Interference unequal area facility layout method based on improved particle swarm optimization algorithm

Abstract

The invention discloses an improved particle swarm optimization algorithm-based unequal-area facility layout method with interference. The method belongs to the field of intelligent optimization algorithms, and comprises the following main steps: S1, constructing a mathematical model with an interference unequal area facility layout problem; s2, initializing a population, and calculating an objective function value; s3, selecting a global optimal particle by using a target space division method; s4, executing heuristic mutation operation by using an adaptive gradient method to improve the search precision; and S5, using a tabu search rule and a neighborhood transformation rule to prevent the algorithm from being caught in a local optimal solution trap too early. Compared with the existing method, the method has the following main advantages: (1) the influence caused by a physical interference object is considered in the unequal-area facility layout problem, so that the applicability of the problem is enhanced, and the method can be more suitable for actual application scenes such as factory workshop transportation scenes; and (2) a tabu search rule is introduced into the multi-target particle swarm optimization algorithm, so that the convergence speed and the global search capability of the algorithm are improved.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent optimization algorithms, and particularly relates to a method for arranging unequal-area facilities with interference based on an improved particle swarm optimization algorithm. Background Art

[0002] With the rapid progress of information technology and the continuous development of human social civilization, the manufacturing industry has also made remarkable progress. However, the increasing engineering problems that follow have brought huge pressure and challenges to enterprises. The rapid change of market demand and the innovation of production methods have promoted the manufacturing industry to move towards high efficiency. Among them, the layout problem, as a key link in manufacturing design, directly affects the long-term and efficient operation of enterprises. The layout design theory is widely applied in fields such as aerospace, mechanical manufacturing, large-scale integrated circuit design, and transportation. Its core lies in reasonably placing objects with known areas or shapes in a given space to meet specific layout requirements and constraints, such as non-overlap between objects and compact layout, so as to optimize production efficiency and operation safety.

[0003] The Facility Layout Problem (FLP) has been widely studied, and most methods focus on the relative positioning of equal-area departments, which is usually referred to as the Quadratic Assignment Problem (QAP). However, the assumption of equal-area facilities has significant limitations in practical applications because it imposes strict geometric constraints that rarely match the actual situation. In reality, the sizes of facilities often vary, so it is necessary to solve the Unequal-Area Facility Layout Problem (UA-FLP). This shift in focus is driven by several key factors: Real-world relevance: The assumption of equal-area facilities is too simplistic to capture the complexity of real-world layouts. In practice, due to different operational requirements, the sizes of facilities also vary, making the UA-FLP a more realistic and applicable research focus. Complexity and flexibility: The UA-FLP introduces additional complexities, such as adapting to environmental constraints, stochastic disturbances, and unforeseen variables. For example, dynamic layout problems have been explored to optimize the layout for different production cycles in a fuzzy stochastic environment. These studies emphasize the need for flexible solutions that can adapt to the uncertainties of the real world. Human factors and practicality: Some researchers have incorporated the individual quality preferences of expert designers or decision-makers (DMs) into UA-FLP research to obtain more comprehensive and realistic solutions. However, these studies often neglect physical disturbances, which limits their practical applicability. To address a key gap in the current research on the Unequal-Area Facility Layout Problem (UA-FLP), this study focuses on the impact of physical disturbances, a feature that has been largely overlooked in existing research. While most studies on UA-FLP have addressed the non-overlap constraints and the variation in facility sizes, the impact of physical disturbances (such as obstacles, structural barriers, or space constraints) has not been systematically considered. This omission limits the practicality and applicability of existing solutions in real-world scenarios where physical disturbances are a common and important factor. In this study, we explicitly integrate physical disturbances into the UA-FLP framework, aiming to fill this research gap. By constructing a mathematical model that simultaneously considers unequal-area facilities and physical disturbances, we seek to develop layout strategies that are not only space-saving but also robust and adaptable to the complexity of the real world.

[0004] The Multi-Objective Particle Swarm Optimization (MOPSO) algorithm has become a popular choice for solving multi-objective optimization problems due to its simplicity, minimal parameter tuning, and fast convergence. Additionally, MOPSO typically incorporates diversity maintenance mechanisms, such as crowding distance calculation and external archiving, to ensure that the solution set maintains both optimality and diversity simultaneously. Despite these advantages, MOPSO still faces a major limitation when applied to the UA-FLP with physical interference: it is prone to getting trapped in local optima, a phenomenon known as "solution space expansion". In such cases, particles tend to concentrate their search within a limited region of the solution space and are unable to explore the entire domain, thereby hindering the discovery of the global optimal solution.

