Application method and device of optimization algorithm in cell traction force calculation

Abstract

The invention discloses an application method and device of an optimization algorithm in cell traction calculation, and relates to the technical field of computer systems based on biological models. The method comprises the following steps: taking a simulated cell time sequence data set provided by a deep learning cell traction microscopy method as a training, verification and test sample; constructing a fitness function by using an average relative error of a test set, and randomly initializing candidate solutions; an optimization algorithm is adopted, the position is updated until the number of iterations meets the maximum number of iterations, and an optimal solution is output; the hyper-parameter search process is optimized, and the parameter quantity of the model is remarkably reduced; the 3DU-Net architecture embedded with the attention module is used for efficiently extracting and reconstructing stress-strain vector field features, and the traction prediction precision of the model is better than that of original deep learning cell traction microscopic calculation. Under the guidance of an optimization algorithm, the architecture disclosed by the invention automatically completes network structure and parameter optimization, so that the model scale is remarkably compressed while high precision is kept.

Description

Technical Field

[0001] This application relates to the field of computer system technology based on biological models, and in particular to a method and apparatus for applying an optimization algorithm in the calculation of cellular traction force. Background Technology

[0002] Traction Force Microscopy (TFM) is a key technique for studying cellular mechanical behavior and is widely used in fields such as cancer migration, tissue engineering, and cell-matrix interactions. Traditional traction force inversion methods (such as the boundary element method and Fourier transform method) rely on physical model assumptions and suffer from low computational accuracy and poor stability in complex biomechanical environments. In recent years, deep learning methods (such as 3D U-Net) have been introduced into TFM computation, significantly improving the accuracy of force field reconstruction. However, they still face two major challenges: first, the inefficiency of Neural Architecture Search (NAS): traditional Bayesian optimization (BO) methods converge slowly and are computationally expensive in high-dimensional search spaces (such as the number of layers, channels, and attention module combinations); second, the contradiction between model complexity and computational resources: existing deep learning TFM models have a large number of parameters (usually >50M), making them difficult to deploy efficiently on ordinary computing devices.

[0003] Currently, Bayesian optimization (BO) is the mainstream method in the field of neural network architecture search. However, it has obvious limitations in the task of calculating cellular traction force: such methods are difficult to efficiently handle the high-dimensional discrete search space required to reconstruct the traction force vector field, which makes it impossible to automatically design a physically reliable model with both high accuracy and lightweight at an acceptable cost, thus hindering its practical deployment in biomedical research. Summary of the Invention

[0004] Therefore, it is necessary to provide a method and apparatus for applying an optimization algorithm in cellular traction force calculation to address the aforementioned technical problems.

[0005] The present invention adopts the following technical solution: This invention provides a method for applying an optimization algorithm in calculating cellular traction force, comprising: A hybrid optimization algorithm based on reinforcement learning is constructed. This algorithm treats each individual in the population as an independent learning agent. The execution action of each learning agent is determined from the action space according to a preset exploration rate. A Q-table is created to represent the expected cumulative reward obtained by the learning agent during historical action executions. The Q-table is iteratively updated based on the learning agent's execution actions, and the position of the individual with the largest expected cumulative reward value in the last updated Q-table is taken as the optimal solution. The action space of the learning agent includes exploitation actions and exploration actions. When the execution action is an exploitation action, an L-SHADE-based differential evolution strategy is executed. When the execution action is an exploration action, an SBO-inspired elite interaction strategy is executed. Obtain a simulated cell time series dataset and divide it into a training set and a test set according to a specified ratio; then input the training set into a 3D U-Net model to output predicted cell traction force values; The hyperparameters and network structure of the 3DU-Net model are used as the individual positions in the population of the hybrid optimization algorithm. With the goal of minimizing the fitness function value, the hyperparameters and network structure of the 3DU-Net model are optimized through the hybrid optimization algorithm until a preset maximum number of iterations is reached. The hyperparameters and network structure that reach the maximum number of iterations are determined as the hyperparameters and network structure of the optimized 3D U-Net model. The fitness function value is constructed based on the average relative error between the predicted cell traction force output by the 3D U-Net model and the actual cell traction force calculated from the test set. The optimized 3DU-Net model is used to predict the simulated cell data to obtain the cell traction force in future time periods.

[0006] Preferably, the learning agent shares an L-SHADE-based differential evolution strategy and an SBO-inspired elite interaction strategy.

[0007] Preferably, the Q table is a matrix of size N×2, where N is the state of the learning agent and is the row data of the matrix, and 2 is the number of actions executed by the learning agent in the action space and is the column data of the matrix.

[0008] Preferably, the classic ε-greedy strategy is used to determine the execution action of each learning agent, specifically including: When the random number generated by the random number function is greater than or equal to the preset exploration rate ε, the learning agent queries the execution action corresponding to the row of the learning agent in its Q table and selects the execution action with the highest expected cumulative reward from the action space. When the random number generated by the random number function is less than the preset exploration rate ε, the learning agent randomly selects an action from the action space to execute.

[0009] Preferably, if a new solution is generated after the current learning agent completes its execution strategy and is superior to the current solution, then a reward value is obtained. Conversely, you will receive a reward value. ; After the agent completes the selected execution strategy and receives the reward value, update the expected cumulative reward in the Q table using the following formula: ; In the formula, For the expected cumulative reward in the updated Q table, The expected cumulative reward in the Q table before updates, where α is the learning rate. This is the reward value.

[0010] Preferably, the preset exploration rate gradually decreases during the iteration process; the preset exploration rate is set to 0.99 during the first iteration.

