Method for constructing x-structure steiner minimum tree based on dynamic particle swarm optimization

Abstract

The application relates to a dynamic particle swarm optimization-based X structure Steiner minimum tree construction method. The method mainly comprises the following three effective strategies: (1) a dynamic subgroup and information exchange strategy enables subgroups to exchange information with other subgroups while maintaining independence, and increases subgroup diversity; (2) an improved particle learning strategy can combine the advantages of local topological structure in particle diversity and optimization precision with the advantages of global topological structure in algorithm convergence speed; and (3) a transition from multi-group local learning to single-group global learning strategy enables particles to obtain a better line length optimization rate. The application takes optimization of line length as the target, and finally optimizes the important target of line length.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated circuit computer-aided design, in particular to a method for constructing an X-structured Steiner minimum tree based on dynamic particle swarm optimization. Background Art

[0002] Routing, a critical stage in Very Large Scale Integration (VLSI) physical design, requires determining the routing topology for each net on the circuit while maximizing circuit performance. The Steiner tree algorithm is the best approach for solving routing problems. The X-architecture Steiner Minimal Tree (XSMT) more fully utilizes routing space resources, shortening interconnect lengths, reducing interconnect latency, and reducing chip area, significantly improving chip performance.

[0003] Particle swarm optimization (PSO) has the advantages of fast convergence and a small number of parameters. Therefore, it has been widely used by researchers in recent years and is a highly effective optimization tool. Although PSO has certain optimization performance, it still has many areas for improvement. Numerous experiments have shown that basic particle swarm methods suffer from premature convergence, primarily due to their rapid convergence and loss of diversity in the early stages of optimization. In most cases, premature convergence traps particles in local optima, resulting in low-quality solutions. Further research is also needed to determine the method's ability to balance exploration and exploitation. Summary of the Invention

[0004] The purpose of the present invention is to provide an X-structure Steiner minimum tree construction method based on dynamic particle swarm optimization, which can obtain a wiring solution that minimizes the wire length cost.

[0005] To achieve the above object, the technical solution of the present invention is: a method for constructing an X-structured Steiner minimum tree based on dynamic particle swarm optimization, comprising:

[0006] (1) Wiring topology initialization phase: Use Prim's algorithm to initialize the population and initialize the historical optimal position P of each particle i and the historical optimal position P of the entire population g ;

[0007] (2) Search phase based on dynamic particle swarm optimization: Dynamic sub-groups and information exchange strategies, particle learning strategies and mutations, and the transition from multi-group local learning to single-group global learning strategies are added to the PSO algorithm. An algorithm based on dynamic particle swarm optimization is proposed. The particle swarm is then iteratively updated based on the algorithm until it converges to the global optimal particle, which is used as the X-structured Steiner wiring tree.

[0008] Compared with the existing technology, the present invention has the following beneficial effects: The method of the present invention mainly includes the following three effective strategies: (1) The dynamic subgroup and information exchange strategy allows subgroups to exchange information with other subgroups while maintaining independence, thereby increasing subgroup diversity; (2) The improved particle learning strategy can combine the advantages of local topology structure in particle diversity and optimization accuracy with the advantages of global topology structure in algorithm convergence speed; (3) The transition from multi-group local learning to single-group global learning strategy enables particles to obtain a better line length optimization rate. The present invention aims to optimize line length and ultimately achieves the optimization of this important goal. BRIEF DESCRIPTION OF THE DRAWINGS

[0009] Figure 1 (a) Figure 1 (b) Figure 1 (c) Figure 1 (d) Four types of interconnection lines.

[0010] Figure 2 Mutation operation.

[0011] Figure 3 Crossover operation.

[0012] Figure 4 Pairwise exchange of particles.

[0013] Figure 5 Learning directions of ordinary particles and subswarm optimal particles.

