields, especially in large-scale and complex problems. Especially for the problem of earthwork allocation, such as an earthwork allocation method based on an improved ant colony algorithm (publication number: CN116882573A) and an earthwork allocation method based on an ant colony algorithm (Journal of Civil Engineering and Management, 2019), they focus on optimizing the construction process of earthwork allocation, can consider nonlinear factors and can show the construction process, transportation flow and flow direction of the optimized construction plan.

[0004] At present, more and more metaheuristic algorithms are designed to solve continuous optimization problems, but there is a lack of metaheuristic algorithms designed specifically for earthwork allocation problems. Traditional continuous metaheuristics are difficult to apply to earthwork allocation problems because it is impossible to build a suitable and accurate mapping relationship between the algorithm continuous domain and the problem discrete domain. Summary of the invention

[0005] In order to solve the above problems, an embodiment of the present invention provides an earthwork allocation optimization method based on a discrete marine predator algorithm (Discrete Marine Predators Algorithm, DMPA), comprising: initializing a population of earthwork allocation schemes to obtain an initialized allocation scheme; the earthwork allocation scheme is in the form of a triple (s i , d j, t) is encoded, where s i is the excavation node whose remaining construction volume is not 0, d j is the filling node whose remaining construction volume is not 0, and t is the node s i To node d j transportation construction volume; in the high speed ratio stage, a population grouping strategy is adopted for the initialized deployment plan: the first half of the population uses the predator to perform Brownian motion, and the prey updates its position according to the Brownian motion of the predator; the second half of the population uses the prey to perform Brownian motion; in the same speed ratio stage, half of the prey moves in a small range by Levy flight, and the other half of the prey updates its position by using the large-scale motion of the predator; in the low speed ratio stage, the prey uses the predator position to move in a small range; for environmental problem factors, large neighborhood jumps are performed according to probability during the iteration process to avoid falling into the local optimal solution.

[0006] The embodiment of the present invention successfully improves the marine predator algorithm and designs a new discrete group heuristic algorithm - discrete marine predator algorithm, which has obvious solution advantages over the traditional ant colony algorithm in the optimization problem of earthwork allocation; the triple encoding method designed for the earthwork allocation problem is simple and clear, which can accurately map the phenotype of the discrete problem individuals in the algorithm, and facilitate the subsequent perturbation and update mechanism of the algorithm design. Based on the triple encoding perturbation and mutation mechanism, a new design idea is provided for converting the continuous optimization algorithm into a discrete optimization algorithm.

[0007] Optionally, the earthwork allocation scheme is initialized to obtain an initialized allocation scheme, including: half of the population is generated by a random dynamic target strategy, and the other half of the population is generated by a greedy dynamic target strategy; the random dynamic target strategy is as follows: for a triple allocation scheme, first randomly select a node s from the excavation nodes whose remaining construction volume is not 0 i Then randomly select a node d from the filling nodes whose remaining construction volume is not 0 j , generate transportation construction volume t = min (a i , b j ), where a i and b j Node s i and node d j The initial construction quantity constraint generates a triple solution (s i , d j , t), and then update the remaining construction volume of the node, that is, s i =s i -t,d i =d i-t, and so on, multiple triplet solutions are generated until the remaining construction volume of all construction nodes is 0; the greedy dynamic target strategy is as follows: when selecting a filling node, select the filling node closest to the excavation node from the set of filling nodes whose remaining construction volume is not 0.

[0008] The embodiment of the present invention designs a triple encoding method to accurately express the phenotype of discrete problem individuals, and designs a heuristic perturbation and mutation mechanism based on this.

[0009] Optionally, in the high speed ratio stage, the mathematical model of the first half of the population is:

[0010]

[0011]

[0012]

[0013] in, is the step vector, is the predator vector, is the prey vector, Iter is the current iteration number, Max Iter is the maximum iteration number, and the symbol represents element-by-element multiplication, O R The symbol represents the random key-based sorting operator used to simulate Brownian motion. The symbol represents a random vector consisting of {0, 1}, which is used to randomly select Part of the triple information in O RP The symbol represents the optimal pairing operator, which uses the selected triple information to repair or regenerate individuals;

[0014] O RP Used to obtain the triplet encoding of the mining node sequence s i , and then assign each s i Node A uniformly distributed random number between [0, 1], for all s i The random numbers corresponding to the nodes are sorted from small to large to obtain a new excavation node sequence make After reorganization, a new triplet code is obtained, and finally the triplet code is optimally repaired.

