CN113919280A - Time delay driving XSMT construction method based on two-stage competition particle swarm optimization - Google Patents

Time delay driving XSMT construction method based on two-stage competition particle swarm optimization Download PDF

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CN113919280A
CN113919280A CN202111185378.XA CN202111185378A CN113919280A CN 113919280 A CN113919280 A CN 113919280A CN 202111185378 A CN202111185378 A CN 202111185378A CN 113919280 A CN113919280 A CN 113919280A
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刘耿耿
周茹平
郭文忠
陈国龙
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Abstract

The invention relates to a time delay driving XSMT construction method based on two-stage competition particle swarm optimization. The method comprises the following four effective strategies: (1) and (5) competing particle swarm optimization. And simultaneously optimizing the line length and the maximum source sink path by using a multi-target particle swarm optimization algorithm, and adding a competition mechanism to select a learning object of the particles, thereby improving the population diversity and reducing the calculation cost. (2) A two-stage learning strategy. The particles better balance the exploration and development capabilities of the algorithm through edge learning and point learning. (3) A hybrid crossover strategy. Different cross strategies are used for different particles, and the convergence quality of the algorithm is further improved. (4) Design of discretized frameworks. And a reasonable objective function and particle coding mode is designed by combining a mutation crossover operator, so that discretization of the algorithm is realized, and the problem of discrete time delay driven Steiner minimum tree is better solved.

Description

Time delay driving XSMT construction method based on two-stage competition particle swarm optimization
Technical Field
The invention belongs to the technical field of computer aided design of integrated circuits, and particularly relates to a time delay driving XSMT construction method based on two-stage competition particle swarm optimization.
Background
A. Time delay driving
The optimization goal of conventional Integrated Circuit (IC) layout design is mainly to minimize the total length of interconnect lines. However, as the feature size of IC is moving to the nanometer level, as one of the important targets of performance-driven IC design, the speed performance of the chip has been determined by the interconnect delay, so the delay has become a key index for the physical design of the chip. Global routing is also a significant loop in physical design, and its routing quality greatly affects the final chip performance. However, most of the construction algorithms of the Steiner tree, which is an optimal connection model for the overall routing, are dedicated to minimizing the total interconnection line length of the routing tree, thereby saving routing resources, improving the routing quality, and often neglecting the effect of time delay. Therefore, constructing a time-delay Driven Steiner Minimum Tree (TD-SMT) is a research direction that needs to be emphasized by the global routing algorithm today. In addition, because the traditional Steiner tree construction algorithm taking reduction of wire length as an optimization target is difficult to ensure that the minimum time delay is obtained while the shortest bus length is solved, and because the bus length and the maximum source sink path of the wiring tree have direct influence on the time delay, the TD-SMT construction algorithm requires that the minimum maximum source sink path is considered while the total length of the wiring is optimized, so that the total time delay and the maximum source sink delay are reduced, and the quality of VLSI physical design is improved.
B.X Structure
At present, most of research work of Steiner minimum trees is based on the expansion of a Manhattan structure straight line interconnection line model, namely, the connection direction of interconnection lines in a wiring tree is horizontal or vertical, the solution space of the Steiner tree is limited, and the Steiner tree can only change the interconnection lines in the horizontal and vertical directions during optimization. Relatively speaking, the non-Manhattan structure wiring in more directions is more diversified, and the adjustment of the interconnection line in the optimization of the Steiner tree has more choices, so that the algorithm can find a more excellent wiring solution. Today, many routing algorithms for line length optimization have introduced non-manhattan architectures. However, the wiring algorithm considering the delay driving rarely relates to a non-manhattan structure, so that designing a delay-Driven X-architecture Steiner Minimum Tree (TD-XSMT) construction algorithm based on an X structure has important theoretical value and practical significance.
C. Multi-objective optimization algorithm
Because the two objective functions of the line length and the maximum source sink path are in a mutual constraint relationship, the maximum source sink path is increased when the line length is reduced, and conversely, the line length is also deteriorated when the maximum source sink path is reduced. Therefore, the TD-XSMT problem, as a multi-objective optimization problem, also requires the design of an appropriate multi-objective optimization algorithm. The TD-XSMT optimization is carried out by using a classical multi-Objective Particle Swarm optimization algorithm (MOPSO). However, the MOPSO also has the defect of the traditional PSO, namely, the convergence effect is not good due to the fact that premature convergence is easy to occur.
Disclosure of Invention
The invention aims to provide a time delay driving XSMT construction method based on two-stage competition particle swarm optimization.