[0014] Figure 6 Multi-group local learning and single-group global learning. DETAILED DESCRIPTION

[0015] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0016] The present invention provides a method for constructing an X-structured Steiner minimum tree based on dynamic particle swarm optimization, comprising:

[0017] (1) Wiring topology initialization phase: Use Prim's algorithm to initialize the population and initialize the historical optimal position P of each particle i and the historical optimal position P of the entire population g ;

[0018] (2) Search stage based on dynamic particle swarm optimization: Incorporate the dynamic subgroup and information exchange strategy, particle learning strategy and mutation, and the transition from multi-group local learning to single-group global learning strategy into the PSO algorithm to propose an algorithm based on dynamic particle swarm optimization. Then, based on this algorithm, iterate and update the particle swarm until it converges to the global optimal particle, which is used as the X-structure Steiner routing tree.

[0019] The following is the specific implementation process of the present invention.

[0020] 1. Encoding of X-structure Steiner tree:

[0021] Definition 1 Interconnection method. In the X-structure, the connection method c of the interconnection line is divided into the following four types:

[0022] Definition 1.1 Interconnection method 0. First, connect the starting pin and the pseudo-Steiner point through a horizontal or vertical edge, and then connect the pseudo-Steiner point and the ending pin through a 45° or 135° edge.

[0023] Figure 1 In, p1(x1,y1) and p2(x2,y2) are the starting pin and the ending pin of an edge respectively, where x1 < x2. As Figure 1 (a) shows, the pin p1 is connected to the pseudo-Steiner point through a horizontal edge and then connected to the pin p2 through a 45° edge.

[0024] Definition 1.2 Interconnection method 1. First, connect the starting pin and the pseudo-Steiner point through a 45° or 135° edge, and then connect the pseudo-Steiner point and the ending pin through a horizontal or vertical edge.

[0025] As Figure 1 (b) shows, the pin p1 is connected to the pseudo-Steiner point through a 45° edge and then connected to the pin p2 through a horizontal edge.

[0026] Definition 1.3 Interconnection method 2. First, connect the starting pin and the pseudo-Steiner point through a vertical edge, and then connect the pseudo-Steiner point and the ending pin through a horizontal edge.

[0027] As Figure 1 (c) shows, the pin p1 is connected to the pseudo-Steiner point through a vertical edge and then connected to the pin p2 through a horizontal edge.

[0028] Definition 1.4 Interconnection method 3. First, connect the starting pin and the pseudo-Steiner point through a horizontal edge, and then connect the pseudo-Steiner point and the ending pin through a vertical edge.

[0029] As Figure 1As shown in (d), pin p1 is connected to the pseudo Steiner point via a horizontal edge and then connected to pin p2 via a vertical edge.

[0030] The present invention designs an edge pair coding scheme for an X-structured Steiner tree. First, unique digital numbers are set for pins and obstacles in order, and then a digital string (pqc) is used to encode the edges. n-1 f encodes each edge in the tree separately. Among them, p represents the number of the predecessor node in the tree, q represents the number of the successor node in the tree, c represents the interconnection method of this edge, n represents the number of pins, and f represents the fitness value of the particle.

[0031] 2. Population initialization:

[0032] The PSO algorithm is a population-based search algorithm, where each particle in the population represents a potential solution to the problem. Therefore, the present invention uses Prim's algorithm to construct a minimum spanning graph as the initial solution for the particles. The entire population is randomly divided into five subpopulations, and the historical best position of each particle and the current best position of the entire population are initialized. The algorithm then iteratively searches for the optimal solution to the problem. Simultaneously, a series of PSO algorithm parameters, including population size, number of iterations, inertia weight, and learning factor, are initialized.

[0033] 3. Mutation operation:

[0034] The principle of mutation operation on wiring tree is as follows Figure 2 As shown in the figure, after randomly selecting an edge in the tree and deleting it, a union-find operation is introduced to split the tree nodes after the edge is deleted into two sets of points. A point is then randomly selected from each set and connected to form a new edge, ultimately constructing a new wiring tree. The mutation operation increases the algorithm's randomness and global search capabilities by changing the interconnections between pins.

[0035] 4. Crossover operation:

[0036] The principle of cross operation on the wiring tree is as follows Figure 3 As shown in Figure 2. The edges in the two wiring trees are compared sequentially based on their pin numbers. A union-find operation is introduced, adding identical edges from both trees to one edge set and the remaining edges to another. Edges in the identical edge set are directly used as edges in the new wiring tree. Edges are then randomly selected from the remaining edge sets and added to the new wiring tree until a new wiring tree is constructed.