[0015] Optionally, in the high speed ratio stage, the mathematical model of the second half of the population is:

[0016]

[0017] Optionally, in the same speed ratio stage, the mathematical model is as follows:

[0018]

[0019]

[0020]

[0021] Among them, O S The symbol represents the exchange operator based on contribution. Its specific operation is to first calculate the total cost of the individual code as the identification attribute of each triple - contribution, sort all triples from large to small according to contribution, and select the two different s with the largest contribution. i The node triples and records their index positions in the individual codes, exchanging their s i After the node, replace the original position, and finally perform the optimal repair on the individual code; S The (P) operator represents a repeated operation, where P is the probability of repeated operation. Based on the number of triples m in the individual code, it is repeated ceil(m*p) times O S operate;

[0022]

[0023]

[0024] Among them, O RP (CF) operator is O RP The extension of the operator is used for repeated operations. CF is the probability of repeated operations. Based on the number of triplets m in the individual code, repeat ceil(m*CF) times O RP Operation, and finally optimally repair the individual code.

[0025] Optionally, in the low speed ratio stage, the mathematical model is as follows:

[0026]

[0027] Optionally, for environmental factors, the mathematical model is as follows:

[0028]

[0029] FADF=FADs(1-r)+r

[0030] Among them, LM is a large-scale mutation operator, which is used to realize large-scale mutation of encoded individuals. C is the coding combination operator, which is used to randomly combine the triples of two individuals to form a new coding individual, and then repair the individual. NPIt is the neighboring optimal pairing operator, which is used to randomly obtain 3 consecutive triplets from the individual code. The Select function selects the first k triplets in the individual code, k = ceil (m*FADF), m is the number of triplets in the individual code, and r, r1, r2, r3 are uniformly distributed random numbers between [0, 1].

[0031] Optionally, the O LM operator, which is used to calculate the contribution of each triple in the individual code, sort all the triples from large to small according to their contribution, and then sort the d j The filling node sequence is symmetrically exchanged and finally optimally repaired.

[0032] The embodiment of the present invention defines the operations and operators of each stage of the discrete marine predator algorithm in detail, and can construct a suitable and accurate mapping relationship between the continuous domain of the algorithm and the discrete domain of the problem. Based on the triple coding perturbation and mutation mechanism, it provides a new design idea for converting the continuous optimization algorithm into a discrete optimization algorithm.

[0033] Optionally, the deployment scheme is a set of all triples.

[0034] In the embodiment of the present invention, the deployment schemes that are not zero in the matrix are represented by triples. The complete deployment scheme is a set of all triples. A complete deployment scheme is an individual in the algorithm.

[0035] An embodiment of the present invention provides an earthwork allocation optimization system based on a discrete ocean predator algorithm, which is used to execute any of the methods described above.

[0036] The earthwork allocation optimization system based on the discrete ocean predator algorithm provided by the embodiment of the present invention can achieve the same technical effect as the earthwork allocation optimization method based on the discrete ocean predator algorithm mentioned above. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] 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 or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0038] Figure 1 This is an optimized schematic diagram of a loop composed of six cities in an embodiment of the present invention;

[0039] Figure 2 A flow chart of an earthwork allocation optimization method based on a discrete marine predator algorithm provided in an embodiment of the present invention;

[0040] Figure 3 is a random key sorting operator O in the embodiment of the present invention. R Operation diagram of

[0041] Figure 4 is the optimal pairing operator O in the embodiment of the present invention. RP Operation diagram of

[0042] Figure 5 is the large-scale mutation operator O in the embodiment of the present invention. LM Operation diagram of

[0043] Figure 6 is the coding combination operator O in the embodiment of the present invention. C Operation diagram of

[0044] Figure 7 It is a convergence comparison diagram of the DMPA algorithm and the ACO algorithm in an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to make the above-mentioned objects, features and advantages of the present invention more clearly understood, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0046] The embodiment of the present invention uses the Marine Predators Algorithm (MPA) to design a discrete marine predator algorithm based on a population exchange and update mechanism in a triple encoding method. The algorithm is superior to the traditional ant colony algorithm in terms of solution performance and solution accuracy. The embodiment of the present invention provides a new design idea for converting a continuous optimization algorithm into a discrete optimization algorithm to solve the earthwork allocation optimization problem.

[0047] Specifically, the existing scheme for optimizing earthwork allocation has the following disadvantages:

[0048] 1. Combinatorial optimization problems, mainly represented by linear programming problems, are difficult to handle nonlinear factors in the model. Once faced with large-scale problems, due to the large number of constraints, it is very cumbersome to adjust the model, and the model is less versatile. This method can only statically present the overall final result, and cannot specifically present the construction process flow, which is not conducive to the construction personnel to organize the transportation plan.