[0011] Preferably, the simulated cell time series dataset is generated based on a cell migration model, has multiple spatial resolutions, and includes displacement field and stress field tensor information.

[0012] Preferably, the 3D U-Net model includes an encoder, a decoder, and a channel space attention mechanism module, used to extract and reconstruct stress-strain vector field features from a simulated cell time series dataset.

[0013] Preferably, the expression for the fitness function is: ; In the formula, For the fitness function value, and These refer to the predicted values ​​of cellular traction force in the horizontal and vertical directions, respectively. and These represent the actual values ​​of cellular traction force in the horizontal and vertical directions, respectively. N This is to simulate the number of pixels in a displacement field map within a cell time series dataset.

[0014] This invention provides an application device for optimizing algorithms in calculating cellular traction force, comprising: An algorithm construction module is used to construct a hybrid optimization algorithm driven by reinforcement learning. This algorithm treats each individual in the population as an independent learning agent. It determines the action to be performed by each learning agent from the action space based on a preset exploration rate. A Q-table is created to represent the expected cumulative reward obtained by the learning agent during historical actions. The Q-table is iteratively updated based on the learning agent's actions, and the position of the individual with the largest expected cumulative reward in the last updated Q-table is taken as the optimal solution. The action space of the learning agent includes exploitation actions and exploration actions. When the action is an exploitation action, an L-SHADE-based differential evolution strategy is executed. When the action is an exploration action, an SBO-inspired elite interaction strategy is executed. The data acquisition module is used to acquire a simulated cell time series dataset and divide it into a training set and a test set according to a specified ratio; and input the training set into the 3D U-Net model to output cell traction force. The algorithm application module uses the hyperparameters and network structure of the 3DU-Net model as the individual positions in the population of a hybrid optimization algorithm. With the goal of minimizing the fitness function value, the hybrid optimization algorithm optimizes the hyperparameters and network structure of the 3DU-Net model until a preset maximum number of iterations is reached. The hyperparameters and network structure that reach the maximum number of iterations are then determined as the optimized and trained 3D U-Net model's hyperparameters and network structure. The fitness function value is constructed based on the average relative error between the cell traction force output by the 3D U-Net model and the actual cell traction force calculated from the test set. The model prediction module is used to input the simulated cell data to be predicted into the optimized and trained 3D U-Net model to obtain the cell traction force of the simulated cell data to be predicted.

[0015] This invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned method for applying an optimization algorithm in cell traction force calculation.

[0016] The present invention provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the above-mentioned method for applying an optimization algorithm in cell traction force calculation.

[0017] The above-mentioned at least one technical solution adopted in this invention can achieve the following beneficial effects: In the application method of the optimization algorithm in cellular traction force calculation provided by this invention, the algorithm is driven by reinforcement learning, treating each individual in the population as an independent learning agent. It intelligently explores actions at a preset exploration rate, employs an L-SHADE differential evolution strategy for global breadth-of-field search, effectively avoiding the algorithm from getting trapped in local optima. It utilizes an elite interaction strategy inspired by SBO (Self-Optimization-Based Learning) to deeply mine known high-quality regions, accelerating convergence. The two approaches are adaptively and dynamically switched based on the preset exploration rate. Simultaneously, the algorithm constructs a Q-table to record the expected cumulative reward obtained by the learning agent in historical actions, and iteratively updates it accordingly to achieve adaptive adjustment of the strategy. In cellular traction force calculation, a 3D U-Net model is trained using a simulated cell time-series dataset, and the average relative error of the predicted cellular traction force is used as the fitness function. The RLDSBO algorithm efficiently optimizes by minimizing this error, significantly improving the accuracy and computational efficiency of force field reconstruction. The optimized model not only has a significantly reduced number of parameters, enabling efficient operation on mid-range GPUs, but also exhibits significantly better prediction accuracy than the original method, providing strong computational support for cellular mechanics research in complex biomechanical environments. Attached Figure Description

[0018] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0019] Figure 1 This is a schematic diagram illustrating the application method of an optimization algorithm in cell traction force calculation provided by the present invention. Figure 2 A comparison of convergence curves of RLDSBO-based and Bayesian optimization in the 3DU-Net architecture search task, which is an application method of the optimization algorithm provided by this invention in cell traction force calculation; Figure 3 A schematic diagram of a device for applying an optimization algorithm in cell traction force calculation provided by the present invention; Figure 4 A diagram of a computer device for implementing an optimization algorithm in calculating cellular traction force, as provided by this invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments in the specification without creative effort are within the scope of protection of this application.

[0021] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0022] Figure 1 This is a flowchart illustrating the application of an optimization algorithm in cellular traction force calculation according to the present invention, specifically including the following steps: S101: Construct a hybrid optimization algorithm based on reinforcement learning; the hybrid optimization algorithm treats each individual in the population as an independent learning agent; determines the action to be performed by each learning agent from the action space according to a preset exploration rate; creates a Q-table for the expected cumulative reward obtained by the learning agent when performing historical actions, and iteratively updates the Q-table according to the actions performed by the learning agent, taking the position of the individual with the largest expected cumulative reward value in the Q-table of the last iteration as the optimal solution; wherein, the action space of the learning agent includes exploitation actions and exploration actions; when the action is an exploitation action, a differential evolution strategy based on L-SHADE is executed; when the action is an exploration action, an elite interaction strategy inspired by SBO is executed.

[0023] Alternatively, individuals in the population can share resources through an L-SHADE-based differential evolution strategy and an SBO-inspired elite interaction strategy.