In order to achieve the purpose, the technical scheme of the invention is as follows: a time delay driving XSMT construction method based on two-stage competition particle swarm optimization comprises the following steps:
step S1, designing an objective function to represent the line length and the maximum source-sink distance of the Steiner tree, and coding each Steiner tree by using an edge point coding strategy;
step S2, when optimizing the wire length and the maximum source sink path of the Steiner tree, firstly, using a method of fast non-dominated sorting and congestion degree calculation to obtain an elite particle pool with the size of 10, and using a competition mechanism in the elite pool to obtain a winner as a learning object of the current particle;
step S3, in the optimizing process of iterative learning, a multi-objective particle swarm optimization algorithm is used for optimizing the line length and the maximum source sink path of the Steiner tree, a frame of the multi-objective particle swarm optimization algorithm is redesigned, a two-stage learning strategy is designed, in the first stage of the two-stage learning strategy, namely a learning stage, the cross operation aiming at the side structure is used, a particle learning object is a winner particle which is selected for the individual history optimization and competition, and the particle learns partial topological structure of an excellent individual through learning; in the second stage of the two-stage learning strategy, namely a point learning stage, a mutation crossover operation aiming at point selection is used, wherein the mutation operation randomly changes the pseudo Steiner point selection of partial edges of the particles, a crossover operation learning object is also selected as a winner particle for individual history optimization and competition, and the crossover operation enables the particles to learn partial point selection of excellent particles; designing a mixed crossing strategy in a point learning stage, and using a multipoint crossing mode for the particles with better quality to enable the partial particles to learn partial genes of excellent particles with a preset probability; a uniform crossover strategy was used for the poor quality particles, allowing this fraction of particles to learn all the genes of the superior particles.
In an embodiment of the present invention, in step S1, the objective function construction process is as follows:
the time delay driving X structure Steiner minimum tree is used as a multi-objective optimization problem, and a maximum source-sink path and a bus length need to be optimized simultaneously, so that two optimization objectives are designed: the total line length and radius; the bus length represents the sum of all edge line lengths of the wiring tree, and the radius represents the sum of the edge line lengths on the maximum source sink path in the wiring tree; the total line length and radiusThe functions are respectively expressed as fwlAnd fplThe calculation formula is as follows:
Figure BDA0003298733560000021
Figure BDA0003298733560000022
wherein e iskThe k-th edge segment, e, in the wiring tree TjFrom the source s0To a sink siIs taken along the path of (1).
In an embodiment of the present invention, in step S1, the method for encoding each Steiner tree by using the edge point pair encoding policy is as follows:
considering the characteristics of Steiner tree, the coding mode of edge point pair represents wiring tree by edge as unit, one edge in the tree is composed of pins at two ends of the edge and PSP selection mode among the pins, in order to connect n pins in the net to form wiring tree T, n-1 edges are needed, each edge is composed of coding string (e)start,eendPspc) indicating that the PSP in the edge is connected to the pin e in the selection mode of the pspcstartAnd pin eendTherefore, in order to represent all edges of T, a code length of 3X (n-1) is needed, and in addition, two more bits are added to represent the line length cost and the radius cost of the Steiner tree in consideration of two optimization targets of the time delay driven X structure Steiner minimum tree, so that the complete code string length of T is 3X (n-1) + 2.
In an embodiment of the present invention, step S2 is implemented as follows:
first, an elite pool X of size t is found in the population by fast non-dominated sorting and calculation based on the crowdedness distance { X ═ X }0,x1,...,xtAnd randomly selecting two of the elite particles xa、xbCompeting by comparing xaAnd xbThe included angle formed between the current particle and the current particle is smaller, the winner is the competition, and the loser is the loser if the included angle is larger.