[0049] 2. Designing a group heuristic algorithm with good performance to solve engineering problems is the main trend of engineering optimization. Most of them are designed for continuous problems, and there is a lack of new metaheuristic algorithms specifically for earthwork allocation. The embodiment of the present invention uses the Marine Predator Algorithm (2020) to propose a new discrete metaheuristic algorithm for earthwork allocation optimization for the first time, the Discrete Marine Predator Algorithm (DMPA);

[0050] 3. Traditional continuous metaheuristics are difficult to apply to earthwork allocation problems. The main reason is that it is impossible to build a suitable and accurate mapping relationship between the algorithm continuous domain and the problem discrete domain. The embodiment of the present invention designs a triple encoding method based on the problem characteristics, accurately expresses the phenotype of discrete problem individuals, and designs a heuristic perturbation and mutation mechanism on this basis. It provides a new design idea for converting continuous optimization algorithms into discrete optimization algorithms.

[0051] The linear programming model for earthwork allocation is as follows.

[0052] The optimization problem of earthwork allocation belongs to the combinatorial optimization problem. This part establishes a linear programming model for earthwork allocation with the minimum transportation cost as the optimization goal. The basic model is as follows:

[0053] minmize: z = f(x)

[0054]

[0055] 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 j are the upper and lower bounds respectively. For the general earthwork allocation problem, it can be described as a linear programming model: suppose there are m excavations and n fills for the earthwork project; a i is the supply of the i-th excavation, i = 1, 2, ..., m; b j is the demand for the jth filling, j = 1, 2, ..., n; c ij is the unit freight from excavation i to filling j; x ij is the transportation quantity from excavation i to filling j. The model should give a reasonable allocation plan so that the total transportation cost Reach a minimum.

[0056] Its mathematical model can be divided into cut-fill balance, cut less than fill, and cut more than fill according to the supply relationship between cut and fill. The final allocation plan is presented in matrix form as follows.

[0057]

[0058] Table 1 shows the final deployment plan in matrix form, where the dotted line part is an example.

[0059]

[0060] Table 1

[0061] Before introducing the basic principles of the marine predator algorithm, the concept of algorithm neighborhood must be introduced: in optimization algorithms, neighborhood refers to a set of solutions that are "close" to the current solution under a certain definition. Specifically, if there is a solution x, its neighborhood N(x) contains all solutions obtained from x through changes within a certain range (such as perturbations of addition and subtraction) or a series of finite operations (such as transformations, modifications, etc.). The solution space of a continuous neighborhood is continuous, usually involving real numbers or points in a real number interval. For example, in an optimization problem, it may be necessary to find the minimum value of a function, and the value of the solution can be any real number. The discrete solution space is discrete, usually involving integers or specific discrete values. For example, the solution in a combinatorial optimization problem (such as the traveling salesman problem) is a permutation or combination of a finite number of elements.

[0062] 3-opt is a classic neighborhood search algorithm for the Traveling Salesman Problem (TSP), which finds a better solution by rearranging the three edges of the path. In 3-opt, the neighborhood structure is defined as the set of new paths generated by the operation of three edges. Assuming that the problem of optimizing a loop consisting of 6 cities is to find the shortest path, 8 new loops can be generated in the current loop through 3-opt operations. Figure 1 The figure shows an optimized schematic diagram of a loop composed of 6 cities, where solid points represent cities, solid lines represent new paths, and dotted lines represent original paths. The structure of these 8 solutions is the so-called neighborhood structure. The concepts of "large-scale movement", "small-scale movement", and "large neighborhood jump" mentioned below all refer to a choice determined in the neighborhood structure of the current solution. "Large range" and "large neighborhood" mean that there are more solutions to choose from, and the differences in solutions in the neighborhood structure are often large, while "small range" is a small disturbance to the current solution.

[0063] Basic principles of the ocean predator algorithm

[0064] Similar to most metaheuristic methods, MPA is a population-based approach, where the initial solutions are uniformly distributed in the search space as initial values:

[0065] X0=X min +rand(X max -X min ) (1.1)

[0066] Among them, X min and X maxare the lower and upper bounds of the variable, and rand is a uniform random vector in the range of 0 to 1. According to the theory of survival of the fittest, the top predators in nature are more talented in foraging. Therefore, the fittest solutions are named top predators to construct a matrix called elite. The array of this matrix supervises the search and discovery of prey based on the location information of the prey.