[0037] 5. Dynamic subgroups and information exchange:

[0038] In the present invention, the algorithm controls the exchange learning of particles with a certain strategy. In order to ensure the randomness of information exchange and the invariance of subgroup size, the present invention adopts a method of exchanging particles with each other, that is, at regular intervals, each subgroup randomly selects an exchange particle to exchange with the exchange particles of other subgroups, and the total number of particles in the subgroup remains unchanged before and after the exchange. First, all particles in the population are evenly and randomly divided into N subgroups. During the optimization process, M particles are randomly selected from each subgroup, and information exchange is performed every R generations, where R is called the information exchange period. Figure 4 As shown, the population is divided into four subgroups, each subgroup has 10 particles, and 3 particles are used for exchange learning each time.

[0039] In this example, all X-structured Steiner trees are divided into N subgroups, and each of these N subgroups is updated separately. After every R generations, M X-structured Steiner trees are randomly selected from each subgroup and exchanged between them. This strategy enables information exchange between subgroups during optimization, increasing the diversity of learning objects during the X-structured Steiner tree optimization process, reducing the probability of particles falling into local optima, and ultimately optimizing the resulting X-structured Steiner tree.

[0040] In order to strike a balance between exploration and exploitation, this paper uses a linear reduction method to control the information exchange rate between subgroups during the evolution process. The update formula of R is defined as:

[0041] R=R max -(R max -R min )t / t max (1)

[0042] Among them, R max and R min are the maximum and minimum iteration intervals for information exchange between subgroups, t max is the maximum number of iterations, and t is the current number of iterations.

[0043] 6. Particle Learning Strategy and Mutation

[0044] The present invention sets the learning object of the ordinary particles in the subgroup to be the subgroup optimal particle, and the learning object of the subgroup optimal particle to be the global optimal particle. The learning directions of the two particles are as follows: Figure 5 Compared with global topology, local topology has advantages in particle diversity and accuracy. The global topology structure can make the algorithm converge faster. In this way, the sub-group tends to the global optimum while maintaining individual diversity. The particles with the best fitness value in each sub-group are selected for mutation, and some connections within the XSMT are changed to help the sub-group particles escape the local optimum. The goal is to have a chance to obtain a better fitness value than the current sub-group optimal value during mutation.

[0045] In this example, during the optimization process, the non-optimal X-structured Steiner trees in the subgroups are set to learn from the optimal X-structured Steiner tree in the subgroups, while the optimal X-structured Steiner tree in the subgroups learns from the global optimal X-structured Steiner tree. This strategy enables the subgroups to maintain good individual diversity as they approach the global optimum, which is beneficial for further optimization of the obtained X-structured Steiner tree.

[0046] 7. Transition from multi-group local learning to single-group global learning strategy

[0047] Compared with global learning, local learning has advantages in particle diversity and accuracy, while global learning can make the algorithm converge faster. Therefore, the present invention adopts a strategy of transitioning from multi-group local learning to single-group global learning. This strategy is as follows: Figure 6 As shown in the figure. Local learning uses edge learning to find excellent topological structures, while global learning uses point learning to optimize internal topological connections. This allows XSMT to optimize internal topological connections based on excellent topological structures to achieve better line length optimization rates. Furthermore, to prevent the algorithm from over-exploring and lacking development, and to overcome the drawback of insufficient convergence in the later stages, the present invention sets an iteration threshold. When the number of iterations reaches the threshold, the algorithm transitions from local learning to global learning.

[0048] In this example, during the optimization process, the update of the X-structured Steiner tree transitions from multi-swarm local learning to single-swarm global learning. In local learning, particles use edge learning to learn from a more optimal X-structured Steiner tree, thereby obtaining a better topology. In global learning, particles use point learning to optimize the internal topology of the current X-structured Steiner tree, achieving a higher line length optimization rate. To increase the diversity of particles in the entire population, the transition from local learning to global learning is set to begin after the number of iterations reaches a threshold.

