Earthwork allocation optimization method and system based on discrete ocean predator algorithm

Abstract

The present invention provides a method and system for optimizing earthwork allocation based on a discrete marine predator algorithm. The method comprises: initialization, in which the earthwork allocation plan is encoded in triple form; a high-speed ratio phase, a population clustering strategy is applied to the initialized allocation plan; a constant-speed ratio phase, in which half of the prey perform a small-scale movement using Lévy flight, while the other half update their positions using the predator's large-scale movement; a low-speed ratio phase, in which the prey utilize the predator's position to perform a small-scale movement; and considering the fish aggregation effect caused by environmental changes, probabilistic large-neighborhood jumps are performed during the iteration process to avoid falling into local optimal solutions. The present invention's discrete marine predator algorithm, based on a population exchange and update mechanism using triple encoding, outperforms traditional ant colony algorithms in both solution performance and accuracy, providing a novel design approach for converting continuous optimization algorithms into discrete optimization algorithms for solving earthwork allocation optimization problems.

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 projects are complex system projects that are affected by many factors, making their construction organization design and management 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 the combinatorial optimization problem for the actual engineering problem and use optimization methods to solve it. Due to the high efficiency and accuracy of linear programming, the mathematical model of earthwork allocation in engineering projects is often simplified to a linear programming model, mainly considering the material constraints in the actual earthwork allocation optimization problem. However, when it comes to 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 can only show the overall static plan and 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, such as genetic algorithms and ant colony optimization (ACO), have demonstrated excellent versatility in solving practical problems across various engineering fields, particularly large-scale and complex problems. Specifically, for earthwork allocation, a method for earthwork allocation 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) have been proposed. These methods focus on optimizing the construction process for earthwork allocation, taking into account nonlinear factors and demonstrating the construction procedures, transportation flow, and flow directions of optimized construction solutions.

[0004] Currently, a growing number of metaheuristic algorithms are being designed to solve continuous optimization problems, but there is a lack of metaheuristic algorithms specifically designed for earthwork allocation. Traditional continuous metaheuristics struggle to apply to earthwork allocation due to the inability to establish a suitable and accurate mapping between the algorithm's continuous domain and the problem's discrete domain. Summary of the Invention

[0005] To solve the above problems, an embodiment of the present invention provides an earthwork allocation optimization method based on 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 For the excavation node where the remaining construction volume is not 0, d j is the filling node with a remaining construction volume not equal to 0, and t is the node from node s i To node d j transportation construction volume; in the high speed ratio stage, a population clustering 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 predator's Brownian motion; 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 Lévy flight, and the other half of the prey updates its position by using the predator's large-scale motion; in the low speed ratio stage, the prey uses the predator's 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 present invention successfully improves the marine predator algorithm and designs a novel discrete swarm heuristic algorithm—the discrete marine predator algorithm. This algorithm has significant advantages over traditional ant colony algorithms for solving earthwork allocation optimization problems. The simple and clear triple encoding scheme designed for earthwork allocation problems accurately maps the phenotypes of discrete problem individuals within the algorithm, facilitating subsequent perturbation and update mechanisms in the algorithm design. Based on the triple encoding perturbation and mutation mechanism, this provides a novel design approach for converting continuous optimization algorithms into discrete ones.

[0007] Optionally, the earthwork allocation scheme is initialized to obtain an initialized allocation scheme, which includes: half of the population is generated using a random dynamic target strategy, and the other half of the population is generated using 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 amount 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, the filling node closest to the excavation node is selected 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-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;

[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 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.

[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 individual coding 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 position in the individual code, swapping 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 the repetition operation, P is the probability of repetition, 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 triples m in the individual code, repeat ceil(m*CF) times O RP operation, and finally perform optimal repair on 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 O LM is a large-scale mutation operator, used to achieve large-scale mutation of encoding individuals, O 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 three 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, and 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 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 provides detailed definitions of the operations and operators at each stage of the discrete marine predator algorithm, 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 solution is a set of all triples.

[0034] In the embodiment of the present invention, the deployment solutions that are not zero in the matrix are represented by triples. A complete deployment solution is a set of all triples. A complete deployment solution 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 following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0038] Figure 1 This is a schematic diagram of an optimization circuit consisting 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 ocean 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 This 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 following detailed description of the specific embodiments of the present invention is given 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 intended to limit the present invention.

[0046] This embodiment of the present invention utilizes the Marine Predators Algorithm (MPA) to design a discrete marine predator algorithm with a population exchange and update mechanism based on triple encoding. This algorithm outperforms traditional ant colony algorithms in both solution performance and accuracy. This embodiment of the present invention provides a novel design approach for converting continuous optimization algorithms into discrete ones for solving earthwork allocation problems.