[0067]

[0068] In the formula Represents the top predator vector, which is replicated n times to construct the elite Elite matrix. n is the number of search agents and d is the dimension of the search agent. It is worth noting that both predators and prey are considered search agents. Because when the predator is looking for prey, the prey is also looking for its own food. At the end of each iteration, if the top predator is replaced by a better predator, the elite will be updated. Another matrix of the same dimension as Elite is called Prey, and the predator updates its position based on it. In short, initialization creates the initial prey, and the individuals with the best fitness (predators) construct the elite. The prey matrix is ​​shown below:

[0069]

[0070] In the above formula, X ij represents the jth dimension of prey i. The entire optimization process is mainly and directly related to the above two matrices.

[0071] The MPA optimization process is mainly divided into three optimization stages, considering different speed ratios between predators and prey, and simulating three different stages of predators and prey at the same time:

[0072] (1) High speed ratio stage: the prey moves faster than the predator;

[0073] (2) Same speed ratio stage: predator and prey move at almost the same speed;

[0074] (3) Low speed ratio stage: the predator moves faster than the prey.

[0075] For each defined phase, a specific iteration cycle is specified and assigned. The steps are defined based on the nature of the movement of predators and prey, while mimicking the movement of predators and prey in nature. The three phases include:

[0076] Phase 1: In the high speed ratio phase, the prey moves faster than the predator. This happens in the initial iterations of the optimization, when the algorithm is important for individual exploration. In the high speed ratio state, the best strategy for the predator is to stay still, while the prey chooses to use Brownian motion to move over a large area. The mathematical model of this rule is:

[0077]

[0078] Where R B is a vector containing random numbers, based on a normal distribution, representing Brownian motion. The symbol Represents element-by-element multiplication. B Multiply it by the prey to simulate the movement of the prey. P=0.5 is a constant, and R is a vector of uniform random numbers in [0,1]. This happens in the first third of the maximum number of iterations. Iter is the current iteration, and Max Iter is the maximum number of iterations. Stepsize is the step size.

[0079] Phase2: In the same speed ratio phase: both the predator and the prey move at the same speed, which simulates that both of them are looking for prey. This part occurs in the middle stage of the optimization, where individual exploration attempts temporarily turn into individual exploitation. In this phase, both exploration and exploitation are important. Therefore, half of the population is designated for exploration and the other half is used for exploitation. In this phase, the prey is responsible for exploitation, while the predator is responsible for exploration, and if the prey flies in Levy flight, the best strategy for the predator is Brownian motion. Therefore, in this phase, the algorithm considers that the prey moves in Levy flight, while the predator is updated in Brownian motion:

[0080]

[0081] in is a vector of random numbers based on the Levy distribution, representing a Levy flight. The product of and Prey simulates the movement of prey in Levy flight. Since most of the step sizes in the Levy distribution are associated with small step sizes, this section helps in algorithm development. For the second half of the population:

[0082]

[0083] when is considered as an adaptive parameter that controls the predator's movement step size. The sum-elite product simulates that the predator moves in a Brownian motion, while the prey updates its position according to the Brownian motion of the predator.

[0084] Phase 3: In the low speed ratio stage: the prey moves slower than the predator. This happens at the end of the optimization process, which is related to the high development ability of the algorithm. The best strategy for the predator in the low speed ratio state is to perform Levy flight. This stage is presented as:

[0085]

[0086] In the above formula, Multiplying with Elite simulates the movement of the predator, while adding the corresponding step size to the Elite position simulates the movement of the predator to help update the position of the prey.

[0087] The algorithm simulates the movement of predators and prey according to their hunting strategies in different phases, based on what happens in nature. These phases simulate the step size rules of the movement of the predator to catch its prey. In the first phase, the predator is not moving, while in the second phase, it is a Brownian motion and finally in the third phase, it exhibits a Lévy flight strategy. This also happens with the prey, where the prey is another potential predator, such as the silky shark and the tuna. They are both considered marine predators, but the tuna is the prey of the silky shark, which is a predator of bony fish and marine invertebrates.

[0088] Phase 4: Another factor that causes changes in the behavior of marine predators is environmental issues, such as eddy formation or the Fish Aggregation Devices (FADs) effect. According to research, marine predators like sharks spend more than 80% of their time near FADs, and the remaining 20% ​​of the time, they will make longer jumps in different dimensions, probably to find another environment where prey is distributed. FADs are considered to be local optima in the algorithm, and during the simulation process, predators consider making longer step jumps to avoid stagnation in the local optimum. Therefore, the FADs effect is mathematically expressed as:

[0089] Where FADs=0.2 is the probability of FADs affecting the optimization process. U is a binary vector containing arrays of 0 and 1. This is constructed by generating a random vector in [0, 1] and changing its array to 0 if it is less than 0.2 and to 1 if it is greater than 0.2. r is a uniform random number in [0, 1]. and represents the upper and lower limits of individuals, and the subscripts r1 and r2 represent random individuals in the prey matrix.