In an embodiment of the present invention, in step S3, the redesigned particles of the multi-objective particle swarm optimization algorithm follow the following updated formula:
Figure BDA0003298733560000031
where ω is the inertial weight, c1And c2For acceleration factor, iter is current iteration number, threshold is set iteration threshold, when iteration number is less than threshold, the updating learning operation of the first stage is executed, and when iteration number is greater than threshold, the updating learning operation of the second stage is executed, wherein EF1And EF2Respectively representing the historical and elite lead components, PF, of the side learning phase1、PF2And PF3Respectively representing a self-guiding component, a history guiding component and an elite guiding component in the point learning stage;
(1) learning stage
1) History guide component
EF implementation by introducing cross-operations for edge learning1The components, expressed as follows:
Figure BDA0003298733560000032
wherein, Cu() Is an edge-crossing operation in which the edges are crossed,
Figure BDA0003298733560000033
is the historical optimal solution of the particle, r1Is a random number within [0,1),
Figure BDA0003298733560000034
through EF1After operation, particles are obtained
Figure BDA0003298733560000035
If a random number r is generated1<c1The particle performs an edge crossing operationOtherwise, maintaining the current state of the particles; the specific steps of the edge crossing operation are as follows: 1) for the current particle
Figure BDA0003298733560000036
Corresponding Steiner tree, determining the edge set as E ═ E1,e2,...,en-1}, learning objects thereof
Figure BDA0003298733560000041
The edge set of the corresponding Steiner tree is E '═ E'1,e'2,...,e'n-1}; 2) judging and storing the same edge set and different edge sets of two trees, wherein the same edge is used as a new particle
Figure BDA0003298733560000042
The initial edge of (2); 3) continuously randomly selecting edges from different edge sets and adding new particles until a complete and legal Steiner tree is constructed, wherein a parallel-searching method is used in the process to ensure that no loop occurs in the wiring tree;
2) elite guide component
By EF2The elite lead component of the finished particle, expressed as follows:
Figure BDA0003298733560000043
wherein the content of the first and second substances,
Figure BDA0003298733560000044
is a winner elite particle obtained by competition;
(2) point learning phase
1) Component of self-induction
Implementing PF by introducing mutation operations for point-to-point learning1The components, expressed as follows:
Figure BDA0003298733560000045
wherein M isp()Is a point mutation operation, r1Is a random number within [0,1),
Figure BDA0003298733560000046
passing through PF1After operation, particles are obtained
Figure BDA0003298733560000047
If a random number r is generated1<Omega, the particle performs point mutation operation, otherwise, the particle maintains the current state; the point mutation adopts a two-point mutation mode, and the specific operation is as follows: randomly selecting a routing tree
Figure BDA0003298733560000048
The two edges of the PSP are replaced by PSP selection modes of the two edges;
2) history guide component
Implementing PF by introducing cross-operations for point learning2The components, expressed as follows:
Figure BDA0003298733560000049
wherein, Cv() Representing point-crossing operations, the object of cross-learning being optimized for individual history
Figure BDA00032987335600000410
r2Is a random number within [0,1),
Figure BDA00032987335600000411
passing through PF2After operation, particles are obtained
Figure BDA00032987335600000412
When a random number r is generated2＜c1Performing a point-crossing operation on the particles;
3) elite guide component
Implementing PF by introducing cross-operations for point learning3Components, are represented as follows：
Figure BDA0003298733560000051
Wherein the content of the first and second substances,
Figure BDA0003298733560000052
is a winner elite particle, C, obtained by competitionv() The operation also uses a hybrid interleaving strategy.
In an embodiment of the present invention, the particle performing point crossing operation in step (2) adopts a mixed point crossing strategy, specifically, the particles in the population are divided into two types of excellent and laggard particles according to the fast non-dominated sorting, and the mixed point crossing strategy uses different point learning manners for different particles:
a. multipoint intersection
Implementing PF using multi-point intersection for the first half of the particles in the sequence2The method comprises the following specific operations: for a Steiner tree containing n pins, the current particle is randomly selected
Figure BDA0003298733560000053
Between edge zones requiring crossing [ E ]s,Ee]And find the individual history optimum
Figure BDA0003298733560000054
Coding of the corresponding edge, then
Figure BDA0003298733560000055
Code replacement of
Figure BDA0003298733560000056
Coding of the interval;
b. uniform crossing
The second half of the particles in the sequence are uniformly crossed to realize PF2(ii) a This intersection method differs from the multipoint intersection in that it does not require determining an interval to be intersected, but rather traverses the current particle
Figure BDA0003298733560000057
Optimized with its individual history
Figure BDA0003298733560000058
Find the same interconnection line edge set Esame＝{e1,e2,…,ej}, particles
Figure BDA0003298733560000059
Study EsameThe PSP selection mode of all edges.
Compared with the prior art, the invention has the following beneficial effects: the invention can better solve the problem of discrete time delay driving Steiner minimum tree.
Drawings
Fig. 1 is a schematic diagram of a contention mechanism.
FIG. 2 is a crossover operation for edge learning.
Fig. 3 is a mutation operation for point learning.
Fig. 4 is a multipoint intersection operation for point learning.
Fig. 5 is a uniform crossover operation for point learning.