[0005] After retrieval, the application publication number is CN111222220A, which is a method for optimizing the layout design of a large ship power component production workshop. First, combined with the marine crankshaft production workshop, the production layout is analyzed to determine the processing process route, processing time, and equipment processing variable conditions; then some assumptions are made about the equipment model, ignoring the shape details of the workshop equipment; according to the variables and assumptions, the optimization objectives and constraints of the model are reasonably set to establish a mathematical model; then an improved particle swarm optimization algorithm (DIPSO) is designed, which is a particle swarm optimization algorithm that can adjust the inertia weight and particle flight route in real time; finally, the DIPSO algorithm is used to optimize the layout design of the marine crankshaft production workshop and compared with the basic particle swarm algorithm to verify the practical feasibility of the DIPSO algorithm.

[0006] The above invention analyzes the production layout of the marine crankshaft production workshop, establishes a mathematical model for this workshop, and in order to improve the optimization efficiency of the algorithm, uses an improved particle swarm optimization algorithm that can adjust the inertia weight and particle flight route in real time to optimize the model. However, its mathematical model does not take into account the influence brought by physical interference objects (such as obstacles, structural obstacles, or space constraints), and this omission limits the practicality and applicability of the existing solutions in real-world scenarios. At the same time, the above invention improves the inertia weight and particle flight route of the particle swarm optimization algorithm, mainly improving the particle update process of the particle swarm algorithm. Although the real-time adjustment mechanism helps to avoid premature convergence, in some complex problems, the algorithm may still get trapped in local optima, especially in multi-objective optimization problems. Considering the above two points, the present invention first takes into account the influence brought by physical interference objects when establishing the mathematical model, making its constraint conditions more complex and enhancing its applicability in actual scenarios; for the improved particle swarm optimization algorithm DIPSO algorithm, aiming at the situation that it is prone to getting trapped in the local optimal solution trap, a taboo rule and a neighborhood transformation rule are introduced to improve the exploration ability of particles in the solution space and enhance the global search ability of the algorithm. Summary of the Invention

[0007] The present invention aims to solve the above problems of the prior art. A method for layout of non - equal - area facilities with interference based on an improved particle swarm optimization algorithm is proposed. The technical solution of the present invention is as follows:

[0008] A method for layout of non - equal - area facilities with interference based on an improved particle swarm optimization algorithm, comprising the following steps:

[0009] S1, constructing a mathematical model for the layout problem of non - equal - area facilities with interference;

[0010] S2, initializing the population, and then calculating the fitness function based on the objective function, that is, minimizing the material handling amount, maximizing the sum of adjacency values, and maximizing the workshop utilization rate;

[0011] S3, using the objective - space partitioning method to control the neighborhood topology and the local best group, calculating the global fitness, and selecting the global best particle;

[0012] S4, then performing a heuristic configuration mutation operation using the adaptive gradient method with acceleration and deceleration strategies to improve the search process, and enhancing the search accuracy and search speed;

[0013] S5, finally using the adjacency transformation criterion and the tabu criterion in the tabu search algorithm to avoid falling into the local - optimal solution trap.

[0014] Further, in the step S1, constructing a mathematical model for the layout problem of non - equal - area facilities with interference, as Figure 1 shown, specifically including: adding a physical interference constraint to the constraint conditions, where the distributed object is not allowed to overlap with the physical interference object, that is where, a i represents the i - th facility, b j represents the j - th physical interference, N is the number of facilities, M is the number of interference objects, and the specific expression is as follows:

[0015]

[0016] where, x i represents the abscissa of the center point of facility i, y i represents the ordinate of the center point of facility i, x bi and y bi respectively represent the abscissas of the center points of interference objects i and j; y bi and y bj respectively represent the ordinates of the center points of interference objects i and j; l bi and l bj represent the lengths of interference objects i and j; and w bi and w bj represent the widths of interference objects i and j.