[0024] Optionally, the Q table is a matrix of size N×2, where N is the state of the learning agent (the row data of the matrix) and 2 is the number of actions executed by the learning agent in the action space (the column data of the matrix).

[0025] Optionally, the classic ε-greedy strategy is used to determine the action to be executed by each learning agent. Specifically, when the random number generated by the random number function is greater than or equal to the preset exploration rate ε, the learning agent queries the action to be executed in the corresponding row of its Q table and selects the action to be executed with the highest expected cumulative reward from the action space; when the random number generated by the random number function is less than the preset exploration rate ε, the learning agent randomly selects an action to be executed from the action space.

[0026] Specifically, if a new solution is generated after the current learning agent executes the strategy and is better than the current solution, a reward value is obtained. Conversely, you will receive a reward value. Once the agent has executed the selected execution strategy and received the reward value, update the expected cumulative reward in the Q table using the following formula: ; In the formula, For the expected cumulative reward in the updated Q table, The expected cumulative reward in the Q table before updates, where α is the learning rate. This is the reward value.

[0027] Optionally, the preset exploration rate is gradually reduced during the iteration process; the preset exploration rate is set to 0.99 in the first iteration.

[0028] Specifically, the RLDSBO algorithm introduces a novel hybrid framework based on the SBO algorithm, inspired by observations of human learning and decision-making processes. In the real world, individual progress depends not only on imitating high achievers but also on exploring new methods in different environments. This ability to intelligently switch between different behavioral patterns is key to solving complex problems. RLDSBO translates this dual process into a computational model aimed at achieving iterative refinement in optimization. The core idea of ​​the algorithm is to create a multi-policy collective intelligence system driven by reinforcement learning (RL), where: agents share knowledge through multiple mechanisms; diverse search strategies are dynamically invoked rather than following a single fixed behavioral pattern; and the system achieves an explicit, adaptive balance between exploration and exploitation.

[0029] In short, the working principle of RLDSBO can be summarized as a hierarchical decision-making and execution process, including: Exploitation Phase (SBO Operator): When exploitation is selected, the agent executes an operator inspired by the SBO optimization algorithm. This phase simulates the behavior of individuals in society seeking guidance from high-status "mentors," deeply exploring known high-quality areas by learning from the global optimum and other elites in the population.

[0030] Exploration Phase (L-SHADE Operator): When exploration is selected, the agent employs an advanced differential evolution strategy. This phase focuses on a breadth-first search across the entire search space, discovering new promising regions through inter-individual differential information.

[0031] Reinforcement learning-driven strategy selection (top-level decision-making): Each agent uses its learned experience (Q-table) to autonomously decide whether to take exploratory or exploitative actions in each iteration. This simulates the core decision-making process by which an individual decides whether to continue taking risks or play it safe based on past successes and failures.

[0032] While numerous optimization algorithms inspired by human social behavior and educational interactions have successfully solved complex problems—for example, Human Behavior Optimization (HBBO) mimics collective behaviors such as cooperation, competition, and social learning—RLDSBO similarly incorporates ideas of social learning, but explicitly defines it as a "utilization" strategy. Simultaneously, it utilizes powerful, non-social behavior-inspired evolutionary mechanisms (such as the L-SHADE operator) as its "exploration" strategy. This structured separation and integration is a key innovation of RLDSBO.

[0033] Specifically, the exploration phase is based on adaptive differential evolution using the L-SHADE operator. Within the RLDSBO framework, when the agent performs an "exploration" action based on the decision of the reinforcement learning module, the algorithm activates a core mechanism derived from L-SHADE (Success-History based Adaptive Differential Evolution with Linear Population Size Reduction). The goal of this phase is to conduct a broad and diverse search across the entire search space to discover new and promising regions, thereby effectively avoiding the algorithm from getting trapped in local optima. L-SHADE, as an advanced variant of differential evolution (DE), is powerful due to its ingenious parameter adaptation mechanism and efficient mutation strategy.

[0034] The core idea of ​​the L-SHADE operator is within the RLDSBO framework, where the exploration task is undertaken by the L-SHADE (Success-History-based Adaptive Differential Evolution with Linear Population Size Reduction) operator. It's worth noting that the code implements the core mechanisms of L-SHADE, namely parameter adaptation based on success history and external archiving, but not its linear population reduction mechanism. This stage aims to maintain population diversity and perform global search through efficient parameter control and mutation strategies. Adaptive parameter generation: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] Before generating test vectors for each agent, RLDSBO generates a set of dedicated control parameters Fi and CRi. This process is as follows: Selecting the bootstrap mean from the memory: The algorithm maintains two historical memories of size N, MF and MCR. These memories do not store individual successful parameter values, but rather the statistical mean of the set of successful parameters from recent iterations. The first step in generating parameters is... We randomly select an index k to determine the historical mean on which this generation is based, where the value of H is taken as the population size N.

[0035] ; The cross rate CRi is generated from a value derived from... It is a random sample from a Gaussian normal distribution with a mean of 0.1 and a standard deviation of 0.1. Its mathematical model is:

[0036] ; The generated CR i The value will then be truncated to Within a certain range, to ensure its effectiveness. This strategy allows new CR values ​​to be exploratoryly perturbed within a small range near a region (mean) that has historically proven effective.

[0037] Generate scaling factor F i :F i The value is from a... Random sampling is performed from a Cauchy distribution with location parameter 0.1 and scale parameter 0.1. The mathematical model is as follows:

[0038] ; The Cauchy distribution was chosen due to its significant "heavy-tail" property. Compared to the normal distribution, it produces extreme values ​​far from the center with a higher probability. This allows the Fi value to occasionally become large, thus contributing to larger step sizes of variation, which is crucial for the algorithm to effectively escape local optima. Similarly, the generated F... i The value will be truncated to the (0,1) range to prevent it from being negative or zero.