[0049] 8. Fitness function design:

[0050] The main optimization goal of the XSMT problem is to minimize the wiring length, that is, to minimize the length of the optimal X-structure Steiner tree. Therefore, the present invention takes the wire length cost as the optimization goal and sets the fitness of the particle as a function related to the wire length cost. The fitness function is defined as:

[0051]

[0052] Among them, Fitness is a particle Fitness function. l is the calculation edge e jFunction of length.

[0053] 9. Search for updates:

[0054] Each particle in the population has a speed that determines its search direction and distance, as well as a fitness value determined by the optimization function, and based on this, it iteratively searches for the optimal solution in the solution space. In each round of iterative search, the particle completes its own update by following two extreme values: one is the particle's own historical best position, called the individual extreme value; the other is the current best position of the entire sub-swarm, called the global extreme value. In the tth round of iteration, the i-th particle The update formula is defined as:

[0055]

[0056] Where w is the inertia weight used to balance the algorithm's exploration and exploitation capabilities. c1 and c2 are acceleration (learning) factors, adjusting the weights of a particle's flight toward its historically optimal position (pbest) and the global optimal position (gbest), respectively. D1 is the particle's own velocity inertia, while D2 and D3 represent the particle's individual and global learning cognition, respectively. The represented Steiner tree of the X structure is updated according to the following three parts:

[0057] (1) The inertia retention part, that is, the previous velocity of the particle, represents the search ability of the particle. The updated particle is defined as:

[0058]

[0059] Wherein, M represents the mutation operation, the inertia weight w represents the probability of particle mutation, and r1 is a random number between 0 and 1. The representative mutation operations are edge reconstruction and point mutation. Edge reconstruction randomly selects an edge within a particle and removes it. The X-structured Steiner tree represented by the particle then becomes two disconnected subtrees. Connecting these two points forms a new edge, ultimately constructing a new X-structured Steiner tree. The newly generated edge is connected in the same way as the deleted edge. Point mutation randomly selects two edges within a particle and changes their connection. This has the potential to result in a better line length than the original, without changing the tree structure.

[0060] (2) The self-cognition part, that is, the distance between the current position of the particle and the individual extreme value, represents the particle's learning from its own historical experience. The updated particle is defined as:

[0061]

[0062] Among them, C pIt represents the crossover operation. The learning factor c1 represents the probability that the particle crosses with the individual extreme value, and r2 is a random number within 0 to 1.

[0063] (3) The social experience part, that is, the distance between the current position of the particle and the global extreme value, represents the cooperation and information sharing between particles. The updated particle is defined as:

[0064]

[0065] Among them, the learning factor c2 represents the probability that the particle crosses with the global extreme value, and r3 is a random number within 0 to 1. In the present invention, there are two types of crossover operations for D2 and D3: edge learning and point learning. Edge learning means retaining the edges that are the same as the learning object and removing the edges that are different from the learning object, and then continuously randomly selecting new edges to add to the new particle until the new particle forms a complete X - structure Steiner tree; point learning means generating two random integers S1 and S2 that are less than the number of edges in the X - structure Steiner tree, generating a set of edge numbers S = {k|k≥S1 and k≤S2, k∈N *} and changing the connection method of some edges in the set S to the connection method of the corresponding numbered edges in the learning object.

[0066] The inertia weight w and the learning factors c1 and c2 have a great impact on the optimization process of the X - structure Steiner tree; a larger w makes the particle more likely to mutate, has better global search ability, and is not easily trapped in local optima; while a smaller w makes the particle more likely to stay in the current local area for search, has better development ability, and speeds up convergence; too large c1 easily makes the particle continuously develop in the local area; and too large c2 easily makes the particle prematurely fall into the vicinity of local optima; therefore, in order to balance the parameter settings and balance the development and exploration capabilities, the present invention is based on a linear adjustment strategy and adaptively adjusts w, c1, c2 according to the number of iterations. The adjustment formulas are as follows:

[0067]

[0068] Among them, w_max and w_min respectively represent the maximum and minimum w values, c1_max and c1_min respectively represent the initial and final c1 values, and c2_max and c2_min respectively represent the initial and final c2 values.

[0069] The above are the preferred embodiments of the present invention. All changes made according to the technical solutions of the present invention, when the functions and effects produced do not exceed the scope of the technical solutions of the present invention, shall fall within the protection scope of the present invention.