Fig. 6 is a flow chart of the present invention.
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
The invention discloses a time delay driving XSMT construction method based on two-stage competition particle swarm optimization, which comprises the following steps of:
step S1, designing an objective function to represent the line length and the maximum source-sink distance of the Steiner tree, and coding each Steiner tree by using an edge point coding strategy;
step S2, when optimizing the wire length and the maximum source sink path of the Steiner tree, firstly, using a method of fast non-dominated sorting and congestion degree calculation to obtain an elite particle pool with the size of 10, and using a competition mechanism in the elite pool to obtain a winner as a learning object of the current particle;
step S3, in the optimizing process of iterative learning, a multi-objective particle swarm optimization algorithm is used for optimizing the line length and the maximum source sink path of the Steiner tree, a frame of the multi-objective particle swarm optimization algorithm is redesigned, a two-stage learning strategy is designed, in the first stage of the two-stage learning strategy, namely a learning stage, the cross operation aiming at the side structure is used, a particle learning object is a winner particle which is selected for the individual history optimization and competition, and the particle learns partial topological structure of an excellent individual through learning; in the second stage of the two-stage learning strategy, namely a point learning stage, a mutation crossover operation aiming at point selection is used, wherein the mutation operation randomly changes the pseudo Steiner point selection of partial edges of the particles, a crossover operation learning object is also selected as a winner particle for individual history optimization and competition, and the crossover operation enables the particles to learn partial point selection of excellent particles; designing a mixed crossing strategy in a point learning stage, and using a multipoint crossing mode for the particles with better quality to enable the partial particles to learn partial genes of excellent particles with a preset probability; a uniform crossover strategy was used for the poor quality particles, allowing this fraction of particles to learn all the genes of the superior particles.
The following is a specific implementation process of the present invention.
1. An objective function:
the time delay driving X structure Steiner minimum tree is used as a multi-objective optimization problem, and a maximum source-sink path and a total line length need to be optimized simultaneously, so that the invention designs two optimization objectives: the total line length and the radius. The bus length represents the sum of all edge segment lengths of the wiring tree, and the radius represents the sum of the edge segment lengths on the largest source sink path in the wiring tree. The total line length and radius functions are respectively expressed as fwlAnd fplThe calculation formula is as follows:
Figure BDA0003298733560000061
Figure BDA0003298733560000062
wherein e iskThe k-th edge segment, e, in the wiring tree TjFrom the source s0To a sink siIs taken along the path of (1).
2. Particle encoding:
in order to better encode the Steiner tree, the invention selects the edge points which are more suitable for being applied to the evolutionary algorithm to carry out particle encoding on the encoding mode. Considering the characteristics of the Steiner tree, the edge point pair coding mode represents the wiring tree by taking an edge as a unit. One edge of the tree consists of pins at both ends of the edge and a PSP selection mode among the pins. To connect n pins in a net to form a routing tree T, n-1 edges are required, each edge consisting of a coded string (e)start,eendPspc) indicating that the PSP in the edge is connected to the pin e in the selection mode of the pspcstartAnd pin eend. Therefore, in order to represent all the edges of T, a code length of 3 × (n-1) is required. In addition, considering two optimization objectives of TD-XSMT, two more bits are added to represent the wire length cost and the radius cost of the Steiner tree, so that the complete code string length of T is 3 (n-1) + 2. For example, a particle code with 7 pin lengths TD-XSMT can be expressed as follows:
562 672 722 740 732 133 21 10
wherein 6 substrings of length 3 distinguished by underlining represent the corresponding 6 sides, e'740' indicating that pin 7 and pin 4 are connected by means of the select 0, bold numbers ' 21 ' and ' 10 ' of the tail are the wire length and radius of the routing tree, respectively.
3. The competition mechanism is as follows:
the invention uses the idea of a competition mechanism to enhance the optimizing performance of the multi-target particle swarm optimization algorithm, thereby more effectively solving the multi-target optimization problem of TD-XSMT. First, an elite pool X of size t is found in the population by fast non-dominated sorting and calculation based on the crowdedness distance { X ═ X }0,x1,...,xtAnd randomly selecting two of the elite particles xa、xbCompetition, the competition mode is generalOver-comparison xaAnd xbThe included angle formed between the current particle and the current particle is smaller, the winner is the competition, and the loser is the loser if the included angle is larger. FIG. 1 is a schematic diagram of the competition mechanism, wherein solid particles are the current generation elitism pool, particles s are the particles to be learned currently, and hollow particles are the other particles in the population. Randomly selecting x in elite poola、xbTwo particles compete through xa、xbS objective function values f1And f2Can calculate xa、xbAngle theta formed with saAnd thetab. Theta in FIG. 1aSmaller, then xaWins the competition and becomes the learning object of s. The competition mechanism of win-loss is judged through the included angle, so that the particle s finally flies to the elite particle winner x closer to the convergence direction of the particle saAnd the method is more favorable for accelerating population convergence.
