A three-valued fprm logic circuit area optimization method based on agent-assisted risk perception adaptive two-stage group optimization

Abstract

The application provides a ternary FPRM logic circuit area optimization method based on agent-assisted risk perception adaptive two-stage population optimization. The method comprises the following steps: reading a ternary FPRM logic circuit; initializing parameters such as population size, accurate evaluation total budget and stagnation detection threshold; evaluating an initial polarity and writing the result into a database DB, constructing an initial population and completing a pre-first fitting; synchronously updating an agent model according to a trigger condition, and fusing population signals to drive adaptive switching between two stages; in stage one, a TLBO learning rule is used to generate a candidate polarity, and an accurate evaluation object is selected; in stage two, a discrete particle swarm position updating rule is switched to, and an improved amount is used as an in-queue condition to screen the accurate evaluation object; detection is performed after each round of iteration; and iteration calculation is performed, and the algorithm is terminated when the number of accurate evaluations reaches the total budget. The application reduces the number of evaluations, reduces the search cost, effectively improves the utilization efficiency of the limited accurate evaluation budget, and improves the area optimization effect.

Description

Technical Field

[0001] This invention relates to the field of FPRM (Fixed Polarity Reed-Muller) logic circuit area optimization, and in particular to a three-valued FPRM logic circuit area optimization method based on agent-assisted risk perception adaptive two-stage group optimization. Background Technology

[0002] With the rapid development of integrated circuit technology and the continuous expansion of circuit scale, circuit area optimization has become one of the core objectives in chip design. Digital logic circuits can be implemented using Boolean logic based on AND / OR / NOT, or Reed-Muller (RM) logic based on modular arithmetic. For certain arithmetic logic circuits, parity check circuits, etc., the RM logic implementation has significant advantages over the Boolean logic implementation, such as compact structure, small area, low power consumption, and good testability. The ternary fixed polarity Reed-Muller (FPRM) expansion is the most common canonical form of RM logic expansion. For circuits containing... A three-valued logic function with input variables, comprising a total of Each different polarity configuration corresponds to There are various complex and simplified ternary FPRM expansions, each corresponding to a significantly different circuit area. Therefore, searching for the optimal polarity configuration with the minimum area in an exponential polarity space has become the core task of optimizing the logic circuit area of ​​ternary FPRMs. With the development of deep submicron technology and the continuous increase in circuit scale, area has become an important factor affecting the development of large-scale and very large-scale integrated circuits.

[0003] Existing area optimization methods for ternary FPRM logic circuits are mostly based on exhaustive search, genetic algorithms, and population migration algorithms. While exhaustive search-based area optimization methods can find the global optimum, their computational complexity increases exponentially with the number of input variables, making them suitable only for small-scale circuits and unable to meet the needs of current medium- and large-scale circuits. Area optimization methods based on swarm intelligence optimization methods such as genetic algorithms and population migration algorithms have features such as distributed search and adaptive learning, but they require precise circuit area calculation for candidate polarities in each iteration. As the circuit size increases, the computational cost increases dramatically, making it difficult to guarantee search quality under limited computing resources, thus leading to poor area optimization results.

[0004] Proxy-assisted optimization algorithms are an effective means of solving high-cost evaluation optimization problems. They construct surrogate models to approximate precise evaluations at a low computational cost, thereby guiding the algorithm to concentrate computational resources on more promising candidate solutions within a limited evaluation budget. However, most existing surrogate-assisted optimization methods are designed for continuous optimization problems and have significant limitations when applied to discrete polarity search in ternary FPRMs: the prediction error of the surrogate model in sparse regions is difficult to quantify, easily leading to optimistic bias, causing the precise evaluation budget to be wasted in regions where the surrogate accuracy is unreliable; furthermore, existing methods lack adaptive control mechanisms for the search state, making it difficult to achieve a dynamic balance between exploration and development on circuits of different sizes. Therefore, for the field of ternary FPRM logic circuit area optimization, there is an urgent need to study an area optimization method that can efficiently search for the optimal polarity within a limited precise evaluation budget. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a method for optimizing the area of ​​a three-valued FPRM logic circuit based on agent-assisted risk perception adaptive two-stage group optimization.