[0017] Further, in step S2, the population is initialized and the fitness function based on the objective function is calculated, specifically including:

[0018] Initialize the population, that is, the positions and velocities of the particles, x i (0) represents the position at the 0th iteration, v i (0) represents the velocity at the 0th iteration; randomly generate the initial positions and velocities of all particles; that is, minimize the total material handling volume, maximize the total adjacency value, and maximize the workshop utilization rate; in the construction site layout, the position of the particle represents the possible allocation of all on-site facilities. The specific objective function is as follows:

[0019] 1) Minimize the material handling cost

[0020] The material handling cost between facilities i and j is determined by the material flow F ij between them, the transportation cost C ij per unit distance between facilities, and their Manhattan distance d ij . The material handling cost objective MHC min (X) can be described as:

[0021]

[0022] 2) Maximize the sum of adjacency values

[0023]

[0024] where TAV max (X) is modeled by maximizing the total adjacent value. The adjacent factor af ij reflects the adjacency situation between facilities a i and a j , depending on the actual distance df i between facilities a j and a ij and the maximum possible distance d i between facilities a j and a max . The adjacent value AV ij represents a functional relationship corresponding to the adjacency requirement, which is not always quantifiable and is sometimes difficult to give. In this article, a common AV ij quantifiable value is used.

[0025] 3) Maximize the workshop utilization rate

[0026] The workshop space utilization rate is expressed as the ratio of the actual occupied area of the facilities in the layout area to the total area of the workshop. The goal is to improve the use efficiency of the limited space and reduce the ineffective idle area.

[0027]

[0028] Among them, UR max (X) is the area utilization rate of the workshop. Since S i represents the area of facility a i , and the total area of all facilities is a constant. S R represents the area of the envelope rectangle of all facilities in the workshop.

[0029] Furthermore, in step S3, the target space division method is used to control the neighborhood topology and the local best group. After the particles complete the current iteration, a search strategy based on target space division is adopted to guide the particles to search for appropriate Pareto optimal solutions, specifically including:

[0030] (1) Divide the m-dimensional target space into k1*k2*......*k m cells, where k i (i = 1, 2,......, m) is the number of cells into which each dimension of the target space is divided, and each component d i of the cell width is: Among them, X ∈ D, X is a configuration, D is the decision space, and k i is the number of divisions of the i-th dimension of the target space;

[0031] (2) Let F i max = max X∈D f i (X), F i min = min X∈D f i (X). Assume is the origin of the target space at the current selected step number, that is, O is the intersection point of all targets in the target space. For a particle S, its corresponding target quantities are (S1, S2,......, S m ), then in each dimension of the target space, the distance between S and O is (t1, t2,......, t m ), where t i = S i - F i min , i = 1, 2,......, m. Then for the i-th dimensional component, the address h i of particle S is: h i = mod(t i , d i ) + 1;

[0032] Among them, mod(t i , d i ) represents ti / d i For the integer part of, particles with the same "address" for each component dimension of the target vector belong to the same grid, and all particles belonging to the same grid are called "grid members".

[0033] Furthermore, after the target space is divided into several units, two indicators are designed to determine the fitness function value of the particles: (1) Health indicator, the number of particles dominated by a certain particle in a certain iteration; (2) Crowding indicator, the number of "grid members" in the grid where a certain particle is located in a certain iteration; Therefore, in the k-th iteration, the fitness of particle S is:

[0034]

[0035] The more particles a particle dominates, the healthier this particle is considered to be, and the higher the obtained fitness is.

[0036] Furthermore, in step S4, the heuristic configuration mutation operation is performed using an adaptive gradient method with acceleration and deceleration strategies to improve the search process, specifically including:

[0037] In the local search process, an adaptive gradient method with acceleration and deceleration strategies is used to find the particle with the lowest elastic potential energy configuration. Specifically including:

[0038] First, initialize the step size h, the minimum step size h min , scaling factor u, and elastic coefficient e parameters, aiming to control the update dynamics of the particle position; the main loop iterates to the predetermined maximum number of iterations, and initially adjusts the particle position by shrinking by 90%;

[0039] Then, perform dynamic adjustment according to the energy difference between the current configuration and the new configuration; perform dynamic adjustment according to the difference in elastic potential energy energy k between the current configuration and the new configuration; if the elastic potential energy of the new configuration is not satisfactory, modify the step size h: if the energy increases, decrease the step size; if the energy decreases, keep it unchanged; if stagnant, reset the step size;

[0040] This function evaluates convergence by checking the absolute energy difference and adaptively adjusts the position by scaling it using the updated step size h; if the loop converges or the step size is below the minimum threshold, the loop will interrupt to ensure that the search does not stagnate or diverge, thus helping to efficiently navigate to the optimal configuration.