[0039] Mutation Strategy: RLDSBO employs a current-to-pbest / 1 mutation strategy during the exploration phase. This strategy cleverly balances greediness (learning from the optimal solution) and diversity (utilizing population differences). Mutation Vector The formula for generating it is as follows:

[0040] ; in: This is the current target vector, i.e., the agent currently performing the operation. This is the elite-leading vector. It is a solution randomly selected from the top p% (e.g., p=0.1) of individuals in the current population based on their fitness. Guiding individuals to move towards superior regions within the population enhances the algorithm's convergence speed. The individual is randomly selected from the current population (r1≠i). This is an individual randomly selected from the external archive Archive (r2≠i). External archive A stores all recently successfully updated parent individuals. This is the difference vector. This part is the essence of the DE algorithm; it uses the differences between individuals in the population (including the archive) to generate perturbations, which is key to maintaining population diversity and exploring new areas. By combining elite guidance and population differences, this mutation strategy can quickly converge to promising areas without easily losing its exploration capabilities.

[0041] Crossover and Update: Generating Mutation Vectors Then, through a standard binomial crossover operation, it is compared with the original target vector. Combined, the final test vector is generated. .

[0042] ; If the test vector Its fitness is better than If so, the update is successful. At this point, the update used... and These will be recorded. At the end of each generation t, all recorded success F-values ​​and CR-values ​​will be weighted by the Lehmer Mean and the arithmetic mean, respectively, and this new average will be used to update the history memory bank. and One of the entries in the history memory bank. At the end of each generation t, if the set of successful solutions generated by the exploration strategy is not empty, then the history memory bank... and The update at the circular index k will be performed according to the following rules:

[0043] renew (arithmetic mean): ; in: This is the set of crossover rates for agents that, in this generation t, chose an exploration strategy and successfully improved their solution. In other words, only when an agent successfully improves its solution through an exploration strategy will its corresponding crossover rate CR be included. middle, Represents a set The number of elements in the solution is the number of agents that have chosen the exploration strategy and successfully improved the solution. CR is the cross rate used for each successfully updated agent.

[0044] renew (Lymer Mean): ; in: It is the set of scaling factors F used by agents who chose the exploration strategy (action=1) and successfully improved the solution. In other words, It includes scaling factors for solutions that are successfully obtained through the exploration strategy, where F represents the scaling factor used in a certain agent update process. This represents the Lymer mean updated at the k-th position in the memory bank. It is used to adjust the scaling factor for the next generation. The Lymer mean of the F values ​​used in all successful updates will be used to update the k-th position in MF, and the arithmetic mean of the CR values ​​used in all successful updates will be used to update the history memory bank. The index is then incremented cyclically (back to 1 if it exceeds the memory size) to sequentially update entries in the memory. This mechanism ensures that the algorithm learns only from successful search attempts and, through memory updates, drives the next generation of entries to adjust in the parameter space in a more efficient direction, thus achieving dynamic adaptive control of the search process. This "success-oriented + stepwise memorization" closed-loop learning framework is the key to L-SHADE's high convergence and robustness.

[0045] Dynamic Maintenance Mechanism of External Archive: To enhance population diversity and preserve valuable historical solution information, RLDSBO integrates an external archive, Archive. The maintenance of this archive follows a simple yet efficient dynamic update strategy, executed at the beginning of each generation iteration. The archive update process can be summarized in the following two steps:

[0046] Information Injection: After all individuals X in the current generation have completed their evaluation, all individuals X in the entire population will be directly merged into the external archive A. This operation can be represented as:

[0047] ; This step ensures that complete state information of each generation of the population is captured in the archive, providing a rich source of historical diversity for subsequent differential mutations.

[0048] After the information is injected, the algorithm will check the current size of the archive. Has the preset upper limit, Archivelimit, been exceeded? If it is exceeded, a size control mechanism will be triggered: the algorithm will randomly select Archivesizelimit individuals from all individuals in the current archive without replacement to form a new archive. All unselected individuals will be discarded. At the end of generation t, the external archive... from Updated to The process can be summarized as follows:

[0049] ; in: It is the save file at the beginning of generation t. It is the entire population at the end of generation t. This means merging all individuals in the current population into the storage. This is the size of the merged archive. This is the preset maximum size for the archive. (S,k) is an operation representing the random selection of k elements without replacement from set S. This "add first, then prune randomly" strategy effectively controls the size of the archive. It ensures that the archive always contains the latest population information while continuously discarding old or redundant solutions through random discarding, thus maintaining a dynamic set of fixed size containing diverse historical solutions. The individuals in this archive will then serve as candidate sources for difference vectors in the DE / current-to-pbest / 1 mutation strategy, significantly improving the algorithm's exploration capability and performance in avoiding premature convergence.

[0050] Exploitation Phase: Inspired by SBO, the elite interaction operator in the RLDSBO framework activates an operator designed to deeply explore promising regions in the current search space when the agent performs an "exploitation" action based on the decision of the reinforcement learning module. This operator is inspired by the State Optimization (SBO) algorithm, which simulates the behavior of individuals in society improving their status and abilities by interacting with high-status members (elites). The core objective of this phase is to accelerate convergence and refine the discovered high-quality solutions. Its core idea is learning from a "high-status circle." The SBO algorithm analogizes the optimization process to the upward mobility of individuals in a social hierarchy. Individuals (solutions) improve their position (solution quality) by learning from members of higher status (solutions with better fitness). The exploitation operator in RLDSBO inherits and improves upon this core idea, constructing a dynamic "high-status circle" to guide individuals in efficient local searches.