4. Two-stage learning strategy:
considering the balance of TD-XSMT problem line length and radius and the balance of population diversity and convergence, the invention designs different learning methods, so that the particle updating formula is divided into two stages, further considering the characteristics of different learning methods, combining a competition mechanism with individual cognitive components of PSO, redefining the particle updating formula components, and designing a new learning strategy suitable for TD-XSMT optimization. The particles follow the following updated formula:
Figure BDA0003298733560000071
where ω is the inertial weight, c1And c2For the acceleration factor, iter is the current iteration number, and threshold is the set iteration threshold (the total iteration number is set to be 1000, and the iteration threshold is set to be 200). And when the iteration times are less than the threshold value, executing the updating learning operation of the first stage, and when the iteration times are more than the threshold value, executing the updating learning operation of the second stage. According to different learning methods, the first stage is called an edge learning stage, and the second stage is called a point learning stage. The invention redefinesUpdating the respective components in the formula, wherein EF1And EF2Respectively representing the historical and elite lead components, PF, of the side learning phase1、PF2And PF3The self-guidance component, the historical guidance component, and the elite guidance component of the point learning phase are represented, respectively.
(1) Learning stage
1) History guide component
The invention realizes EF by introducing cross operation aiming at side learning1The components, expressed as follows:
Figure BDA0003298733560000081
wherein, Cu() Is an edge-crossing operation in which the edges are crossed,
Figure BDA0003298733560000082
is the historical optimal solution of the particle, r1Is a random number within [0,1),
Figure BDA0003298733560000083
through EF1After operation, particles are obtained
Figure BDA0003298733560000084
If a random number r is generated1<c1And if not, maintaining the current state of the particle. The specific steps of the edge crossing operation are as follows: 1) for the current particle
Figure BDA0003298733560000085
Corresponding Steiner tree, determining the edge set as E ═ E1,e2,...,en-1}, learning objects thereof
Figure BDA0003298733560000086
The edge set of the corresponding Steiner tree is E '═ E'1,e'2,...,e'n-1}; 2) judging and storing the same edge set and different edge sets of two treesSet of edges, wherein the same edge is as a new particle
Figure BDA0003298733560000087
The initial edge of (2); 3) and continuously randomly selecting edges from different edge sets and adding new particles until a complete and legal Steiner tree is constructed, wherein a concurrent set checking method is used in the process to ensure that no loop occurs in the wiring tree. Fig. 2 shows a schematic diagram of such a cross operation for edge learning by taking a 7-pin routing tree as an example (the coding corresponding to the particle is below each routing tree), where the bold edge is
Figure BDA0003298733560000088
And
Figure BDA0003298733560000089
the same edge of both wiring trees, i.e., the edge coded as (561672742),
Figure BDA00032987335600000810
keeping the same edge and then randomly selecting
Figure BDA00032987335600000811
Edge e of6(133)、
Figure BDA00032987335600000812
Edge e of4(722) And e6(732) Adding into
Figure BDA00032987335600000813
A new routing tree is constructed.
2) Elite guide component
Invention by EF2The elite lead component of the finished particle, expressed as follows:
Figure BDA00032987335600000814
wherein the content of the first and second substances,
Figure BDA00032987335600000815
is a winner elite particle, C, obtained by competitionu() The operation is implemented as above, and is not described herein.
(2) Point learning phase
1) Component of self-induction
The invention realizes PF by introducing mutation operation aiming at point learning1The components, expressed as follows:
Figure BDA00032987335600000816
wherein M isp() Is a point mutation operation, r1Is a random number within [0,1),
Figure BDA00032987335600000817
passing through PF1After operation, particles are obtained
Figure BDA00032987335600000818
If a random number r is generated1<ω, the particle performs a point mutation operation, otherwise, the particle maintains the current state. The point mutation adopts a two-point mutation mode, and the specific operation is as follows: randomly selecting a routing tree
Figure BDA0003298733560000091
The PSP selection method (selection 0 to 3) of these two sides is replaced. FIG. 3 is a schematic diagram of point variation in which particles are randomly selected
Figure BDA0003298733560000092
Two sides e of1(561) And e2(742) After a point mutation operation, e1And e2The wiring scheme of (1) is changed from selection 1, selection 2 to selection 2 and selection 0, respectively.