[0041] Furthermore, the adjacency transformation criterion and taboo criterion in the taboo search algorithm are incorporated into the particle swarm optimization algorithm to avoid premature convergence to local optimal solutions, specifically including:

[0042] (1) The principle of tabu search is to modify the current solution through a series of small changes, i.e., moves, so as to iteratively explore the solution space. This exploration space is the neighborhood in the tabu search algorithm. The following is the definition of the neighborhood:

[0043] S(x) = {s|s = x + ud, s ∈ X}

[0044] Among them, x is the candidate solution, u is the unit step size, d is the direction, and X is the candidate solution set;

[0045] (2) S(x) is the set of solutions that can be reached through neighborhood moves; after each move, the algorithm checks whether the final solution can improve the objective function. The following are the rules of neighborhood search:

[0046] S k (x) = Opt{s(x)|s(x) ∈ S(x) - T}

[0047] Among them, S k (x) is the neighborhood of the k-th iteration, and T is the tabu list in the tabu search rule;

[0048] (3) Incorporating the tabu search rule into the search process of the particle swarm optimization algorithm, TS avoids redundant searches and encourages the exploration of unexploited regions by recording and excluding recently visited solutions, thus promoting a more comprehensive search of the solution space.

[0049] An electronic device, which includes a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes the program, it implements the method for unequal-area facility layout with interference based on the improved particle swarm optimization algorithm as described in any one of the above.

[0050] A non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the method for unequal-area facility layout with interference based on the improved particle swarm optimization algorithm as described in any one of the above.

[0051] The advantages and beneficial effects of the present invention are as follows:

[0052] 1. Regarding the facility layout problem, traditional methods usually focus on the relative positions of facilities with equal areas within a workshop. Due to the high complexity and computational cost of the problem, the situation with external interference is generally not considered. However, in most applications, the FLP of facilities with unequal areas, especially in realistic scenarios with physical interference, is quite common. It is worth noting that most existing methods study quantitative single-objective FLP or transform multi-objective FLP problems into single-objective problems using weighted coefficients. In contrast, this study focuses on the multi-objective unequal-area problem FLP with physical interference, which is more realistic in real-world scenarios. The objectives of the problem include Material Handling Cost (MHCost), Workshop Utilization Rate (UR), and Total Adjacency value (TAV).

[0053] 2. Based on the above content, a multi-objective particle swarm optimization algorithm integrated with the tabu search rule is proposed. Through neighborhood transformation and tabu rules, it is avoided that particles are overly concentrated in local areas. The tabu search mechanism defines the concept of "neighborhood" in the solution space and explores potential solutions within the neighborhood, thus breaking through the limitation of the local optimal solution. In addition, by recording and excluding the recently visited solutions, the tabu search prevents backtracking and repeated searches, thereby achieving a more comprehensive exploration of the solution space. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a mathematical model diagram of the layout of facilities with interference and unequal areas established by the present invention;

[0055] Figure 2 is a flowchart of a method for the layout of facilities with interference and unequal areas based on an improved particle swarm optimization algorithm provided by the preferred embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] Next, the technical solutions in the embodiments of the present invention will be clearly and detailedly described in conjunction with the drawings in the embodiments of the present invention. The described embodiments are only a part of the embodiments of the present invention.

[0057] The technical solution of the present invention to solve the above technical problems is:

[0058] An improved particle swarm optimization algorithm provided by the present invention for solving the problem of the layout of facilities with interference and unequal areas includes the following steps:

[0059] S1, based on the engineering practice of the layout of factory mechanical equipment, construct a mathematical model for the problem of the layout of facilities with interference and unequal areas;

[0060] S2. Initialize the population, and then calculate the fitness function based on the objective function, that is, minimize the material handling amount, maximize the sum of adjacency values, and maximize the workshop utilization rate.

[0061] S3. Use the objective space partitioning method to control the neighborhood topology and the local best group, for evaluating the global fitness of the solution and selecting the global best particle.

[0062] S4. Then use the adaptive gradient method with acceleration and deceleration strategies to perform heuristic configuration mutation operations to improve the search process, enhance the search accuracy and search speed.

[0063] S5. Finally, use the adjacency transformation criterion and the tabu criterion in the tabu search algorithm to avoid falling into the local optimal solution trap.

[0064] Furthermore, the mathematical model of the unequal area facility layout problem with interference constructed in step S1 specifically includes:

[0065] (1) Assumptions

[0066] The statement of this model is based on the following basic assumptions:

[0067] 1) The shape of each facility is fixed but irregular.

[0068] 2) All facilities must be located within the workshop.

[0069] 3) Overlapping between facilities is not allowed.

[0070] 4) Overlapping conflicts between facilities and physical interference objects are not allowed.