[0051] Using mathematical modeling of operators, for the selection of the first action to perform the exploitation action... An agent, its new test location It was generated through a three-way interactive mathematical model. This model combines information about its own position, a randomly selected elite, and a globally optimal elite.

[0052] Elite Mentor Selection: To introduce diverse guidance information and prevent all individuals from converging towards a single global optimum, this operator first selects a "random elite mentor" from the current population. This selection process is implemented using Roulette Wheel Selection, where the probability of each individual being selected is proportional to the inverse of its fitness. This means that the lower the fitness value (i.e., the higher the quality of the solution), the greater the probability of it being selected as an elite mentor. This mechanism ensures that the guidance direction has both an elitist bias and a certain degree of randomness.

[0053] High-position circle update equation: new trial vector Each dimension j is updated by the following linear combination formula: ; in: It represents the current position of agent i in dimension j, indicating the inertia or current state of the individual. Random elite mentors The position of the current agent i on dimension j represents excellent guidance information from within the population. It is the globally optimal solution. The position in dimension j represents a strong attraction from the globally optimal direction. , These are two from the standard normal distribution The algorithm employs randomized weights in the mid-sample. These weights are dynamic, providing great flexibility in the search direction, allowing individuals to exploratoryly move within a triangular region formed by "themselves," "elite mentors," and "global elites." This equation constructs a dynamic, elite-oriented search pattern that effectively performs a fine-grained search around the known optimal solution.

[0054] Adaptive Random Perturbation: Balancing Exploitation and Escape. Pure exploitation strategies can lead to premature convergence to a local optimum. To address this issue, this operator integrates a novel adaptive random perturbation mechanism. This mechanism aims to introduce strong random perturbations late in the exploitation phase or when the algorithm stagnates, helping the agent escape local optima. This mechanism is based on a probability threshold that changes non-linearly with the algorithm's progress. control:

[0055] ; MaxFEs and FEs represent the maximum and current function evaluation counts, respectively, and t is the current iteration count. Operations such as tanh and sqrt make... The variation curves are very complex and dynamic. The overall trend is that as FEs approach MaxFEs, It tends to become smaller. The behavioral characteristics of this perturbation mechanism are:

[0056] In the early stages of the algorithm: Relatively large, rand> The conditions are difficult to meet, therefore the probability of perturbation is low. This allows the algorithm to converge stably to the elite mentor's solution. In the later stages or during the stagnation period of the algorithm: The value will decrease, and the probability of a perturbation will increase accordingly. Once triggered, the perturbation may be strong enough to "kick" an individual out of its current attraction basin, thereby reigniting its search activity.

[0057] Reinforcement Learning-Driven Policy Selection: The core innovation of RLDSBO lies in its hierarchical, adaptive hybrid framework. Unlike traditional metaheuristic algorithms that employ fixed or simple rule-based hybrid strategies, RLDSBO introduces a reinforcement learning (RL) module as its decision engine. This module aims to autonomously and dynamically select the most suitable search operator for each agent in the population. This process simulates the core decision-making process by which an individual, based on past successes and failures, decides whether to continue taking risks (exploration) or consolidate existing achievements (utilization).

[0058] To implement this decision-making mechanism, we model the optimization process as a simplified multi-agent reinforcement learning problem, whose key components are defined as follows: Agents: N solution vectors in the population (i=1,…,N) are considered as N independent learning agents. Each agent has its own decision model.

[0059] State: In this algorithm implementation, state is simplified. Each agent... The decision point at the beginning of each iteration t is considered an independent state. Therefore, the learning model does not rely on complex environmental features, but focuses on the historical performance of each agent itself.

[0060] Action Space: Each agent has two discrete actions to choose from: Action=1 (Explore): Executes an L-SHADE-based differential evolution strategy. This action aims to perform a wide-area search to discover new promising regions.

[0061] Action=2 (Exploitation): Executes an elite interaction strategy inspired by SBO. This action aims to deeply mine and refine the vicinity of known optimal solutions.

[0062] Q-Table: This is the core of the RL module, a matrix of size N×2. The value of Q(i,Action) represents the agent. The expected cumulative reward obtained from performing actions in the past. It quantifies each agent's evaluation of the "goodness" or "badness" of each action and is a direct reflection of its "experience".

[0063] Reward Function: To align the learning objective with the optimization objective, we designed a simple yet effective reward function. When an agent performs an action and produces a new solution that is better than its current solution, it receives a positive reward of Reward = 1. Conversely, if there is no improvement, the reward is Reward = 0. This immediate reward mechanism directly incentivizes behaviors that lead to improved fitness.

[0064] ε-greedy dynamic decision-making process: In each iteration, each agent... All actions are selected using the classic ε-greedy strategy. This strategy aims to balance the utilization of known effective strategies with the exploration of unknown strategies. The decision rule is as follows:

[0065] ; Exploitation: When the generated random number is greater than or equal to ε, the agent will execute an exploit strategy. It will query the corresponding row Q(i,:) in its Q table and select the action with the highest 'a' value. This means that the agent, based on its past experience, believes that this action is most likely to succeed. Let 'a' represent the set of all possible actions, i.e., the action space that the agent can choose in the current state. Q(i,:) in the formula represents the agent's... Given the expected cumulative reward of choosing action 'a' in the current state, the agent will execute an exploration strategy when the generated random number is less than ε, i.e., ignore the Q-table and explore from the action space. The agent randomly selects an action. This gives the agent the opportunity to try non-optimal strategies, which is crucial for avoiding premature convergence and adapting to different stages of the optimization process.