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

[0048] 1. Combinatorial optimization problems, primarily represented by linear programming, struggle to handle nonlinear factors within the model. Furthermore, when faced with large-scale problems, adjusting the model becomes cumbersome due to the numerous constraints, resulting in limited model versatility. This approach can only statically present the overall final result, failing to specifically represent the construction process flow, hindering construction personnel from organizing transportation plans.

[0049] 2. Designing high-performance swarm heuristic algorithms to solve engineering problems is a major trend in engineering optimization. However, most of these algorithms are designed for continuous problems, and there is a general lack of new metaheuristic algorithms specifically for earthwork allocation. This embodiment of the present invention utilizes 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, primarily due to the inability to establish a suitable and accurate mapping between the algorithm's continuous domain and the problem's discrete domain. Based on the characteristics of the problem, this embodiment of the present invention designs a triple encoding method that accurately expresses the phenotype of discrete problem individuals. Based on this, a heuristic perturbation and mutation mechanism is designed. This provides a novel design approach for converting continuous optimization algorithms into discrete ones.

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

[0052] The optimization problem of earthwork allocation belongs to combinatorial optimization problem. This part establishes a linear programming model of 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 The general earthwork allocation problem 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 cut i to fill 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 the minimum.

[0056] The mathematical model can be categorized into cut-fill balance, cut less than fill, and cut greater than fill based on the supply relationship between cut and fill. The final allocation plan is presented in matrix form below.

[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 Ocean Predator algorithm, the concept of algorithmic neighborhood must be introduced: In optimization algorithms, a neighborhood refers to a set of solutions that are "close" to the current solution under some definition. Specifically, if there is a solution x, then 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 solution value can be any real number. The discrete solution space is discrete, usually involving integers or specific discrete values. For example, the solution to 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). It finds optimal solutions by rearranging three edges in a path. In 3-opt, the neighborhood structure is defined as the set of new paths generated by operations on three edges. For example, suppose we are optimizing a six-city loop and seeking the shortest path. Using 3-opt operations, we can generate eight new loops within the current loop. Figure 1 The figure shows an optimized schematic diagram of a loop composed of 6 cities, where solid dots 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 method, 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, top predators in nature are more talented at foraging. Therefore, the fittest solutions are named top predators, and a matrix called the elite is constructed. This matrix's array oversees search and discovery of prey based on their location information.

[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 j-th 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 preys, and simulating three different stages of predators and preys at the same time:

[0072] (1) High speed ratio stage: prey moves faster than 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. These steps are defined based on the inherent laws of predator and prey movement, while mimicking the movement of predators and prey in nature. The three phases include:

[0076] Phase 1: During the high speed ratio phase, the prey moves faster than the predator. This occurs during the initial iterations of the optimization, when the algorithm prioritizes individual exploration. At this high speed ratio, the predator's optimal strategy is to remain stationary, while the prey chooses to use Brownian motion to move extensively. The mathematical model for 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-wise multiplication. B Multiplying by the prey simulates prey movement. P = 0.5 is a constant, and R is a vector of uniform random numbers in [0, 1]. This occurs within 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] Phase 2: In the same speed ratio phase: both the predator and the prey move at the same speed, which simulates that they are both searching 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 is flying in Lévy flight, the optimal strategy for the predator is Brownian motion. Therefore, in this phase, the algorithm assumes that the prey moves in Lévy 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 a Lévy flight. Since most step sizes in the Lévy 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 the predator moving in a Brownian motion, while the prey updates its position according to the predator's Brownian motion.

[0084] Phase 3: Low speed ratio: The prey moves slower than the predator. This occurs at the end of the optimization process and is associated with the algorithm's high exploitation capability. The predator's optimal strategy at low speed ratios is to perform Lévy flight. This phase is represented as follows:

[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 movements of predators and prey according to their hunting strategies in different phases, based on what happens in nature. These phases mimic the step-size rules of the predator's movements to capture its prey. In the first phase, the predator is stationary, while in the second phase, it exhibits Brownian motion, and finally, in the third phase, it exhibits a Lévy flight strategy. This also happens with prey, as the prey is another potential predator, such as silky sharks and tuna. While both are considered marine predators, tuna are prey to silky sharks, which prey on 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 with prey distribution. 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 0s and 1s. 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 Represent the upper and lower limits of individuals, and subscripts r1 and r2 represent random individuals in the prey matrix.

[0090] Marine predators have an excellent memory, allowing them to recall locations where they have successfully foraged. After updating the prey and implementing the FAD effect, a matrix is ​​constructed to evaluate the fitness of the updated elite. The fitness of each solution in the current iteration is compared with the equivalent solution in the previous iteration. If the current solution is more fit, it is replaced. This process improves the quality of the solution over time and also simulates the predator returning to the location of the prey-rich area where it successfully foraged.

