The potential low-energy feature of the spiking neural network (SNN) engages the attention of the AI community. Only CPU-involved SNN processing inevitably results in an inherently long temporal span in the cases of large models and massive datasets. This study introduces the MAC array, a parallel architecture on each processing element (PE) of SpiNNaker 2, into the computational process of SNN inference. Based on the work of single-core optimization algorithms, we investigate the parallel acceleration algorithms for collaborating with multi-core MAC arrays. The proposed Echelon Reorder model information densification algorithm, along with the adapted multi-core two-stage splitting and authorization deployment strategies, achieves efficient spatio-temporal load balancing and optimization performance. We evaluate the performance by benchmarking a wide range of constructed SNN models to research on the influence degree of different factors. We also benchmark with two actual SNN models  on the neuromorphic multi-core hardware SpiNNaker 2. The echelon optimization algorithm with mixed processors realizes 74.28% and 85.78% memory footprint of the original MAC calculation on these two models, respectively. The execution time of echelon algorithms using only MAC or mixed processors accounts for ≤ 24.56% of the serial ARM baseline. Accelerating SNN inference with algorithms in this study is essentially the general sparse matrix-matrix multiplication (SpGEMM) problem. This article explicitly expands the application field of the SpGEMM issue to SNN, developing novel SpGEMM optimization algorithms fitting the SNN feature and MAC array. Coupling spatial and temporal information, the SNN shows promise in simulating biologically related models more comprehensively and efficiently. The CPU-based system is widely used for simulating these brain-inspired neural networks by taking advantage of flexibility. However, the efficient input spike encoding way is still in the exploration stage, and a gap still exists between the current encoding efficiency and that of the human brain, which reduces the expected sparsity of the input signal and extends the CPU running time. Moreover, to accommodate the serial operation mechanism, the model needs to introduce additional information when deployed to the hardware, such as the storage address of neurons, extra memory occupation owing to non-equivalent connections, and intermediate state storage buffers. This not only burdens the memory space but also inevitably requires more time to execute the corresponding pre- and post-neuron matching algorithm for information transfer and neural update, which is detrimental to the operation of real-time SNN inference.To address these issues caused by pure CPU systems, we introduced the parallel computing concept into SNN inference. The feasibility of parallel architecture processing SNN lies in the neurons of SNN being typically governed by the same type of equations :i and post-neuron j are summed if the spikes arrive at the post-neuron after traveling across the synapse for time interval d. Then, in the neural update step, the membrane potential decays by factor α  and is updated by checking the neuron states t. If the sum of the first two terms exceeds the threshold Vth, neuron states are set to 1 and neuron spikes, otherwise 0. This equation refers to  according to the modification of operand B (weight-delay map) which is discussed in Section 3.1.1. To be specific, we record how the row of operand B is reordered and apply it to the column reorder of the operand A. Unlike the operand B, the operand A is unknown in advance because there is no way to predict the input spike status, so we cannot reorder operand A offline and have to adjust the operand A when executing the SNN inference. This adjustment can be achieved on the host PC with Python or on SpiNNaker 2 with C language. To make a fair comparison with the pure ARM baseline in Section 4 and to extend the capability of SpiNNaker 2 of directly handling the spikes from the sensor peripheral, we propose the Circle Reverse algorithm  to onlinFind circles: During the reorder process of the operand B, we get the target index list that corresponds to the source index list, that is, which source row of the operand B should be placed in which target row in the generated echelon matrix, as presented in Reverse circles: Now we consider adjustment of the operand A (input-spike-train map). If we directly move columns of operand A based on the order given by original circles, the previous column overwrites the current column, and then the current column cannot assign the correct values to the next column. To solve this issue, we reverse the index order of each original circle and preserve the start column before executing the column movement for the operand A, as shown on the right side of m in this figure represents the remainder of dividing the column number of the echelon matrix by that of MAC array (16). The data contained in this set of rectangles consume the least memory resources when deploying on SpiNNaker 2.Considering the MAC array exclusively supporting the acceleration of the rectangular matrix, we employed a set of rectangles to enclose all the meaningful data and as few zeros as possible. The length of the rectangle is a consecutive integer  multiple of 16, and the width is an integer multiple of 4. The multipliers derive from the hardware characteristic of the MAC array of SpiNNaker 2. Using the alignment splitting algorithm, we obtained a set of rectangles with the smallest total area, as Now, length and width of the rectangles meet the requirements of the MAC calculation, and its time to discuss the load balancing issue. The amount of data outlined by rectangles varies. All data in some rectangles might occupy little memory if we simply distribute each small rectangle to one PE without combination. In contrast, all data in other rectangles may be far beyond the maximum available SRAM space of one PE. Even if the data in the largest rectangle barely fit into one PE, the unbalanced weight loading of the rectangle set among multiple PEs can prolong the overall processing time, and partial computing power of the core with a low weight load is wasted. Therefore, based on the set of rectangles obtained in the above steps, we execute the core splitting algorithm to achieve a spatial-temporal load balancing deployment on multiple cores. This step splits the rectangles obtained by alignment splitting into more and smaller rectangles horizontally and then divides them into several groups with an equal amount of weight values, as Equally distributing weights across multiple cores has many possibilities. Here, we put weights into as few