2) History guide component
The invention realizes PF by introducing cross operation aiming at point learning2The components, expressed as follows:
Figure BDA0003298733560000093
wherein, Cv() Representing point-crossing operations, the object of cross-learning being optimized for individual history
Figure BDA0003298733560000094
r2Is a random number within [0,1),
Figure BDA0003298733560000095
passing through PF2After operation, particles are obtained
Figure BDA0003298733560000096
When a random number r is generated2＜c1And performing point crossing operation on the particles, specifically using a mixed point crossing mode.
Hybrid point crossing strategy
The multi-objective optimization algorithm is difficult to define the advantages and disadvantages of the particles, and the method can divide the particles in the population into excellent particles and laggard particles according to the rapid non-dominated sorting. The hybrid crossover strategy uses different point learning approaches for different particles.
a. Multipoint intersection
The invention realizes PF by using a multipoint intersection mode on the particles arranged in the first half in the sorting2The method comprises the following specific operations: for a Steiner tree containing n pins, the current particle is randomly selected
Figure BDA0003298733560000097
Between edge zones requiring crossing [ E ]s,Ee]And find the individual history optimum
Figure BDA0003298733560000098
Coding of the corresponding edge, then
Figure BDA0003298733560000099
Code replacement of
Figure BDA00032987335600000910
And coding the interval. As shown in fig. 4, select
Figure BDA00032987335600000911
The edge interval of (a)672 722 740) I.e. by
Figure BDA00032987335600000912
Corresponding to edge e of Steiner tree1、e2And e3，
Figure BDA00032987335600000913
The corresponding edge is the edge e of the Steiner tree corresponding to the corresponding edge1、e2And e3(671 722 740) (ii) a Mixing the particles
Figure BDA00032987335600000914
Code replacement on the interval
Figure BDA00032987335600000915
Corresponding to the value of the code string. Edge e of the particle obtained after the crossover operation1、e2And e3The wiring pattern of (2) is changed from select 2, and select 0 to select 1, select 2, and select 0, respectively.
b. Uniform crossing
The second half of the particles in the sequence are uniformly crossed to realize PF2. This intersection method differs from the multipoint intersection in that it does not require determining an interval to be intersected, but rather traverses the current particle
Figure BDA00032987335600000916
Optimized with its individual history
Figure BDA00032987335600000917
Find the same interconnection line edge set Esame＝{e1,e2,…,ej}, particles
Figure BDA00032987335600000918
Study EsameThe PSP selection mode of all edges. As shown in fig. 5, the traversal results in
Figure BDA00032987335600000919
All edges of the winner are the same edges, will
Figure BDA00032987335600000920
Code replacement on the interval
Figure BDA00032987335600000921
For coding over intervals.
3) Elite guide component
The invention realizes PF by introducing cross operation aiming at point learning3The components, expressed as follows:
Figure BDA0003298733560000101
wherein the content of the first and second substances,
Figure BDA0003298733560000102
is a winner elite particle, C, obtained by competitionv() The operation also uses the hybrid crossover strategy, which is not described in detail here.
5. The method comprises the following steps:
the time delay driving X structure Steiner minimum tree construction method based on two-stage competition particle swarm optimization optimizes the maximum source-sink path and the bus length, and therefore the maximum source-sink time delay and the total time delay of a wiring tree are optimized. The general flow chart of the invention is shown in fig. 6, and the steps are as follows:
step 1, loading circuit data and initializing algorithm parameters.
And 2, generating an initial wiring tree as an initial population by using a Prim-Dijkstra model based on an X structure.
And 3, calculating and constructing an elite particle pool according to the rapid non-dominated sorting and the crowdedness.
And 4, randomly selecting two elite particles, and calculating an included angle formed between the elite particles and the current particle to obtain the winner particle.
Step 5, if the current iteration number is smaller than the threshold value, performing a side learning stage updating operation on the particles, namely step 6 (a); if the current iteration number is greater than the threshold, performing a point phase update operation on the particle, namely step 6 (b).
And 6(a), according to the formula (4) and the formula (5), the particles are crossed aiming at the edge structure to realize updating.
And 6(b), carrying out variation crossing aiming at point selection on the particles according to the formulas (6) to (8) so as to realize updating.
And 7, updating the individual history optimal pbest of the particles.