[0006] Specifically, a three-valued FPRM logic circuit area optimization method based on agent-assisted risk perception adaptive two-stage group optimization includes the following steps: Step 1: Read the ternary FPRM logic circuit; Step 2: Initialize the population size, total budget for accurate assessment, initial sampling ratio, initial risk coefficient, and stagnation detection threshold; Step 3: Determine the number of initial precise evaluations based on the initial sampling ratio and total budget. Perform precise evaluations on each initial polarity and write the results into the precise evaluation database DB. Select the N polarities with the best fitness from DB to form the initial population. Initialize the individual optimality and global optimality of each particle and complete the first fitting of the prediction agent and error agent. Step 4: At the beginning of each iteration, if the refitting trigger condition is met, the prediction agent and error agent are updated synchronously. Population diversity signal, agent accuracy signal and search stagnation signal are collected and fused to obtain the overall readiness. The stage switching trigger amount is obtained by Sigmoid transformation. When the trigger amount is not lower than the threshold for 3 consecutive rounds, or when NFEs reach 0.5·maxNFEs, the algorithm irreversibly switches from stage one to stage two. Step 5: Based on the current stage, generate candidate polarities and update particle positions using the corresponding position update rules. Select precise evaluation objects through the candidate polarity screening mechanism, perform precise fitness evaluation on the selected candidate polarities, update individual optimal and global optimal, and update the error exponential moving average and risk coefficient online. Step 6: Perform stagnation detection. If the cumulative number of stagnation precise evaluations reaches the stagnation detection threshold, trigger platform escape. Apply random perturbation to the global optimum to generate candidate polarities. After precise evaluation, write the candidate polarity into the database and update the global optimum. Replace the particle with the worst individual fitness in the population with the candidate polarity. Reset the cumulative number of stagnation precise evaluations to 0. If the distance constraint is still not met after reaching the maximum number of attempts, set the cumulative number of stagnation precise evaluations to half of the stagnation detection threshold. Step 7: If the number of precise evaluations (NFEs) does not reach the total budget (maxNFEs), then proceed to step 4; otherwise, output the optimal polarity vector and the corresponding minimum circuit area.

[0007] Furthermore, the method for determining the initial number of precise evaluations in step 3 is expressed as follows:

[0008] in This is the initial sample ratio. Number of input variables for the circuit For population size, The minimum number of samples required for the error proxy to fit the first time; the prediction proxy uses a cubic radial basis function to fit the mapping relationship between the polar one-hot feature vector and the circuit area, and the error proxy uses the same cubic RBF structure as the prediction proxy, with the error label replacing the area label as the fitting target for modeling.

[0009] Furthermore, the two-stage position update rules described in step 5 are as follows: In Phase 1, the TLBO learning rule is used to generate candidate polarities. In each iteration, another particle is randomly selected for each particle, and their respective reference area values ​​are compared. If the reference area value of the current particle is not inferior to that of the selected particle, the components with the same polarity value are randomly flipped to a different value with a certain probability to maintain the difference between particles. If the reference area value of the current particle is inferior to that of the selected particle, the components with different polarity values ​​are moved towards the selected particle with a certain probability to learn its superior polarity component information. The reference area value is taken as the circuit area value when the particle has an accurate evaluation result; otherwise, the prediction value of the prediction agent is taken. After obtaining the candidate polarities from the learning rule, the greedy acceptance criterion of the prediction agent is adopted. The particle position is updated only when the prediction value of the candidate polarity is better than the prediction value of the current position; otherwise, the original position remains unchanged. Phase 2 uses the discrete PSO rule to generate candidate polarities. For each polarity dimension, three velocity components corresponding to the values ​​are maintained independently. Velocity updates are performed based on inertia weights, individual optimal guidance components, and global optimal guidance components. The updated velocity vectors are transformed by softmax to obtain the selection probability of each value, and then new discrete polarities are determined by class sampling.