[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 For the excavation node where the remaining construction volume is not 0, d j is the filling node with a remaining construction volume not equal to 0, and t is the node from node s i To node d j 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 is 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 earthwork allocation scheme is initialized, and the initialized allocation scheme includes: 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.

[0097] Population initialization: To achieve 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 amount of the node, that is, s i =s i -t,d i =d i -t, and so on, generate multiple triplet plans 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, the fill node closest to the cut node is selected from the set of fill nodes with non-zero remaining construction volume. The greedy dynamic target strategy is similar to the random dynamic target strategy, except that the fill node is no longer randomly selected. Instead, the fill node closest to the cut node is selected from the set of fill nodes with non-zero remaining construction volume.

[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 predator to perform Brownian motion to move, and the prey updates its position according to the predator's Brownian motion; the second half of the population uses the prey to perform Brownian motion.

[0101] Phase 1: Referring to Equation (1.4), during this phase, prey generally engage in large-scale movement, while the optimal strategy for predators is to remain stationary. Because a random and greedy mixed population initialization strategy is used, it is hoped that individuals with better fitness will converge in a better direction while performing large-scale movement, while also encouraging individuals with poorer fitness to perform large-scale movement to explore a larger solution space and maintain population diversity. Therefore, the algorithm preemptively adopts the population segmentation strategy of Phase 2 in this phase. For the first half of the population:

[0102]

[0103] Due to the particularity of the triplet encoding format, that is, each triplet in the individual overall encoding has an information guidance function. Therefore, this method uses the triplet of a portion of elite individuals to simulate the movement distance between prey and predator. R The symbol represents a random key 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. And 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 triple-encoded 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.

[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, and 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 3 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 s 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 Schematic diagram of the operation, which shows the random selection of three triplets, 6 neighborhood structures, the calculation to determine the three triplets with the lowest cost, namely (1, 6, 4) (3, 7, 1) (3, 5, 3), and then the optimal pairing.

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

[0108]

[0109] In S106, during the same speed ratio phase, half of the prey performed small-scale movements using Lévy flight, while the other half updated their positions using the predator's large-scale movements.

[0110] Phase 2: Refer to equations (1.5) and (1.6). In this phase, half of the prey choose to move in a small area using small-step Lévy flights for better exploitation. The other half, on the other hand, use elite individuals to explore the population using large-scale movements. Similarly, the goal is for individuals to converge in a better direction, whether exploring or exploiting. 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 be repeated, where P (for example, P is 0.5) is the probability of repeated 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 extension of the operator is used to perform repeated operations. The probability of repeated operations is retained, and the update formula of the original MPA is retained, that is, Based on the number of triples in the individual code, repeat ceil(m*CF) times O RP operation, and finally perform optimal repair on 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 phase, which is the late stage of the algorithm, most prey tend to converge. We hope that the prey will use the predator's position to move in a small range to get a better position. Therefore, we use O S Update, so the model is:

[0117]

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

[0119] Phase 4: This phase is independent of the number of iterations and must be completed with each iteration. The most important function of this phase is to help the algorithm escape the dilemma of local optimality in FADs. According to the original algorithm formula (1.8), predators spend 80% of their time searching for better locations in FADs, and 20% of their time moving on a large scale to other sea areas. This means that marine predators have an 80% chance of deepening their exploration and moving to better locations, while having a 20% chance of moving on a large scale for exploration. This leads to the following mathematical model:

[0120]

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

[0122] Among them O LM is a large-scale mutation operator, used to achieve large-scale mutation of encoding individuals, O 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. The function Select is to select 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].

[0123] 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 FIG4 is a schematic diagram of the operation of FIG4, 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.

[0124] Based on actual engineering problems, the embodiment of the present invention designs a basic earthwork algorithm example, the specific situation of which is shown in Table 2. This earthwork example belongs to a cut-and-fill balance example and has a unit price in a nonlinear stage, as shown in Table 3.

[0125]

[0126]

[0127] Table 2 Initial earthwork unit engineering information

[0128]

[0129]

[0130] Table 3 Earthwork unit price list

[0131] When the embodiment of the present invention was used for computational experiments, 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 volatility 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 was 7.5813397785e+07. The details of the experimental records of the ant colony algorithm ACO and DMPA are shown in Table 4, and the schematic diagram of the convergence of the 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.

[0132]

[0133]

[0134] Table 4 Comparison of experimental indicators of ACO and DMPA

[0135] From Table 4, it can be concluded that DMPA is significantly better than the ant colony algorithm in all aspects. DMPA is more competitive than the ant colony algorithm in solving the earthwork allocation problem.