Step 8, if the termination condition is met (the set maximum iteration times are reached), reconstructing the elite pool of the current population, finding out the particles which enable the sum of the total delay and the maximum source sink delay to be minimum and outputting the particles as an optimal solution, and finishing the algorithm; otherwise, returning to the step 3.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.

Claims (6)

1. A time delay driving XSMT construction method based on two-stage competition particle swarm optimization is characterized by comprising the following steps:
step S1, designing an objective function to represent the line length and the maximum source-sink distance of the Steiner tree, and coding each Steiner tree by using an edge point coding strategy;
step S2, when optimizing the wire length and the maximum source sink path of the Steiner tree, firstly, using a method of fast non-dominated sorting and congestion degree calculation to obtain an elite particle pool with the size of 10, and using a competition mechanism in the elite pool to obtain a winner as a learning object of the current particle;
step S3, in the optimizing process of iterative learning, a multi-objective particle swarm optimization algorithm is used for optimizing the line length and the maximum source sink path of the Steiner tree, a frame of the multi-objective particle swarm optimization algorithm is redesigned, a two-stage learning strategy is designed, in the first stage of the two-stage learning strategy, namely a learning stage, the cross operation aiming at the side structure is used, a particle learning object is a winner particle which is selected for the individual history optimization and competition, and the particle learns partial topological structure of an excellent individual through learning; in the second stage of the two-stage learning strategy, namely a point learning stage, a mutation crossover operation aiming at point selection is used, wherein the mutation operation randomly changes the pseudo Steiner point selection of partial edges of the particles, a crossover operation learning object is also selected as a winner particle for individual history optimization and competition, and the crossover operation enables the particles to learn partial point selection of excellent particles; designing a mixed crossing strategy in a point learning stage, and using a multipoint crossing mode for the particles with better quality to enable the partial particles to learn partial genes of excellent particles with a preset probability; a uniform crossover strategy was used for the poor quality particles, allowing this fraction of particles to learn all the genes of the superior particles.
2. The time-delay-driven XSMT construction method based on two-stage competition particle swarm optimization according to claim 1, wherein in step S1, the objective function construction process is as follows:
the time delay driving X structure Steiner minimum tree is used as a multi-objective optimization problem, and a maximum source-sink path and a bus length need to be optimized simultaneously, so that two optimization objectives are designed: the total line length and radius; the bus length represents the sum of all edge line lengths of the wiring tree, and the radius represents the sum of the edge line lengths on the maximum source sink path in the wiring tree; the total line length and radius functions are respectively expressed as fwlAnd fplThe calculation formula is as follows:
Figure FDA0003298733550000011
Figure FDA0003298733550000012
wherein e iskThe k-th edge segment, e, in the wiring tree TjFrom the source s0To a sink siIs taken along the path of (1).
3. The time-delay-driven XSMT construction method based on two-stage competition particle swarm optimization as claimed in claim 2, wherein in step S1, each Steiner tree is encoded by using an edge-point pair encoding strategy as follows:
considering the characteristics of Steiner tree, the coding mode of edge point pair represents wiring tree by edge as unit, one edge in the tree is composed of pins at two ends of the edge and PSP selection mode among the pins, in order to connect n pins in the net to form wiring tree T, n-1 edges are needed, each edge is composed of coding string (e)start,eendPspc) indicating that the PSP in the edge is connected to the pin e in the selection mode of the pspcstartAnd pin eendTherefore, in order to represent all edges of T, a code length of 3X (n-1) is needed, and in addition, two more bits are added to represent the line length cost and the radius cost of the Steiner tree in consideration of two optimization targets of the time delay driven X structure Steiner minimum tree, so that the complete code string length of T is 3X (n-1) + 2.
4. The time-delay-driven XSMT construction method based on two-stage competition particle swarm optimization according to claim 1, wherein the step S2 is implemented as follows:
first, an elite pool X of size t is found in the population by fast non-dominated sorting and calculation based on the crowdedness distance { X ═ X }0,x1,...,xtAnd randomly selecting two of the elite particles xa、xbCompeting by comparing xaAnd xbThe included angle formed between the current particle and the current particle is smaller, the winner is the competition, and the loser is the loser if the included angle is larger.