[0071] 5) The frequency of material transportation between facilities is known and does not change along the way.

[0072] (2) Sets

[0073] For the elements existing in this model, fixed sets need to be set for them. Among them, the index set of facility types is N = {1, 2,......, N}, and the index set of interference object types is M = {1, 2,......, M}.

[0074] (3) Parameters

[0075] Among them, C ij is the unit material handling cost per unit distance between facility a i and facility a j ; F ij is the material flow frequency between facility a i and a j ; L is the length of the workshop, W is the width of the workshop; l i is facility ai The length, w i is for facility a i The width; S i is for facility a i The area.

[0076] (4) Objective function

[0077] Under the constraints of meeting the total area limit of the layout workshop and the distance limit between facilities, this paper optimizes the following two objective functions: material handling cost and workshop space utilization rate.

[0078] 4) Minimization of material handling cost

[0079] The material handling cost between facilities i and j is determined by the material flow F ij between them, the transportation cost C per unit distance between facilities ij and their Manhattan distance d ij The material handling cost objective MHC min (X) can be described as:

[0080]

[0081] 5) Maximization of the sum of adjacency values

[0082]

[0083] where TAV max (X) is modeled by maximizing the total adjacency value. The adjacency factor af ij reflects the adjacency situation between facilities a i and a j depending on the actual distance df i between facilities a j and a ij and the maximum possible distance d i between facilities a j and a max . The adjacency value AV ij represents a functional relationship corresponding to the adjacency requirement, which is not always quantifiable and is sometimes difficult to give. In this paper, a common AV ij quantifiable value is used. The reasons for the adjacency requirement may be the presence or absence of noise or safety, the logical organization of the manufacturing system, etc., describing the degree of association between facilities.

[0084] 6) Maximization of workshop utilization rate

[0085] The workshop space utilization rate is expressed as the ratio of the actual occupied area by facilities in the layout area to the total area of the workshop. The goal is to improve the utilization efficiency of the limited space and reduce the ineffective idle area.

[0086]

[0087] Among them, UR max (X) is the area utilization rate of the workshop. Since S i represents the area of facility a i and the total area of all facilities is a constant. S R represents the area of the envelope rectangle of all facilities in the workshop.

[0088] (5) Constraint conditions

[0089] The model of the irregular facility layout problem with physical interference needs to consider the following constraints: non - overlapping constraint, boundary constraint, and physical interference constraint. The detailed descriptions of these constraints will be provided below.

[0090] 1) Non - overlapping constraint

[0091] It is not allowed for different facilities to overlap with each other. That is, the absolute horizontal distance |x i - x j | between the center points of facility i and facility j must be greater than or equal to half of the sum of the lengths of the two facilities, and the absolute vertical distance |y i - y j | between the center points of facility i and facility j must be greater than or equal to half of the sum of the widths of the two facilities. The specific expression of this constraint is as follows:

[0092]

[0093] 2) Boundary constraint

[0094] This model has a fixed outer contour, an irregular shape, and precise boundaries. All facilities are not allowed to be located outside the boundaries. These constraints are expressed as follows:

[0095]

[0096] 3) Interference object constraint

[0097] For the case of physical interference, it is not allowed for all facilities to overlap with physical interference, nor is it allowed for different physical interferences to overlap with each other. That is and The specific expressions are as follows:

[0098]

[0099] Among them, x i represents the abscissa of the center point of facility i, and y i represents the ordinate of the center point of facility i. x bi and y bi represent the abscissas of the center points of interference object i and interference object j respectively; ybi , y bj respectively represent the vertical coordinates of the center points of the interfering object i and the interfering object j. l bi and l bj represent the lengths of the interfering object i and the interfering object j; and w bi and w bj represent the widths of the interfering object i and the interfering object j.

[0100] Furthermore, in the step S2, the population velocity and position are initialized, and at the same time, the non-dominated solution set Rep and the external archive are initialized, specifically including:

[0101] (1) Initialize the population, that is, the position x i (0) and velocity v i (0), where 0 represents the position and rate of the 0th iteration. Randomly generate the initial positions and velocities of all particles. Then calculate the fitness function according to the objective function, that is, minimize the total material handling and maximize the total adjacency value and the workshop utilization rate. In the construction site layout, the positions of the particles represent the possible allocations of all on-site facilities.

[0102] (2) Locate the particles in the objective function space and start the external archive. Generate the objective function space, and all particles are located in the objective function space. The coordinates of each particle are defined according to the fitness value. Compare all particles in the objective function space according to Pareto dominance, and store the non-dominated particles in the external archive. The particles in the external archive represent the candidate site layouts in each iteration.