[0136] This embodiment of the present invention successfully improves the marine predator algorithm and designs a novel discrete swarm heuristic algorithm—the discrete marine predator algorithm. This algorithm has significant advantages over traditional ant colony algorithms for solving earthwork allocation optimization problems. The triple encoding scheme designed for earthwork allocation problems in this embodiment of the present invention is simple and clear, accurately mapping the phenotypes of discrete problem individuals within the algorithm, facilitating subsequent perturbation and update mechanisms in the algorithm design. Based on the triple encoding perturbation and mutation mechanism, this provides a novel design approach for converting continuous optimization algorithms into discrete ones.

[0137] An embodiment of the present invention provides an earthwork allocation optimization system based on a discrete ocean predator algorithm, which is used to execute the steps of the method provided in the above embodiment.

[0138] The earthwork allocation optimization system based on the discrete ocean predator algorithm provided in the embodiment of the present invention has the same implementation principle and technical effects as the aforementioned embodiments. For the sake of brief description, for matters not mentioned in the system embodiment, please refer to the corresponding content in the aforementioned method embodiment.

[0139] 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.

[0140] 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.

[0141] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing a 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.

[0142] In this document, 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 "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0143] 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.

[0144] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily 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 is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing earthwork allocation based on discrete ocean predator algorithm, characterized in that: include: Initialize the population of earthwork allocation plan to obtain the initialized allocation plan; The earthwork allocation scheme adopts the triple form ( Encode, where For the excavation node where the remaining construction volume is not 0, For filling nodes where the remaining construction volume is not 0, For the self node To Node transportation and construction volume; In the high speed ratio stage, the initial deployment scheme adopts a population grouping strategy: the first half of the population uses the predator to perform Brownian motion, and the prey updates its position according to the predator's Brownian motion; 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, while the other half updated their positions using the predator's large-scale movements; In the low speed ratio phase, prey exploits the predator's position to make small movements; For environmental factors, large neighborhood jumps are performed according to probability during the iteration process to avoid falling into the local optimal solution; The concepts of "large-scale motion," "small-scale movement," and "large neighborhood jump" all refer to a choice determined within the neighborhood structure of the current solution. "Large-scale" and "large neighborhood" mean that there are more solutions to choose from, and the differences in solutions within the neighborhood structure are often large, while "small-scale" refers to a small perturbation to the current solution.

2. The method according to claim 1, characterized in that The earthwork allocation scheme is initialized to obtain an initialized allocation scheme, wherein half of the population is generated by adopting a random dynamic target strategy, and the other half of the population is generated by adopting a greedy dynamic target strategy; The random dynamic target strategy is as follows: for a triplet allocation plan, first randomly select a node from the excavation nodes whose remaining construction volume is not 0. Then randomly select a node from the filling nodes where the remaining construction volume is not 0 , generating transportation construction volume , among which and Node and nodes The initial construction quantity constraint generates a triple solution ( , and then update the remaining construction amount of the node, that is , , 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, 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, MaxIter is the maximum number of iterations, 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; O RP Used to obtain the mining node sequence of triple encoding , and then assign each A uniformly distributed random number between [0,1] is assigned to all nodes. 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: in, O S The symbol represents the exchange operator based on contribution. Its specific operation is to first calculate the total cost of individual codes as the identification attribute of each triple - contribution, sort all triples from large to small according to contribution, and select the two different triples with the largest contribution. The node triples and record their index positions in the individual code, swapping their After the node, replace the original position, and finally perform the optimal repair on the individual code; O S (P) operator represents a repeated operation, P is the probability of repeated operation, based on the number of triplets in the individual code m , repeat ceil ( m*p )Second-rate O S operate; in, O RP ( CF ) operator is O RP Extension of the operator for repeated operations. is the probability of repeated operation, , based on the number of triplets in the individual code , repeat ceil ( m*CF )Second-rate O RP operation, and finally perform optimal repair on 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: in O LM is a large-scale mutation operator, used to achieve large-scale mutation of coding individuals. O 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. O NP is the neighboring optimal pairing operator, which is used to randomly obtain three consecutive triplets from individual codes. Select The function is to select the first triples, k=ceil(m*FADF) , m is the number of triplets in the individual code, r、r 1 、r 2 、r 3 is a uniformly distributed random number between [0,1]; FADs is the fish aggregation device effect, and its specific value represents the probability of affecting the optimization process.

8. The method according to claim 7, characterized in that described O LM Operator, used to calculate the contribution of each triple in the individual code, sort all triples from large to small according to the contribution, and then sort the triples in the sorted 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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