5. The time-delay-driven XSMT construction method based on two-stage competition particle swarm optimization according to claim 1, wherein in step S3, the redesigned particles of the multi-objective particle swarm optimization algorithm follow the following update formula:
Figure FDA0003298733550000021
where ω is the inertial weight, c1And c2For acceleration factor, iter is current iteration number, threshold is set iteration threshold, when iteration number is less than threshold, the updating learning operation of the first stage is executed, and when iteration number is greater than threshold, the updating learning operation of the second stage is executed, wherein EF1And EF2Respectively representing the historical and elite lead components, PF, of the side learning phase1、PF2And PF3Respectively representing a self-guiding component, a history guiding component and an elite guiding component in the point learning stage;
(1) learning stage
1) History guide component
EF implementation by introducing cross-operations for edge learning1The components, expressed as follows:
Figure FDA0003298733550000022
wherein, Cu() Is an edge-crossing operation in which the edges are crossed,
Figure FDA0003298733550000023
is the historical optimal solution of the particle, r1Is a random number within [0,1),
Figure FDA0003298733550000024
through EF1After operation, particles are obtained
Figure FDA0003298733550000025
If a random number r is generated1<c1Granule of Chinese medicinePerforming edge crossing operation, otherwise, maintaining the current state of the particles; the specific steps of the edge crossing operation are as follows: 1) for the current particle
Figure FDA0003298733550000026
Corresponding Steiner tree, determining the edge set as E ═ E1,e2,...,en-1}, learning objects thereof
Figure FDA0003298733550000027
The edge set of the corresponding Steiner tree is E '═ E'1,e'2,...,e'n-1}; 2) judging and storing the same edge set and different edge sets of two trees, wherein the same edge is used as a new particle
Figure FDA00032987335500000310
The initial edge of (2); 3) continuously randomly selecting edges from different edge sets and adding new particles until a complete and legal Steiner tree is constructed, wherein a parallel-searching method is used in the process to ensure that no loop occurs in the wiring tree;
2) elite guide component
By EF2The elite lead component of the finished particle, expressed as follows:
Figure FDA0003298733550000031
wherein the content of the first and second substances,
Figure FDA0003298733550000032
is a winner elite particle obtained by competition;
(2) point learning phase
1) Component of self-induction
Implementing PF by introducing mutation operations for point-to-point learning1The components, expressed as follows:
Figure FDA0003298733550000033
wherein M isp() Is a point mutation operation, r1Is a random number within [0,1),
Figure FDA0003298733550000034
passing through PF1After operation, particles of W are obtainedi t；
If a random number r is generated1<Omega, the particle performs point mutation operation, otherwise, the particle maintains the current state; the point mutation adopts a two-point mutation mode, and the specific operation is as follows: randomly selecting a routing tree
Figure FDA0003298733550000035
The two edges of the PSP are replaced by PSP selection modes of the two edges;
2) history guide component
Implementing PF by introducing cross-operations for point learning2The components, expressed as follows:
Figure FDA0003298733550000036
wherein, Cv() Representing point-crossing operations, the object of cross-learning being optimized for individual history
Figure FDA0003298733550000037
r2Is a random number within [0,1 ], Wi tPassing through PF2After operation, particles are obtained
Figure FDA0003298733550000038
When a random number r is generated2＜c1Performing a point-crossing operation on the particles;
3) elite guide component
Implementing PF by introducing cross-operations for point learning3The components, expressed as follows:
Figure FDA0003298733550000039
wherein, Xi wIs a winner elite particle, C, obtained by competitionv() The operation also uses a hybrid interleaving strategy.
6. The delay-driven XSMT construction method based on two-stage competition particle swarm optimization according to claim 5, wherein the particle performing point crossing operation in step (2) is performed by a mixed point crossing strategy, specifically, the particles in the population are divided into excellent and laggard particles according to fast non-dominated sorting, and the mixed point crossing strategy uses different point learning methods for different particles:
a. multipoint intersection
Implementing PF using multi-point intersection for the first half of the particles in the sequence2The method comprises the following specific operations: for a Steiner tree with n pins, the current particle W is randomly selectedi tBetween edge zones requiring crossing [ E ]s,Ee]And find the individual history optimum
Figure FDA0003298733550000041
Coding of the corresponding edge, then
Figure FDA0003298733550000042
Code of (2) replaces Wi tCoding of the interval;
b. uniform crossing
The second half of the particles in the sequence are uniformly crossed to realize PF2(ii) a This intersection method differs from the multipoint intersection in that it is not necessary to determine an interval to be intersected, but rather to traverse the current particle Wi tOptimized with its individual history
Figure FDA0003298733550000043
Find the same interconnection line edge set Esame＝{e1,e2,…,ej}, particle Wi tStudy EsameThe PSP selection mode of all edges.
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