[0090] Marine predators have a good memory and are able to recall where they have successfully foraged. After updating the prey and implementing the FAD effect, a matrix is ​​built to evaluate the fitness of the updated elite. The fitness of each solution of the current iteration is compared to the equivalent solution in the previous iteration, and if the current solution is more fit, the current solution replaces that solution. This process also improves the quality of the solution over iterations and also simulates the return of the predator to the location of the prey-rich area where it foraged successfully.

[0091] This embodiment provides an earthwork allocation optimization method based on the discrete ocean predator algorithm, which successfully improves the ocean predator algorithm and has obvious advantages in solving the earthwork allocation optimization problem. Figure 2 The flow chart of the earthwork allocation optimization method based on the discrete ocean predator algorithm is shown in FIG. 1 , and the method mainly includes the following steps:

[0092] S102, initializing the population of the earthwork allocation plan to obtain an initialized allocation plan.

[0093] The earthwork allocation scheme adopts the triple form (s i ,d j ,t) is encoded, where s i is the excavation node whose remaining construction volume is not 0, d j is the filling node whose remaining construction volume is not 0, and t is the node s i To node d j of transportation construction volume.

[0094] In order to establish a reasonable and accurate individual phenotype for the earthwork allocation problem, inspired by the matrix form of the final allocation plan, a complete allocation plan is encoded in the form of multiple triplets, which are explained in detail using the allocation plan matrix form in Table 1 above.

[0095] Only the allocation plans that are not zero in the matrix are represented by triples. For example, the triple encoding form of transporting 2 from excavation a1 to filling b1 is (a1, b1, 2). Then the complete allocation plan is the set of all triplets, including {(a1, b1, 2), (a1, b4, 1), (a2, b3, 2), …, (a4, b4, 4)}. A complete allocation plan is an individual (search agent) in the algorithm.

[0096] The population of earthwork allocation scheme is initialized, and the initialized allocation scheme includes: half of the population is generated by random dynamic target strategy, and the other half of the population is generated by greedy dynamic target strategy.

[0097] Population initialization: In order to obtain better optimization results, half of the population is generated using a random dynamic target strategy, and the other half is generated using a greedy dynamic target strategy.

[0098] The random dynamic target strategy is as follows: For a triplet allocation plan, first randomly select a node s from the excavation nodes whose remaining construction volume is not 0 i Then randomly select a node d from the filling nodes whose remaining construction volume is not 0 j , generate transportation construction volume t = min (a i , b j ), where a iand b j Node s i and node d j The initial construction quantity constraint generates a triple solution (s i , d j , t), and then update the remaining construction volume of the node, that is, s i =s i -t,d i =d i -t, and so on, generate multiple triplet solutions until the remaining construction volume of all construction nodes is 0;

[0099] The greedy dynamic target strategy is as follows: when selecting a fill node, select the fill node closest to the cut node from the set of fill nodes whose remaining construction volume is not 0. The greedy dynamic target strategy is similar to the random dynamic target strategy, except that when selecting a fill node, it is no longer a random selection, but a fill node closest to the cut node from the set of fill nodes whose remaining construction volume is not 0.

[0100] S104, in the high speed ratio stage, a population segmentation strategy is adopted for the initialized deployment scheme: the first half of the population uses the Brownian motion of the predator to move, and the prey updates its position according to the Brownian motion of the predator; the second half of the population uses the Brownian motion of the prey.

[0101] Phase 1: Refer to formula (1.4). In this phase, prey generally move over a large area, while the best strategy for predators is to stay still. Since a random and greedy mixed population initialization strategy is adopted, it is hoped that individuals with better fitness will converge in a better direction while moving on a large scale, and individuals with poor fitness will move on a large scale to explore a larger solution space and maintain population diversity. Therefore, the algorithm adopts the population segmentation strategy of phase 2 in advance in this phase. For the first half of the population:

[0102]

[0103] Due to the particularity of the triplet encoding form, that is, each triplet in the overall encoding of an individual has an information guiding role. Therefore, this method uses the triplet of a part of elite individuals to simulate the moving distance between prey and predator. R The symbol represents the random key-based sorting operator used to simulate large-scale Brownian motion, and The symbol represents a random vector consisting of {0, 1}, which is used to randomly select Part of the triple information in O RP The symbol represents the optimal pairing operator, which uses the selected triple information to repair or regenerate individuals.