Claims

1. A method for constructing an X-structured Steiner minimum tree based on dynamic particle swarm optimization, characterized in that: include: (1) Wiring topology initialization phase: Use Prim's algorithm to initialize the population and initialize the historical optimal position P of each particle i and the current best position P of the entire population g ; (2) Search phase based on dynamic particle swarm optimization: Dynamic sub-groups and information exchange strategies, particle learning strategies and mutations, and the transition from multi-group local learning to single-group global learning strategies are added to the PSO algorithm. An algorithm based on dynamic particle swarm optimization is proposed. The particle swarm is then iteratively updated based on the algorithm until it converges to the global optimal particle, which is used as the X-structured Steiner wiring tree. The method comprises the following steps: S1, X-structure Steiner tree encoding: Under the X structure, the connection mode c of the interconnection line is divided into four types; a point pair encoding scheme of the X structure Steiner tree is designed: first, unique digital numbers are set for pins and obstacles in sequence, and then a digital string (pqc) is used to encode the pins and obstacles. n-1 f encodes each edge in the X-structure Steiner tree; where p represents the number of the predecessor node in the tree, q represents the number of the successor node in the tree, c represents the interconnection method of the corresponding edge, n represents the number of pins, and f represents the fitness value of the particle; S2. Population initialization: The Prim algorithm is used to construct the minimum spanning graph as the initial solution of the particle, the entire population is randomly divided into 5 subgroups, and the historical optimal position P of each particle is initialized. i and the current best position P of the entire population g , and then iteratively search for the optimal solution to the problem; S3, mutation operation: After randomly selecting an edge in the X-structured Steiner tree and deleting it, a union-find operation is introduced to divide the X-structured Steiner tree node after the edge is deleted into two point sets. Then, a point is randomly selected from each of the two point sets, and the two points are connected to form a new edge, finally constructing a new X-structured Steiner tree. S4, cross operation: The edges in the two X-structured Steiner trees are compared sequentially according to their pin numbers. A union-find operation is introduced to add the identical edges in the two X-structured Steiner trees to one edge set, and the remaining edges to the remaining edge sets. The edges in the identical edge set are directly used as the edges of the new X-structured Steiner tree. Then, edges are randomly selected from the remaining edge sets and added to the new X-structured Steiner tree until a new X-structured Steiner tree is constructed.