[0010] Furthermore, the candidate polarity screening mechanism described in step 5 is as follows: For each candidate polarity, its corresponding one-hot feature vector is input into the prediction agent and the error agent respectively to obtain the predicted area value and the error estimate. The risk prediction value is defined as a weighted combination of the two:

[0011] in As a risk factor, when the error proxy has not yet completed its first fit, the exponential moving average of the historical accurate error is used instead of the error estimate; In Phase 1, candidate polarities that simultaneously meet the following two conditions enter the precise evaluation queue: First, the risk prediction value is better than the reference area value of the current particle; Second, the minimum Hamming distance between the candidate polarity and all evaluated polarities in the database is not lower than the dynamic diversity distance threshold. If none of the particles in this round can simultaneously meet both conditions, the candidate polarity with the smallest risk prediction value is directly selected for evaluation. In Phase 2, the difference between the optimal circuit area value of an individual particle and the predicted risk value of a candidate polarity is used as the improvement amount. Candidate polarities that simultaneously satisfy the condition that the improvement amount is greater than zero and the minimum Hamming distance is not lower than the dynamic diversity distance threshold are sorted in descending order of improvement amount. The number of precise evaluations is determined based on the number of candidate polarities that meet the conditions. If the number of candidate polarities that meet the conditions is zero, the candidate polarity with the smallest predicted risk value is directly evaluated.

[0012] Furthermore, the risk coefficient described in step 5 The online adaptive update method is as follows: After each accurate assessment is completed, the error exponential moving average before the update is weighted and updated with the instantaneous absolute error of the current accurate assessment point to obtain a new error exponential moving average; the risk coefficient is updated as follows: .

[0013] The beneficial effects of this invention are as follows: (1) Existing three-valued FPRM logic circuit area optimization methods require precise circuit area calculation for candidate polarities in each iteration. As the circuit size increases, the computational cost increases sharply, making it difficult to guarantee search quality with limited resources. By introducing a surrogate-assisted two-stage group optimization framework, a cubic radial basis function surrogate model is used to approximate the precise evaluation. The limited precise evaluation budget is concentrated on more promising candidate polarities, which greatly reduces the number of precise evaluations, lowers the search overhead, and improves the efficiency of three-valued FPRM logic circuit area optimization.

[0014] (2) Existing agent-assisted optimization methods lack effective quantification of the uncertainty of the predictive agent. The agent model is prone to optimistic bias in sparse sample regions, resulting in the waste of accurate assessment budget in regions where the agent accuracy is unreliable. By constructing an error agent to model the prediction error of the predictive agent, using the risk prediction value as the basis for candidate polarity screening, and adaptively adjusting the risk coefficient through online learning, the optimism bias of the agent model is effectively suppressed, which misleads the accurate assessment budget and improves the utilization efficiency of the limited accurate assessment budget.

[0015] (3) Existing population optimization methods use fixed search strategies, which are difficult to adapt to the differences in state evolution of circuits of different sizes during the search process, and are prone to insufficient exploration phase or premature convergence in development phase. By integrating three types of state signals—population diversity, surrogate accuracy, and search stagnation—to drive the adaptive switching of the two stages, and combining the Sigmoid dynamic diversity threshold and stagnation platform escape mechanism, the algorithm's ability to balance exploration and development on circuits of different sizes is enhanced, and the area optimization effect is improved. Attached Figure Description

[0016] Figure 1 This is a flowchart of a three-valued FPRM logic circuit area optimization method based on agent-assisted risk perception adaptive two-stage group optimization according to the present invention. Detailed Implementation