[0104] OR The specific operation of the operator is to obtain the digging node sequence s encoded by the triplet i , and then assign each s i Node A uniformly distributed random number between [0, 1], for all s i The random numbers corresponding to the nodes are sorted from small to large to obtain a new excavation node sequence make After reorganization, a new triplet code is obtained, and finally the triplet code is optimally repaired.

[0105] Figure 3 is a random key sorting operator O in the embodiment of the present invention. R Operation diagram of . For each s i The random numbers assigned to the nodes are 0.12, 0.45, 0.78, and 0.27. After sorting, we get The value is 1423, and a new triple sequence is obtained after recombination and repair.

[0106] O RP The operator is the random optimal pairing operator, which is to randomly obtain three filling nodes d from the individual code. j Different triples, and record the position index of each triple in the individual code, and then dig the node sequence s in the selected triple i and fill node sequence d j , re-align i and d j Random pairing is performed, which will generate triplet codes of 6 neighborhood structures. The cost of each neighborhood structure is calculated, and the combination with the smallest cost is selected as the optimal pairing triplet to replace the position of the original triplet in the individual code. Finally, the individual code is optimally repaired. Figure 4 is the optimal pairing operator O in the embodiment of the present invention. RP The operation diagram shows random selection of three triplets, 6 neighborhood structures, calculation to determine the three triplets with the lowest cost, namely (1, 6, 4) (3, 7, 1) (3, 5, 3), and then optimal pairing.

[0107] For the second half of the population, we choose to let individuals directly use O R The operator is updated to increase population diversity, so there is a mathematical model:

[0108]

[0109] S106, in the same speed ratio stage, half of the prey performed a small-scale movement using Levy flight, and the other half updated their positions using the large-scale movement of the predator.

[0110] Phase 2: Refer to equations (1.5) and (1.6). In this phase, half of the prey chooses small-step Lévy flight to move in a small range in order to better exploit. The other half uses the large-scale movement of elite individuals to explore the population. Similarly, it is hoped that individuals can converge in a better direction regardless of exploration or exploitation. Therefore, the mathematical model is as follows:

[0111]

[0112] In the above formula, O S The symbol represents the exchange operator based on contribution. Its specific operation is to first calculate the total cost of the individual code, calculate the contribution of each triple (triple cost divided by the total cost of the individual code), sort all triples from large to small according to contribution, select the triples of two different nodes with the largest contribution and record their index positions in the individual code, exchange their nodes, replace the original positions, and finally perform the optimal repair on the individual code. S The (P) operator can repeat the operation, where P (for example, P is 0.5) is the probability of repeating the operation, that is, based on the number of triples m in the individual code, it is repeated ceil(m*p) times. S operate.

[0113]

[0114] In the above formula, O RP (CF) operator is O RP The expansion of the operator is used for repeated operations. The probability of repeated operations is retained, and the update formula of the original MPA is: Based on the number of triplets in the individual code, repeat ceil(m*CF) times O RP Operation, and finally optimally repair the individual code.

[0115] S108, in the low speed ratio stage, the prey uses the predator's position to move in a small range.

[0116] Phase 3: Refer to formula (1.7). In this stage, which is the late stage of the algorithm, most prey tend to converge. It is hoped that the prey will use the predator's position to move in a small range to obtain a better position, so O is used. S Update, so there is a model:

[0117]

[0118] S110, for environmental problem factors, large neighborhood jumps are performed probabilistically during the iteration process to avoid falling into the local optimal solution.

[0119] Phase 4: This phase does not depend on the number of iterations, and each iteration of the algorithm must go through this phase. The most important role of this phase is to help the algorithm get rid of the dilemma of FADs local optimality. According to the original algorithm formula (1.8), predators spend 80% of their time in FADs searching for better positions, and 20% of their time moving on a large scale to other sea areas to find positions. It is understood that marine predators have an 80% probability of deepening development and updating to a better position, and a 20% chance of moving on a large scale for exploration, so there is a mathematical model:

[0120]

[0121] FADF=FADs(1-r)+r (1.14)

[0123] Among them, LM is a large-scale mutation operator, which is used to realize large-scale mutation of encoded individuals. C It is a coding combination operator, whose main function is to randomly combine the triples of two individuals to form a new coding individual, and then repair the individual. NP is the neighboring optimal pairing operator, and its function is the same as O RP Similarly, three consecutive triplets are randomly obtained from the individual code, and the Select function selects the first triplet in the individual code, where k = ceil(m*FADF), m is the number of triplets in the individual code, and r, r1, r2, and r3 are uniformly distributed random numbers between [0,1].