[0066] Q-table learning and updating: in the agent Complete the selected action After receiving the reward R, the algorithm immediately updates the Q-table to integrate this new experience into its decision model. The update rule uses the core formula of Q-learning:

[0067] ; Here, α is the learning rate (e.g., α = 0.5). Essentially, this formula is a weighted average: it combines the old Q-value (the agent's old beliefs) with the newly acquired reward (new facts). The learning rate α controls the magnitude of the update, determining whether the agent prioritizes historical experience or the most recent feedback.

[0068] Dynamic evolution of algorithmic behavior: The most ingenious aspect of this RL framework lies in the decay mechanism of the exploration rate ε. In RLDSBO, the value of ε gradually decreases as iterations proceed.

[0069] ; In the early stages of the algorithm: the value of ε is relatively high, and the agent has a high probability of exploring random actions. This gives both strategies (L-SHADE and SBO-like operators) ample opportunity to be executed, allowing the algorithm to comprehensively evaluate their effectiveness at different stages and quickly fill the Q-table.

[0070] In the later stages of the algorithm: the value of ε becomes very low, and the decision-making process will rely primarily on the Q-table. The agent will be more inclined to execute the action that has proven more successful in its history. For example, if for an agent that is close to the optimal solution, exploitation strategy (action 2) continues to bring small improvements while exploration strategy (action 1) often fails, then its Q(i,2) value will be much higher than Q(i,1), causing the agent to perform almost only exploitation operations in the later stages.

[0071] In summary, reinforcement learning-driven decision-making provides RLDSBO with a powerful and adaptive top-level control logic. Instead of relying on fixed rules, it allows each agent to "learn" when to perform breadth exploration and when to perform depth exploitation through direct interaction with the optimization problem, thus achieving dynamic matching between algorithmic behavior and problem-solving state.

[0072] S102: Obtain a simulated cell time series dataset and divide it into a training set and a test set according to a specified ratio; input the training set into the 3D U-Net model and output the predicted value of cell traction force.

[0073] Optionally, the simulated cell time series dataset is generated based on a cell migration model, has multiple spatial resolutions, and includes displacement and stress field tensor information.

[0074] Optionally, the 3DU-Net model includes an encoder, a decoder, and a channel space attention mechanism module for extracting and reconstructing stress-strain vector field features from a simulated cell time series dataset.

[0075] Specifically, a simulated cell time-series dataset provided by a deep learning-based cellular traction microscopy method was used as training, validation, and testing samples. This simulated data was generated based on a computational model of cell migration, and displacement and stress tensors were constructed at different spatial resolutions (104×104, 160×160, and 256×256). In the experiments, we selected 104×104 scale time-series data for model training, validation, and testing. The population size for both optimization algorithms was set to 5, and the maximum number of iterations was uniformly set to 20.

[0076] Specifically, the simulated cell data time series dataset is divided into training and testing sets in an 8:2 ratio.

[0077] Specifically, the predicted values ​​of the simulated cell time series dataset and the output of the 3DUNET model are essentially dimensionless cell traction force magnitude and direction. The real cell traction force calculated based on the test set and the cell traction force output by the 3DUNET model are actually cell traction forces with units obtained through further transformation. The transformation formula is output value * conversion = output value * (E / 10 * mag), where E is the base Young's modulus, mag is the image scaling factor, mag = S / 104, and S is the height of the real image.

[0078] S103: Using the hyperparameters and network structure of the 3DU-Net model as the population position of the hybrid optimization algorithm, and aiming to minimize the fitness function value, the hybrid optimization algorithm optimizes the hyperparameters and network structure of the 3DU-Net model until a preset maximum number of iterations is reached. The hyperparameters and network structure that reach the maximum number of iterations are determined as the optimized and trained 3DU-Net model hyperparameters and network structure. The fitness function value is constructed based on the average relative error between the predicted cell traction force output by the 3DU-Net model and the actual cell traction force calculated from the test set. The expression for the fitness function is:

[0079] ; In the formula, and These refer to the predicted values ​​of cellular traction force in the horizontal and vertical directions, respectively. and These represent the actual values ​​of cellular traction force in the horizontal and vertical directions, respectively. N is The number of pixels in a displacement field map in a simulated cell time series dataset.

[0080] Specifically, the optimal solution position is updated until the maximum number of iterations is reached, at which point the optimal solution is output. The optimization algorithm RLDSBO is described in detail below, along with its hybrid design philosophy and mathematical modeling. This invention introduces an improved Status-Based Optimization (SBO), an efficient algorithm inspired by the human desire for status advancement. By simulating how individuals approach and learn from or acquire resources from high-status individuals, SBO transforms these social patterns into a powerful computational method for solving complex optimization tasks.

[0081] S104: The optimized 3DU-Net model is used to predict the simulated cell data to obtain the cell traction force in future time periods.

[0082] Optionally, the optimized 3DU-Net model is determined by the optimal average relative error of the 3DU-Net model through a hybrid optimization algorithm, which sets the network structure and hyperparameters accordingly.

[0083] Specifically, the optimized hyperparameter search process of the 3D U-Net architecture significantly reduces the number of parameters through feature selection.

[0084] The 3D U-Net architecture with embedded attention modules includes encoders, decoders, and channel / spatial attention mechanisms for efficient extraction and reconstruction of stress-strain vector field features.