[0017] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments. Example

[0018] Figure 1 This is a flowchart of a three-valued FPRM logic circuit area optimization method based on agent-assisted risk perception adaptive two-stage group optimization according to the present invention. Figure 1 As shown, the method includes: Step 1: Read the ternary FPRM logic circuit; Step 2: Initialize the population size, total budget for accurate assessment, initial sampling ratio, initial risk coefficient, and stagnation detection threshold; Step 3: Determine the number of initial precise evaluations based on the initial sampling ratio and total budget. Perform precise evaluations on each initial polarity and write the results into the precise evaluation database DB. Select the N polarities with the best fitness from DB to form the initial population. Initialize the individual optimality and global optimality of each particle and complete the first fitting of the prediction agent and error agent. Step 4: At the beginning of each iteration, if the refitting trigger condition is met, the prediction agent and error agent are updated synchronously. Population diversity signal, agent accuracy signal and search stagnation signal are collected and fused to obtain the overall readiness. The stage switching trigger amount is obtained by Sigmoid transformation. When the trigger amount is not lower than the threshold for 3 consecutive rounds, or when NFEs reach 0.5·maxNFEs, the algorithm irreversibly switches from stage one to stage two. Step 5: Based on the current stage, generate candidate polarities and update particle positions using the corresponding position update rules. Select precise evaluation objects through the candidate polarity screening mechanism, perform precise fitness evaluation on the selected candidate polarities, update individual optimal and global optimal, and update the error exponential moving average and risk coefficient online. Step 6: Perform stagnation detection. If the cumulative number of stagnation precise evaluations reaches the stagnation detection threshold, trigger platform escape. Apply random perturbation to the global optimum to generate candidate polarities. After precise evaluation, write the candidate polarity into the database and update the global optimum. Replace the particle with the worst individual fitness in the population with the candidate polarity. Reset the cumulative number of stagnation precise evaluations to 0. If the distance constraint is still not met after reaching the maximum number of attempts, set the cumulative number of stagnation precise evaluations to half of the stagnation detection threshold. Step 7: If the number of precise evaluations (NFEs) does not reach the total budget (maxNFEs), then proceed to step 4; otherwise, output the optimal polarity vector and the corresponding minimum circuit area.

[0019] In step 3, the initial number of precise evaluations is determined based on the initial sample ratio, the total precise evaluation budget, the population size, and the minimum sample size required for the surrogate model to achieve its first normal fit. The determination method is as follows:

[0020] in This is the initial sample ratio. Number of input variables for the circuit For population size, To ensure a minimum sample size lower bound for the initial normal fit of both the prediction and error proxies, random sampling without replacement is used when the polarity space size does not exceed one million; otherwise, Latin hypercube sampling is used to ensure a uniform distribution of initial points across all polarity component dimensions. Both the prediction and error proxies employ a cubic radial basis function structure, with the error proxies using error labels instead of area labels as the fitting objective and solving independently.

[0021] In step 5, the candidate polarity screening mechanism uses risk prediction value as the screening criterion.

[0022] in The risk coefficient is used. When the error proxy has not yet completed its initial fitting, the exponential moving average of the historical accurate error is used instead of the error estimate. In Stage 1, candidate polarities that simultaneously meet the conditions of having a risk prediction value better than the current particle reference area value and a minimum Hamming distance between the candidate polarity and all evaluated polarities in the database not less than the dynamic diversity distance value are entered into the accurate evaluation queue. In Stage 2, the difference between the optimal circuit area value of the individual particle and the risk prediction value of the candidate polarity is used as the improvement amount. The candidate polarities that meet the conditions are ranked according to the improvement amount to determine the number of accurate evaluations. If no candidate polarity meets the entry conditions in either stage, the candidate polarity with the smallest risk prediction value is directly evaluated.

[0023] The online adaptive update method for the risk coefficient mentioned in step 5 is as follows:

[0024] The following is an embodiment of the method for area optimization of a ternary FPRM logic circuit based on agent-assisted risk perception adaptive two-stage group optimization according to the present invention. Taking the area minimization of the MCNC reference circuit ts10 as an example, the method of this embodiment to obtain the ternary FPRM logic circuit with the minimum circuit area includes: Step 1: Read the ternary FPRM logic circuit ts10; Step 2: Set the population size to 40, the total budget for precise evaluation to 1000 times, the initial sampling ratio to 0.15, the initial risk coefficient to 2, the stagnation detection threshold to 50, and the surrogate model refitting period to 3. Step 3: Determine the initial number of precise evaluations based on the initial sampling ratio of 0.15 and the total budget of 1000. Next, each of the 150 randomly sampled polarities is precisely evaluated and the results are written into the DB. The 40 polarities with the best fitness are selected from the DB to form the initial population. The individual optimality and global optimality of each particle are initialized, and the first fitting of the prediction agent and the error agent is completed. Step 4: At the beginning of each iteration, if the number of newly added accurate evaluation samples in DB since the last fitting is not less than 10 and 3 iterations have passed since the last fitting, then the prediction agent and error agent are updated synchronously; population diversity signal, agent accuracy signal and search stagnation signal are collected and fused to obtain the overall readiness, and the stage switching trigger value is obtained by Sigmoid transformation; when the trigger value is not lower than the threshold of 0.6 for 3 consecutive rounds, or when NFEs reach 500 times, the algorithm irreversibly switches from stage one to stage two. Step 5: In Phase 1, the TLBO learning rule is used to generate candidate polarities for each particle. The inclusion criteria for precise evaluation are that the risk prediction value is better than the reference area value and the minimum Hamming distance is not less than the dynamic diversity distance. In Phase 2, the discrete PSO rule is used to generate candidate polarities. The inclusion criteria are that the improvement amount is greater than zero and the distance constraint is met. The number of precise evaluations is determined after sorting by the improvement amount. The selected candidate polarities are subjected to precise fitness evaluation, and the individual optimum and global optimum are updated. The risk coefficient is updated online with a learning step size of 0.1. Step 6: After each iteration, perform stagnation detection. If the cumulative number of stagnation precise evaluations reaches 50, trigger platform escape, apply random perturbation to the global optimum to generate candidate polarities, perform precise evaluations, write them to the database and update the global optimum, replace the particle with the worst individual fitness in the population with this candidate polarity, and reset the cumulative number of stagnation precise evaluations to 0; if the distance constraint is still not met after reaching the maximum number of attempts, set the cumulative number of stagnation precise evaluations to 25. Step 7: If the number of precise evaluations (NFEs) is less than 1000, proceed to step 4; otherwise, output the optimal polarity vector and the corresponding minimum circuit area.

[0025] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the technical scope of the present invention. Therefore, any minor modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention shall still fall within the scope of the technical solution of the present invention.

Claims

1. A method for optimizing the area of ​​a three-valued FPRM logic circuit based on agent-assisted risk perception adaptive two-stage population optimization, characterized in that, Includes the following steps: Step 1: Read the ternary FPRM logic circuit; Step 2: Initialize the population size, total budget for accurate assessment, initial sampling ratio, initial risk coefficient, and stagnation detection threshold; Step 3: Determine the number of initial precise evaluations based on the initial sampling ratio and total budget. Perform precise evaluations on each initial polarity and write the results into the precise evaluation database DB. Select the N polarities with the best fitness from DB to form the initial population. Initialize the individual optimality and global optimality of each particle and complete the first fitting of the prediction agent and error agent. Step 4: At the beginning of each iteration, if the refitting trigger condition is met, the prediction agent and error agent are updated synchronously. Population diversity signal, agent accuracy signal and search stagnation signal are collected and fused to obtain the overall readiness. The stage switching trigger amount is obtained by Sigmoid transformation. When the trigger amount is not lower than the threshold for 3 consecutive rounds, or when NFEs reach 0.5·maxNFEs, the algorithm irreversibly switches from stage one to stage two. Step 5: Based on the current stage, generate candidate polarities and update particle positions using the corresponding position update rules. Select precise evaluation objects through the candidate polarity screening mechanism, perform precise fitness evaluation on the selected candidate polarities, update individual optimal and global optimal, and update the error exponential moving average and risk coefficient online. Step 6: Perform stagnation detection. If the cumulative number of stagnation precise evaluations reaches the stagnation detection threshold, trigger platform escape. Apply random perturbation to the global optimum to generate candidate polarities. After precise evaluation, write the candidate polarity into the database and update the global optimum. Replace the particle with the worst individual fitness in the population with the candidate polarity. Reset the cumulative number of stagnation precise evaluations to 0. If the distance constraint is still not met after reaching the maximum number of attempts, set the cumulative number of stagnation precise evaluations to half of the stagnation detection threshold. Step 7: If the number of precise evaluations (NFEs) does not reach the total budget (maxNFEs), then proceed to step 4; otherwise, output the optimal polarity vector and the corresponding minimum circuit area.