2. The X-structured Steiner minimum tree construction method based on dynamic particle swarm optimization according to claim 1, characterized in that: The method further includes the following steps: S5. Dynamic subgroups and information exchange: Divide all X-structured Steiner trees into N subgroups, and update each of these N subgroups separately. After every R generations, randomly select M X-structured Steiner trees from each subgroup and exchange them pairwise. In order to strike a balance between exploration and exploitation, a linear decrease method is used to control the information exchange rate between subgroups during the evolution process; the update formula of R is defined as: R=R max -(R max -R min )t / t max Among them, R max and R min are the maximum and minimum iteration intervals for information exchange between subgroups, t max is the maximum number of iterations, t is the current number of iterations; S6. Particle learning strategy and mutation: During the optimization process, the non-optimal X-structure Steiner tree in the subgroup is set to learn from the optimal X-structure Steiner tree in the subgroup, and the optimal X-structure Steiner tree in the subgroup is set to learn from the optimal X-structure Steiner tree in the global cluster. S7, Multi-group local learning transition to single-group global learning strategy: During the optimization process, the update of the X-structure Steiner tree transitions from multi-swarm local learning to single-swarm global learning. In local learning, particles adopt edge learning to learn from a more optimal X-structure Steiner tree, thereby obtaining a better topological structure. In global learning, particles use point learning to optimize the internal topology of the current X-structure Steiner tree, achieving a better line length optimization rate. To increase the diversity of particles in the entire population, the transition from local learning to global learning is set after the number of iterations reaches a threshold. S8. Fitness function design: The optimization goal of the X-structure Steiner tree problem is to minimize the optimal X-structure Steiner tree line length. Therefore, the fitness of the particle is set as a function related to the line length cost. At the tth iteration, the i-th particle The fitness function is defined as: Among them, Fitness is a particle The fitness function, l is the calculation edge e j Function of length; S9, search for updates: Each particle in the population has a speed that determines its search direction and distance, as well as a fitness value determined by the optimization function, and based on this, it iteratively searches for the optimal solution in the solution space. In each round of iterative search, the particle completes its own update by following two extreme values: one is the particle's own historical best position, called the individual extreme value; the other is the current best position of the entire subgroup, called the global extreme value. In the tth round of iteration, the i-th particle The update formula is defined as: Where w is the inertia weight used to balance the algorithm's exploration and development capabilities, c1 and c2 are acceleration factors, which adjust the weights of the particle flying to its own historical optimal position (pbest) and the global optimal position (gbest), respectively; D1 is the particle's own velocity inertia, D2 and D3 are the particle's individual learning cognition and global learning cognition, respectively; The represented Steiner tree of the X structure is updated according to the following three parts: The inertia retention part, that is, the previous velocity of the particle, represents the particle's search ability. The updated particle is defined as: Among them, M represents the mutation operation, the inertia weight w represents the probability of particle mutation, and r1 is a random number between 0 and 1; The representative mutation operations are edge reconstruction and point mutation. Edge reconstruction refers to randomly selecting an edge within a particle and removing it. The X-structured Steiner tree represented by the particle then becomes two disconnected subtrees. Connecting these two points forms a new edge, ultimately constructing a new X-structured Steiner tree. The newly generated edge is connected in the same way as the deleted edge. Point mutation refers to randomly selecting two edges within a particle and changing their connection. This may result in a better line length than the original one, but this method does not change the tree structure. The self-cognition part, that is, the distance between the current position of the particle and the individual extreme value, represents the particle's learning from its own historical experience. The updated particle is defined as: Among them, C p represents the crossover operation, the learning factor c1 represents the probability of the particle crossing with the individual extreme value, and r2 is a random number between 0 and 1; The social experience part, that is, the distance between the current position of the particle and the global extreme value, represents the collaboration and information sharing between particles. The updated particle is defined as: Among them, the learning factor c2 represents the probability of the particle crossing with the global extreme value, and r3 is a random number within 0 to 1; there are two types of crossover operations for D2 and D3, namely edge learning and point learning; edge learning means retaining the edges that are the same as the learning object and removing the edges that are different from the learning object, and then continuously randomly selecting new edges to add to the new particle until the new particle forms a complete X - structure Steiner tree; point learning means generating two random integers S1 and S2 that are less than the number of edges in the X - structure Steiner tree, and generating a set of edge numbers S = {k|k≥S1 and k≤S2, k∈N *}, and changing the connection method of some edges in the set S to the connection method of the corresponding numbered edges in the learning object; The inertia weight w and learning factors c1 and c2 have a significant impact on the optimization process of the X-structured Steiner tree. To balance parameter settings and development and exploration capabilities, a linear adjustment strategy is used to adaptively adjust w, c1, and c2 according to the number of iterations. The adjustment formula is as follows: Among them, w_max and w_min represent the maximum and minimum w values ​​respectively, c1_max and c1_min represent the initial and final c1 values ​​respectively, and c2_max and c2_min represent the initial and final c2 values ​​respectively.

3. The X-structured Steiner minimum tree construction method based on dynamic particle swarm optimization according to claim 2, characterized in that: The connection methods c of the interconnection lines are divided into four types, as follows: Interconnection method 0: First connect the starting pin and the pseudo Steiner point through a horizontal edge or a vertical edge, and then connect the pseudo Steiner point and the ending pin through a 45° edge or a 135° edge; Interconnection method 1: First connect the starting pin and the pseudo Steiner point through a 45° edge or a 135° edge, and then connect the pseudo Steiner point and the end pin through a horizontal edge or a vertical edge; Interconnection method 2: First connect the starting pin and the pseudo Steiner point through a vertical edge, and then connect the pseudo Steiner point and the end pin through a horizontal edge; Interconnection method 3: First connect the starting pin and the pseudo Steiner point through a horizontal edge, and then connect the pseudo Steiner point and the end pin through a vertical edge.

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