[0085] The search space includes key factors such as the attention mechanism switches (0 for off, 1 for on) of each layer of the encoder and decoder, the range of the number of channels in the convolutional layers, the initial learning rate, the strength of L2 regularization, and the learning rate decay coefficient. During the search process, the number of channels in the convolutional layers is selected within a given integer range, and the learning rate and regularization parameters are optimized within a continuous interval, thus taking into account the diversity of network structure and training strategies.

[0086] After obtaining the search results, we used the optimal network structure and hyperparameters found by each algorithm to train and test the models under the same training settings. All models used mean squared error (MSE) as the loss function, with a fixed training epoch of 160 epochs, an SGDM optimizer, and a batch size of 20. The initial learning rate and regularization parameters were determined by the search results. The dynamic learning rate adjustment strategy employed piecewise descent, with the decay period and decay coefficient determined by the search results to balance convergence speed and final model accuracy. Except for the hyperparameters obtained from the search, all other training hyperparameters and data preprocessing procedures remained completely consistent in both algorithms.

[0087] Convergence curve as Figure 2 As shown in the results, RLDSBO significantly reduces the validation error within the first five iterations and continues to improve in subsequent iterations. In contrast, BO is slower in the early iteration stages and shows a convergence trend in the middle of the iterations, ultimately performing significantly worse than RLDSBO. This phenomenon indicates that RLDSBO exhibits superior global exploration capability and convergence efficiency in high-dimensional optimization problems. In summary, RLDSBO can not only find high-performance models within a limited number of iterations in architecture search tasks but also significantly improve the prediction accuracy of the final model. This advantage has significant application value and potential for widespread adoption in computationally expensive scientific tasks such as traction force prediction.

[0088] This invention proposes a hybrid optimization algorithm that combines swarm intelligence optimization with a surrogate model acceleration strategy, significantly reducing computational costs while maintaining high accuracy. Experiments demonstrate that, compared to the BO method, the optimization algorithm of this invention achieves significant improvements in convergence speed, force field reconstruction accuracy, and computational resource consumption. Furthermore, by embedding a lightweight attention mechanism in a 3D U-Net architecture, this invention compresses the number of model parameters while maintaining high prediction accuracy, enabling efficient operation on mid-range GPUs (such as the NVIDIA 1080 Ti), providing a more practical computational tool for cell mechanics research.

[0089] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this invention.

[0090] The above describes an application method of an optimization algorithm in cellular traction force calculation, provided by one or more embodiments of the present invention. Based on the same idea, the present invention also provides a corresponding application device for the optimization algorithm in cellular traction force calculation, such as... Figure 3 As shown.

[0091] Figure 3 This is a schematic diagram of an application device for an optimization algorithm in cellular traction force calculation provided by the present invention. The device includes: Algorithm construction module 301 is used to construct a hybrid optimization algorithm based on reinforcement learning. The hybrid optimization algorithm treats each individual in the population as an independent learning agent; determines the action to be performed by each learning agent from the action space according to a preset exploration rate; creates a Q-table for the expected cumulative reward obtained by the learning agent when performing historical actions; iteratively updates the Q-table according to the learning agent's actions, and takes the position of the individual with the largest expected cumulative reward value in the last updated Q-table as the optimal solution; wherein, the action space of the learning agent includes exploitation actions and exploration actions; when the action is an exploitation action, a differential evolution strategy based on L-SHADE is executed; when the action is an exploration action, an elite interaction strategy inspired by SBO is executed. The data acquisition module 302 is used to acquire a simulated cell time series dataset; and input the simulated cell time series dataset into a pre-trained 3DU-Net model to output cell traction force; The algorithm application module 303 is used to use the cell traction force as the population individual position in the hybrid optimization algorithm. With the goal of minimizing the fitness function value, the hyperparameters and network structure of the 3DU-Net model are optimized through the hybrid optimization algorithm until a preset maximum number of iterations is reached. The hyperparameters and network structure that reach the maximum number of iterations are determined as the hyperparameters and network structure of the optimized 3DU-Net model. The fitness function value is constructed based on the average relative error of the cell traction force. The model prediction module 304 is used to input the simulated cell data to be predicted into the optimized and trained 3D U-Net model to obtain the cell traction force of the simulated cell data to be predicted.

[0092] Specific limitations regarding the application device of an optimization algorithm in cellular traction force calculation can be found in the above description of the application method of the optimization algorithm in cellular traction force calculation, and will not be repeated here. Each module in the aforementioned application device of the optimization algorithm in cellular traction force calculation can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the corresponding operations of each module.

[0093] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 This paper presents an optimization algorithm for the calculation of cellular traction force.

[0094] The present invention also provides Figure 4 The schematic diagram of the computer device shown is as follows: Figure 4 As shown, at the hardware level, this computer device includes a processor, internal bus, network interface, memory, and non-volatile memory, and may also include other hardware required for business operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then executes it to achieve the above. Figure 1 This paper presents an optimization algorithm for the calculation of cellular traction force.