[0103] Furthermore, in the step S3, the objective space division method includes the following steps:

[0104] (1) Divide the m-dimensional objective space into k1*k2*......*k m cells, where k i (i = 1, 2,......, m) is the number of cells into which each dimension of the objective space is divided. Among them, X ∈ D, X is a configuration, that is, a decision variable, D is the decision space, k i is the number of divisions of the i-th dimension of the objective space. Obviously, in order to prevent the grid from containing too many or too few particles, k i cannot be too large or too small directly.

[0105] (2) Let F i max = max X∈D f i (X), F i min = min X∈D f i (X), assuming is the origin of the target space at the current selected step number, that is, O is the intersection point of all targets in the target space. For a particle S, its corresponding target quantities are (S1, S2,......, S m ), then in each dimension of the target space, the distance between S and O is (t1, t2,......, t m ), where t i = S i - F i min , i = 1, 2,......, m. Then for the i-th dimensional component, the address h i of the particle S is:

[0106] h i = mod(t i , d i ) + 1

[0107] where mod(t i , d i ) represents the integer part of t i / d i . Particles with the same "address" for each dimensional component of the target vector belong to the same grid, and all particles belonging to the same grid are called "grid members".

[0108] After the target space is divided into several units, we need to design two indicators to determine the fitness function value of the particle: (1) Health indicator, the number of other particles dominated by a certain particle in a certain iteration; (2) Crowding indicator, the number of "grid members" in the grid where a certain particle is located in a certain iteration. Therefore, in the k-th iteration, the fitness of the particle S is:

[0109]

[0110] where H(S, k) is the number of other particles dominated by the particle S in the k-th generation, and density(S, k) is the number of particles in the unit where the particle S is located in the k-th generation.

[0111] The more other particles a particle dominates, the healthier this particle is considered to be, the higher the obtained fitness, and the more excellent such a particle is. The OSD method considers both the dominance relationship of the solutions and the density of the solutions in the grid when calculating the fitness value of the particle, more objectively evaluates the fitness value of the particle, is conducive to obtaining a Pareto front close to the real, evenly distributed, and well-scalable one, and ensures the diversity of the solutions.

[0112] Further, in step S4, the heuristic configuration mutation operation is performed using an adaptive gradient method with an acceleration strategy and a deceleration strategy, specifically including:

[0113] (1) In each iteration, calculate the new positions and velocities of the particles, and calculate the elastic potential energy between each facility in each particle to avoid overlapping conflicts. Then find x according to the fitness value. pbest .

[0114] (2) Initialize the global best particle. The global best particle x gbest is the particle with the best optimization effect in the entire particle swarm configuration. In this study, the roulette wheel method is used to select the global best individual from the non-dominated individual set Rep.

[0115] (3) Update the particle positions and velocities according to the particle swarm update formula to generate new positions x i (t + 1) and velocities v i (t + 1).

[0116] (4) Then, use the heuristic mutation strategy to calculate the relative elastic potential energy energy k (i) among each facility in the particle to solve the overlapping conflict problem between different facilities. First, calculate the overlapping area between facility x i and different facilities, and then calculate the relative elastic potential energy between the facility and all different facilities according to the minimum removal distance between each facility:

[0117]

[0118] Here, u is the elastic coefficient, and minDistance(l) is the minimum removal distance between the kth facility and the lth facility (the minimum removal distance is to move out from the four directions of up, down, left, and right until there is no overlap, and then select the minimum distance of the move out).

[0119] Furthermore, in step S5, the taboo rule and the neighborhood transformation rule are incorporated into the local search process of MOPSO, specifically including:

[0120] The tabu search rule is used to improve the search accuracy and avoid the trap of the algorithm falling into a local optimal solution. It is initialized with the current best position and iteratively generates adjacent solutions, subject to a dynamically updated tabu list that prevents revisiting recent configurations. At each iteration, the function selects the best neighbor not on the tabu list by comparing the objective values, which take into account cost and flow metrics specific to the facility layout problem. If this neighbor represents an improvement over the current best, it becomes the new current position and a potential new best solution. The tabu list is updated by circularly shifting and appending the most recent move, ensuring that past configurations are temporarily blocked to encourage exploration of new areas of the solution space. This process is repeated for a predefined number of iterations or until a convergence criterion is met, typically when there is no further improvement in the solution quality or the adjustment drops below a minimum threshold, ultimately aiming to find the best layout configuration within the given constraints.