[0124] The following focuses on O LM Operator: Calculate the contribution of each triple in the individual code, sort all triples from large to small according to their contribution, then symmetrically exchange the filling node sequence in the sorted triples, and finally perform optimal repair. Figure 5 is the large-scale mutation operator O in the embodiment of the present invention. LM Schematic diagram of the operation of , which shows the symmetric swap forming a new triplet. Figure 6 is the coding combination operator O in the embodiment of the present invention. C Schematic diagram of the operation of, which shows the random combination of triplets of two individuals to form a new encoded individual.

[0125] The embodiment of the present invention designs a basic example of earthwork algorithm based on actual engineering problems, and its specific situation is shown in Table 2. The earthwork example belongs to the cut-and-fill balance example and has a unit price in the nonlinear stage, and its specific situation is shown in Table 3.

[0126]

[0127]

[0128] Table 2 Initial earthwork unit engineering information table

[0129]

[0130]

[0131] Table 3 Earthwork unit price table

[0132] When the computational experiment was conducted in the embodiment of the present invention, the linear programming, ant colony algorithm (publication number: CN116882573A), and DMPA were used to compare the example. For the sake of fairness, the specific parameters of the ant colony algorithm are α=1, β=3, pheromone volatilization factor=0.1, constant coefficient Q=1000000 in the ant colony model, and DMPA was independently run 20 times with a population size of 30 and a total number of iterations of 500. The optimal value, worst value, average value, median value, standard deviation and relative error rate of the algorithm iteration were recorded (the optimal value of the linear programming was taken as the benchmark, and the relative error between the average value and the optimal value was calculated). In this example, the optimal value of the linear programming is 7.5813397785e+07. The experimental records of the ant colony algorithm ACO and DMPA are shown in Table 4 for details, and the schematic diagram of the convergence of a single algorithm is shown in Figure 7 .like Figure 7 The convergence comparison diagram of the DMPA algorithm and the ACO algorithm is shown. The best individuals of the two algorithms are recorded during the iteration process. The best fitness curves of DMPA are all below the best fitness curve of ACO. When the number of iterations is the same, the best fitness of DMPA is less than the best fitness of ACO. The best fitness is the minimum cost.

[0133]

[0134]

[0135] Table 4 Comparison of experimental indicators of ACO and DMPA

[0136] From Table 4, it can be concluded that DMPA is significantly better than the ant colony algorithm in all aspects, and DMPA is more competitive than the ant colony algorithm in solving the earthwork allocation problem.

[0137] The embodiment of the present invention successfully improves the marine predator algorithm and designs a new discrete group heuristic algorithm - discrete marine predator algorithm, which has obvious solution advantages over the traditional ant colony algorithm in the optimization problem of earthwork allocation; the triple encoding method designed for the earthwork allocation problem in the embodiment of the present invention is simple and clear, which can accurately map the phenotype of the discrete problem individuals in the algorithm, and facilitate the subsequent perturbation and update mechanism of the algorithm design. Based on the triple encoding perturbation and mutation mechanism, it provides a new design idea for converting the continuous optimization algorithm into a discrete optimization algorithm.

[0138] An embodiment of the present invention provides an earthwork allocation optimization system based on a discrete marine predator algorithm, which is used to execute the steps of the method provided in the above embodiment.

[0139] The earthwork allocation optimization system based on discrete marine predator algorithm provided in the embodiment of the present invention has the same implementation principle and technical effects as those in the aforementioned embodiment. For the sake of brief description, for matters not mentioned in the system embodiment, reference may be made to the corresponding contents in the aforementioned method embodiment.

[0140] An embodiment of the present invention provides an electronic device, which includes a processor and a storage device. The storage device stores a computer program that can be run on the processor. When the processor executes the computer program, the steps of the method provided in the above embodiment are implemented.

[0141] An embodiment of the present invention provides a computer-readable medium, wherein the computer-readable medium stores computer-executable instructions. When the computer-executable instructions are called and executed by a processor, the computer-executable instructions prompt the processor to implement the method described in the above embodiment.

[0142] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the control device through a computer program, and the program can be stored in a computer-readable storage medium. When the program is executed, it may include the processes of the above-mentioned method embodiments, wherein the storage medium may be a memory, a disk, an optical disk, etc.