2. The method according to claim 1, characterized in that, The method for determining the initial number of precise evaluations in step 3 is expressed as follows: ， in This is the initial sample ratio. Number of input variables for the circuit For population size, The minimum number of samples required for the error proxy to fit the first time; the prediction proxy uses a cubic radial basis function to fit the mapping relationship between the polar one-hot feature vector and the circuit area, and the error proxy uses the same cubic RBF structure as the prediction proxy, with the error label replacing the area label as the fitting target for modeling.

3. The method according to claim 1, characterized in that, The two-stage position update rules described in step 5 are as follows: In Phase 1, the TLBO learning rule is used to generate candidate polarities. In each iteration, another particle is randomly selected for each particle and compared with their respective reference area values. If the reference area value of the current particle is not inferior to that of the selected particle, the components with the same polarity value are randomly flipped to a different value with a certain probability to maintain the difference between particles. If the reference area value of the current particle is inferior to that of the selected particle, the components with different polarity values ​​are moved towards the selected particle with a certain probability to learn its superior polarity component information. The reference area value is taken as the circuit area value when the particle has an accurate evaluation result; otherwise, the predicted value of the prediction agent is taken. After obtaining candidate polarities from the learning rules, the greedy acceptance criterion of the prediction agent is adopted. The particle position is updated only when the predicted value of the candidate polarity is better than the predicted value of the current position; otherwise, the original position is kept unchanged. Phase 2 uses the discrete PSO rule to generate candidate polarities. For each polarity dimension, three velocity components corresponding to the values ​​are maintained independently. Velocity updates are performed based on inertia weights, individual optimal guidance components, and global optimal guidance components. The updated velocity vectors are transformed by softmax to obtain the selection probability of each value, and then new discrete polarities are determined by class sampling.

4. The method according to claim 1, characterized in that, The candidate polarity screening mechanism described in step 5 is as follows: For each candidate polarity, its corresponding one-hot feature vector is input into the prediction agent and the error agent respectively to obtain the predicted area value and the error estimate. The risk prediction value is defined as a weighted combination of the two: ， in As a risk factor, when the error proxy has not yet completed its first fit, the exponential moving average of the historical accurate error is used instead of the error estimate; In Phase 1, candidate polarities that simultaneously meet the following two conditions enter the precise evaluation queue: First, the risk prediction value is better than the reference area value of the current particle; Second, the minimum Hamming distance between the candidate polarity and all evaluated polarities in the database is not lower than the dynamic diversity distance threshold. If none of the particles in this round can simultaneously meet both conditions, the candidate polarity with the smallest risk prediction value is directly selected for evaluation. In Phase 2, the difference between the optimal circuit area value of an individual particle and the predicted risk value of a candidate polarity is used as the improvement amount. Candidate polarities that simultaneously satisfy the condition that the improvement amount is greater than zero and the minimum Hamming distance is not lower than the dynamic diversity distance threshold are sorted in descending order of improvement amount. The number of precise evaluations is determined based on the number of candidate polarities that meet the conditions. If the number of candidate polarities that meet the conditions is zero, the candidate polarity with the smallest predicted risk value is directly evaluated.

5. The method according to claim 1, characterized in that, The risk coefficient described in step 5 The online adaptive update method is as follows: After each accurate assessment is completed, the error exponential moving average before the update is weighted and updated with the instantaneous absolute error of the current accurate assessment point to obtain a new error exponential moving average; the risk coefficient is updated as follows: 。

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