[0121] The systems, devices, modules, or units illustrated in the above embodiments can be specifically implemented by computer chips or entities, or by products with certain functions.

[0122] Computer-readable media includes both permanent and non-permanent, removable and non-removable media and can implement information storage by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission media that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transitory computer-readable media such as modulated data signals and carrier waves.

[0123] It should also be noted that the term "comprising", "including", or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, commodity, or device comprising a series of elements not only includes those elements but also includes other elements not explicitly listed, or elements inherent to such process, method, commodity, or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the existence of additional identical elements in the process, method, commodity, or device comprising the element.

[0124] The above embodiments should be understood as being only for illustrative purposes of the present invention and not for limiting the protection scope of the present invention. After reading the content described in the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. An unequal area facility layout method with interference based on an improved particle swarm optimization algorithm, characterized in that, It includes the following steps: S1. Construct a mathematical model for the unequal-area facility layout problem with interference; S2. Initialize the population, and then calculate the fitness function based on the objective function, that is, minimize the material handling volume, maximize the sum of adjacency values, and maximize the workshop utilization rate; S3. Use the objective space partitioning method to control the neighborhood topology and the local best group, calculate the global fitness, and select the global best particle; S4. Then use the adaptive gradient method with acceleration and deceleration strategies to perform heuristic configuration mutation operations to improve the search process, and enhance the search accuracy and speed; S5. Finally, use the adjacency transformation criterion and the tabu criterion in the tabu search algorithm to avoid falling into the local optimal solution trap.

2. The unequal area facility layout method with interference based on the improved particle swarm optimization algorithm according to claim 1, characterized in that In the step S1, a mathematical model of the unequal area facility layout problem with interference is constructed, which specifically includes: adding physical interference constraints to the constraint conditions, and it is not allowed for the distributed objects to overlap with the physical interference objects, that is where a i represents the i-th facility, b j represents the j-th physical interference, N is the number of facilities, M is the number of interference objects, and the specific expression is as follows: Among them, x i represents the abscissa of the center point of facility i, and y i represents the ordinate of the center point of facility i, x bi , y bi respectively represent the abscissas of the center points of interferer i and interferer j; y bi , y bj respectively represent the ordinates of the center points of interferer i and interferer j; l bi and l bj represent the lengths of interferer i and interferer j; and w bi and w bj represent the widths of interferer i and interferer j.

3. The unequal area facility layout method with interference based on the improved particle swarm optimization algorithm according to claim 1, characterized in that, In the step S2, when initializing the population and calculating the fitness function based on the objective function, it specifically includes: Initialize the population, that is, the positions and velocities of the particles, x i (0) represents the position at the 0th iteration, v i (0) represents the velocity at the 0th iteration; randomly generate the initial positions and velocities of all particles; the objective function is to minimize the total material handling amount, maximize the total adjacency value, and maximize the workshop utilization rate; in the construction site layout, the position of the particle represents the possible allocation of all on-site facilities, and the objective function is as follows: 1) Minimize the material handling cost The material handling cost between facility i and facility j is determined by the material flow F ij , the transportation cost C per unit distance between facilities ij and their Manhattan distance d ij . The material handling cost target MHC min (X) can be described as: 2) Maximize the sum of adjacency values Among which TAV max (X) is modeled by maximizing the total adjacent value. The adjacent factor af ij reflects the adjacency between facilities a i and a j , depending on the actual distance df i between facilities a j and a ij as well as the maximum possible distance d i between facilities a j and a max . The adjacent value AV ij represents a functional relationship corresponding to the adjacency requirement, which is not always quantifiable and is sometimes difficult to give. In this paper, common AV ij quantifiable values are used. 3) Maximize the workshop utilization rate The workshop space utilization rate is expressed as the ratio of the actual occupied area of the facilities in the layout area to the total area of the workshop. The goal is to improve the utilization efficiency of the limited space and reduce the ineffective idle area. Among them, UR max (X) is the area utilization rate of the workshop. Since S i represents the area of facility a i , and the total area of all facilities is a constant. S R represents the area of the enclosing rectangle of all facilities in the workshop.