[0143] In this article, relational terms such as first and second, etc. are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the statement "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0144] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0145] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing earthwork allocation based on discrete marine predator algorithm, characterized in that: include: Initialize the population of earthwork allocation plan to obtain an initialized allocation plan; The earthwork allocation scheme adopts the triple form (s i ,d j ,t) is encoded, where s i is the excavation node whose remaining construction volume is not 0, d j is the filling node whose remaining construction volume is not 0, and t is the node s i To node d j The transportation and construction volume; In the high speed ratio stage, the population grouping strategy is adopted for the initial deployment scheme: the first half of the population uses the predator to perform Brownian motion, and the prey updates its position according to the Brownian motion of the predator; the second half of the population uses the prey to perform Brownian motion; In the same speed ratio phase, half of the prey performed small-scale movements using Lévy flight, and the other half used the large-scale movements of the predator to update their positions; In the low speed ratio phase, prey exploits the predator’s position to make small movements; For environmental problem factors, large neighborhood jumps are performed probabilistically during the iteration process to avoid falling into the local optimal solution.

2. The method according to claim 1, characterized in that The earthwork allocation scheme is initialized by population initialization to obtain the initialized allocation scheme, including: half of the population is generated by a random dynamic target strategy, and the other half of the population is generated by a greedy dynamic target strategy; The random dynamic target strategy is as follows: for a triplet allocation plan, first randomly select a node s from the excavation nodes whose remaining construction volume is not 0. i Then randomly select a node d from the filling nodes whose remaining construction volume is not 0 j , generate transportation construction volume t = min (a i ,b j ), where a i and b j Node s i and node d j The initial construction quantity constraint generates a triple solution (s i ,d j ,t), and then update the remaining construction volume of the node, that is, s i =s i -t,d i =d i -t, and so on, generate multiple triplet solutions until the remaining construction volume of all construction nodes is 0; The greedy dynamic target strategy is as follows: when selecting a filling node, the filling node closest to the excavation node is selected from the set of filling nodes whose remaining construction volume is not 0.

3. The method according to claim 1, characterized in that In the high speed ratio stage, the mathematical model of the first half of the population is: in, is the step vector, is the predator vector, is the prey vector, Iter is the current iteration number, Max Iter is the maximum iteration number, and the symbol represents element-wise multiplication, O R The symbol represents the random key-based sorting operator used to simulate Brownian motion. The symbol represents a random vector consisting of {0,1}, which is used to randomly select Part of the triple information in O RP The symbol represents the optimal pairing operator, which uses the selected triple information to repair or regenerate individuals; O RP Used to obtain the triplet encoding of the mining node sequence s i , and then assign each s i Node A uniformly distributed random number in [0,1] for all s i The random numbers corresponding to the nodes are sorted from small to large to obtain a new excavation node sequence make After reorganization, a new triplet code is obtained, and finally the triplet code is optimally repaired.

4. The method according to claim 3, characterized in that In the high speed ratio stage, the mathematical model of the second half of the population is:

5. The method according to claim 4, characterized in that In the same speed ratio stage, the mathematical model is as follows: Among them, O S The symbol represents the exchange operator based on contribution. Its specific operation is to first calculate the total cost of the individual code as the identification attribute of each triple - contribution, sort all triples from large to small according to contribution, and select the two different s with the largest contribution. i The node triples and records their index positions in the individual codes, exchanging their s i After the node, replace the original position, and finally perform the optimal repair on the individual code; S The (P) operator represents a repeated operation, where P is the probability of repeated operation. Based on the number of triples m in the individual code, it is repeated ceil(m*p) times O S operate; Among them, O RP (CF) operator is O RP The extension of the operator is used for repeated operations. CF is the probability of repeated operations. Based on the number of triplets m in the individual code, repeat ceil(m*CF) times O RP Operation, and finally optimally repair the individual code.

6. The method according to claim 5, characterized in that In the low speed ratio stage, the mathematical model is as follows:

7. The method according to claim 5, characterized in that For environmental factors, the mathematical model is as follows: Among them, LM is a large-scale mutation operator, which is used to realize large-scale mutation of encoded individuals. C is the coding combination operator, which is used to randomly combine the triples of two individuals to form a new coding individual, and then repair the individual. NP It is the neighboring optimal pairing operator, which is used to randomly obtain 3 consecutive triplets from the individual code. The Select function selects the first k triplets in the individual code, k = ceil (m*FADF), m is the number of triplets in the individual code, and r, r1, r2, r3 are uniformly distributed random numbers between [0,1].

8. The method according to claim 7, characterized in that The O LM operator, which is used to calculate the contribution of each triple in the individual code, sort all the triples from large to small according to their contribution, and then sort the d j The filling node sequence is symmetrically exchanged and finally optimally repaired.

9. The method according to claim 1, characterized in that: The deployment scheme is the set of all triples.

10. A soil and rock allocation optimization system based on discrete ocean predator algorithm, characterized in that: Used to perform the method according to any one of claims 1 to 9.

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