[0095] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the methods described above. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, or optical storage, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

Claims

1. A method for applying an optimization algorithm in calculating cellular traction force, characterized in that, include: Construct a hybrid optimization algorithm based on reinforcement learning; The hybrid optimization algorithm is used to treat each individual in the population as an independent learning agent. The action to be performed by each learning agent is determined from the action space according to a preset exploration rate; a Q-table is created to represent the expected cumulative reward obtained by the learning agent when performing historical actions, and the Q-table is iteratively updated according to the learning agent's actions, with the position of the individual with the largest expected cumulative reward value in the last updated Q-table being taken as the optimal solution; wherein, the action space of the learning agent includes exploitation actions and exploration actions; when the action is an exploitation action, an L-SHADE-based differential evolution strategy is executed; when the action is an exploration action, an SBO-inspired elite interaction strategy is executed; Obtain a simulated cell time series dataset and divide it into a training set and a test set according to a specified ratio; then input the training set into a 3D U-Net model to output predicted cell traction force values; The hyperparameters and network structure of the 3DU-Net model are used as the individual positions in the population of the hybrid optimization algorithm. With the goal of minimizing the fitness function value, the hyperparameters and network structure of the 3DU-Net model are optimized through the hybrid optimization algorithm until a preset maximum number of iterations is reached. The hyperparameters and network structure that reach the maximum number of iterations are determined as the hyperparameters and network structure of the optimized 3D U-Net model. The fitness function value is constructed based on the average relative error between the predicted cell traction force output by the 3D U-Net model and the actual cell traction force calculated from the test set. The optimized 3DU-Net model is used to predict the simulated cell data to obtain the cell traction force in future time periods.

2. The method for applying the optimization algorithm as described in claim 1 to the calculation of cell traction force, characterized in that, The learning agent is shared through an L-SHADE-based differential evolution strategy and an SBO-inspired elite interaction strategy.

3. The method for applying the optimization algorithm as described in claim 1 to the calculation of cellular traction force, characterized in that, The Q table is a matrix of size N×2, where N represents the state of the learning agent (the row data of the matrix) and 2 represents the number of actions executed by the learning agent in the action space (the column data of the matrix).

4. The method for applying the optimization algorithm as described in claim 1 to the calculation of cellular traction force, characterized in that, The method of using the classic ε-greedy strategy to determine the execution action of each learning agent specifically includes: When the random number generated by the random number function is greater than or equal to the preset exploration rate ε, the learning agent queries the execution action corresponding to the row of the learning agent in its Q table and selects the execution action with the highest expected cumulative reward from the action space. When the random number generated by the random number function is less than the preset exploration rate ε, the learning agent randomly selects an action from the action space to execute.

5. The method for applying the optimization algorithm as described in claim 4 to the calculation of cell traction force, characterized in that, If a new solution is generated after the current learning agent executes the strategy and is better than the current solution, a reward value is obtained. Conversely, you will receive a reward value. ; After the agent completes the selected execution strategy and receives the reward value, update the expected cumulative reward in the Q table using the following formula: ； In the formula, For the expected cumulative reward in the updated Q table, The expected cumulative reward in the Q table before updates, where α is the learning rate. This is the reward value.

6. The method for applying the optimization algorithm as described in claim 1 to the calculation of cellular traction force, characterized in that, The preset exploration rate gradually decreases during the iteration process; the preset exploration rate is set to 0.99 during the first iteration.

7. The method for applying the optimization algorithm as described in claim 1 to the calculation of cellular traction force, characterized in that, The simulated cell time series dataset is generated based on a cell migration model, has multiple spatial resolutions, and includes displacement and stress field tensor information.

8. The method for applying the optimization algorithm as described in claim 1 to the calculation of cellular traction force, characterized in that, The 3D U-Net model includes an encoder, a decoder, and a channel space attention mechanism module, which are used to extract and reconstruct stress-strain vector field features from simulated cell time series datasets.

9. The method for applying the optimization algorithm as described in claim 1 to the calculation of cellular traction force, characterized in that, The expression for the fitness function is: ； In the formula, For the fitness function value, and These refer to the predicted values ​​of cellular traction force in the horizontal and vertical directions, respectively. and These represent the actual values ​​of cellular traction force in the horizontal and vertical directions, respectively. N This is to simulate the number of pixels in a displacement field map within a cell time series dataset.

10. A device for applying an optimization algorithm in calculating cellular traction force, characterized in that, include: The algorithm building module is used to build a hybrid optimization algorithm based on reinforcement learning. The hybrid optimization algorithm is used to treat each individual in the population as an independent learning agent. The action to be performed by each learning agent is determined from the action space according to a preset exploration rate; a Q-table is created to represent the expected cumulative reward obtained by the learning agent when performing historical actions, and the Q-table is iteratively updated according to the learning agent's actions, with the position of the individual with the largest expected cumulative reward value in the last updated Q-table being taken as the optimal solution; wherein, the action space of the learning agent includes exploitation actions and exploration actions; when the action is an exploitation action, an L-SHADE-based differential evolution strategy is executed; when the action is an exploration action, an SBO-inspired elite interaction strategy is executed; The data acquisition module is used to acquire a simulated cell time series dataset and divide it into a training set and a test set according to a specified ratio; and input the training set into the 3D U-Net model to output the predicted value of cell traction force. The algorithm application module is used to take the hyperparameters and network structure of the 3DU-Net model as the individual positions of the population in the hybrid optimization algorithm. With the goal of minimizing the fitness function value, the hybrid optimization algorithm is used to optimize the hyperparameters and network structure of the 3DU-Net model until a preset maximum number of iterations is reached. The hyperparameters and network structure that reach the maximum number of iterations are determined as the hyperparameters and network structure of the optimized 3DU-Net model. The fitness function value is constructed based on the average relative error between the predicted cell traction force output by the 3DU-Net model and the actual cell traction force calculated from the test set. The model prediction module is used to predict the cell traction force in future time periods using the optimized and trained 3DU-Net model to simulate the cell data to be predicted.

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