4. A method for layout of facilities with unequal areas and interference based on an improved particle swarm optimization algorithm according to claim 1, characterized in that In the step S3, the objective space partitioning method is used to control the neighborhood topology and the local best group. After the particle finishes the current iteration, a search strategy based on objective space partitioning is adopted to guide the particle to search for the appropriate Pareto optimal solution, which specifically includes: (1) Divide the m-dimensional target space into k1*k2*......*k m units, where k i (i = 1, 2,......, m) is the number of units into which each dimension of the target space is divided, and each component d of the unit width i is: where X ∈ D, X is a configuration, D is the decision space, and k i is the number of divisions of the i-th dimensional objective space; (2) Let F i max = max X∈D f i (X), F i min = min X∈D f i (X), assuming that O(f1 min , f2 min , …, f i min ) is the origin of the target space at the current selected number of steps, that is, O is the intersection point of all targets in the target space. For a particle S, its corresponding target quantities are (S1, S2,......, S m ). Then, in each dimension of the target space, the distance between S and O is (t1, t2,......, t m ), where t i = S i - F i min , i = 1, 2,......, m. Then, for the i-th dimensional component, the address h i of the particle S is: h i = mod(t i , d i ) + 1; where mod(t i , d i ) represents the integer part of t i / d i , and particles with the same "address" for each component of the target vector belong to the same grid. All particles belonging to the same grid are called "grid members".

5. A method for layout of facilities with unequal areas and interference based on an improved particle swarm optimization algorithm according to claim 4, characterized in that After the objective space is divided into several units, two indicators are designed to determine the numerical value of the fitness function of the particle: (1) Health indicator, the number of other particles dominated by a certain particle in a certain iteration; (2) Crowding indicator, the number of "grid members" in the grid where a certain particle is located in a certain iteration; Therefore, in the k-th iteration, the fitness of particle S is: The more other particles a particle dominates, the healthier this particle is considered, and the higher the obtained fitness.

6. The unequal area facility layout method with interference based on the improved particle swarm optimization algorithm according to claim 1, characterized in that, In the step S4, the adaptive gradient method with acceleration and deceleration strategies is used to perform heuristic configuration mutation operations to improve the search process, which specifically includes: In the local search process, the adaptive gradient method with acceleration and deceleration strategies is used to find the particle with the lowest elastic potential energy configuration. Specifically includes: First, initialize the step size h, the minimum step size h min , the scaling factor u, and the elastic coefficient e parameters, aiming to control the update dynamics of the particle positions; the main loop iterates to a predetermined maximum number of iterations, initially adjusting the positions of the particles by shrinking by 90%; Then, perform dynamic adjustment based on the energy difference between the current configuration and the new configuration; perform dynamic adjustment based on the difference in elastic potential energy k between the current configuration and the new configuration; if the elastic potential energy of the new configuration is not satisfactory, modify the step size h: if the energy increases, decrease the step size; if the energy decreases, keep it unchanged; if it stagnates, reset the step size; This function evaluates the convergence by checking the absolute energy difference and adaptively adjusts the position by scaling it with the updated step size h; if the loop converges or the step size is lower than the minimum threshold, the loop will be interrupted to ensure that the search does not stagnate or diverge, thus helping to efficiently navigate to the best configuration.

7. The method for layout of facilities with unequal areas and interference based on the improved particle swarm optimization algorithm according to claim 1, wherein Integrate the adjacency transformation criterion and the tabu criterion in the tabu search algorithm into the particle swarm optimization algorithm to avoid premature convergence to the local optimal solution, specifically including: (1) The principle of tabu search is to modify the current solution through a series of small changes, that is, moves, so as to iteratively explore the solution space. This exploration space is the neighborhood in the tabu search algorithm. The following is the definition of the neighborhood: S(x) = {s|s = x + ud, s ∈ X} where x is the candidate solution, u is the unit step size, d is the direction, and X is the candidate solution set; (2) S(x) is the solution set reachable by neighborhood movement; after each movement, the algorithm checks whether the final solution can improve the objective function; the following are the rules of neighborhood search: S k (x) = Opt{s(x) | s(x) ∈ S(x) - T} Among them, S k (x) is the neighborhood of the k-th iteration, and T is the tabu list in the tabu search rule; (3) Incorporating the tabu search rule into the search process of the particle swarm optimization algorithm, by recording and excluding the recently visited solutions, TS avoids redundant search and encourages exploration of uncharted areas, thus promoting a more comprehensive search of the solution space.

8. An electronic device, characterized in that, Comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, when the processor executes the program, it implements the method for unequal area facility layout with interference based on the improved particle swarm optimization algorithm according to any one of claims 1 to 7.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for unequal area facility layout with interference based on the improved particle swarm optimization algorithm according to any one of claims 1 to 7.

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