PEs as possible to fully utilize the resources of each core. We do this for two reasons: on the one hand, matrix multiplication with MAC array has a considerable time advantage, and the marginal utility of dividing into more cores is tiny; on the other hand, the full utilization of each core is also conducive to simultaneously deploying and executing more tasks on multi-core SpiNNaker 2 platform in future.m, the remainder dividing the column number of the echelon matrix by 16. When m is small, these zero values employed as placeholders occupy a large memory space. We improve this situation by abstracting only the meaningful data, as By observing the biggest rectangle in As for the corresponding core splitting strategy that matches this mixture alignment splitting, we figured out the number of required PEs with the approach mentioned above and outlined the core splitting rectangles for the blue and pink marked area of m is small, or the number of source neurons (corresponds to the row number of echelon matrix) is large, the optimization is particularly effective.This optimization eliminates the extra memory overhead originating from necessary memory alignment alongside the columns of operands B and C. When m represents a number ranging from 1 to 16 in various models. Therefore, it is necessary to analyze the influence of m on processor selection quantitatively. In the pink outlined area in m being 1, as shown in m climbs, the memory gap gradually narrows until it disappears when m reaches the maximum value of 16. As for the time comparison, we found that pure MAC outperforms ARM of the mixed approach except for several cases when m and row number are pretty small, according to The variable After the splitting process, we discuss how to deploy the split echelon matrix and where to process the original input-spike-train map. The MAC array of SpiNNaker 2 supports reading operands from other PEs. Based on this feature, we authorize the core that reads reversed input data from another PE and preloads the split weight rectangular group as the “Subordinate PE.” The PE that provides reversed input data acts as the “Dominant PE.” To evaluate the performance of the information densification and splitting algorithms and the feasibility of the deployment strategy from Section 3, we benchmarked it with constructed and actual SNN models in this section.The optimization performance of our proposed approaches relies on the following five factors: delay range, number of pre-neurons, number of post-neurons, weight connection density, and the selection of splitting strategy. The first four factors are determined by the SNN model itself. Thus, we constructed multiple SNN models based on various combinations of these four factors and explored their influence on spatial and temporal performance. To focus on the scope of our proposed approaches, we experimented on the synaptic processing part of SNN.m in In addition to the impact of the remainder of post-neurons divided by 16 on the spatial performance difference between the two methods, the change of the post-neuron number itself also affects the memory optimization rate. ropt represents the memory optimization rate, which is approximately directly proportional to the delay range d, and inversely to weight connection density p and number of post-neurons npost. The use of the approximately proportional symbol Although the memory optimization rate is unrestricted by the pre-neuron number, the impact of the pre-neuron number on SNN inference performance is mainly reflected in the running time, which basically consists of input data pre-processing  and synaptic processing. The synaptic processing is accelerated by the MAC array, and the input data pre-processing is only calculated by ARM. Therefore, the input data pre-processing consumes most of the temporal resources. The smaller the number of input neurons , the better the algorithms proposed in this study performs in execution time. If only considering the synaptic processing part, the temporal performance of the mixed echelon approach also has an intense dependence on the number of pre-neurons. The mixed echelon algorithm sacrifices some runtime in exchange for a lower memory footprint, and this time is positively correlated with the number of pre-neurons.We selected two actual benchmarks for evaluation of our proposed approaches: an application model from the real scenario (radar gesture recognition SNN model) and a classic structural modeling in neuroscience . The experiments compared serial ARM, original MAC, pure MAC echelon, and MAC and ARM mixture approaches regarding spatial-temporal performance. The data measurement concentrates on the part where the above four approaches behave differently during SNN inference, that is, synaptic processing. As for the multi-core mapping and deployment, we evenly split the weight operand into multiple adjacent PEs and fully utilized each PE's available memory resources (120 KB in our configuration) in conjunction with other necessary data  for serial ARM and original MAC. When a PE can accommodate not less than one weight matrix of one delay, we ensure the integrity of a computational unit, i.e., one weight matrix of one delay, to avoid introducing additional result fusion time. For example, if a kernel can hold 2.5 weight matrices of one delay, we assigned pure MAC echelon and mixture approaches that adopted supporting strategies from Section 3.2 and 3.3.We adopted the following method to calculate memory cost and measure the execution time of the multi-core cooperation system:Two baselines: The memory cost of serial ARM and original MAC comes from the input placeholder, weight, output placeholder, and input current buffer in all activated PEs. Note that the input and weight operands are supposed to be memory aligned in advance. The execution time is comprised of matrix multiplication, output merging from different PEs and input current buffer update.Two echelon approaches: The memory cost consists of the footprint of the Dominant PE  and Subordinate PEs (weight cost and temporary output). In addition to the matrix-multiplication execution time (MAC or mixture processors) and the time of accumulating output into Dominant PE, the execution time also incorporates the input reorder time to guarantee a fair comparison with serial ARM and the original MAC baseline. Since each calculation obtains the same number of results as the delay number instead of only one result of the serial ARM and original MAC approach as Gesture recognition is an important and active area of AI research, with relevant models and hardware deployment acting as the fundamental verification unit for more sophisticated real-world scenarios. For the first benchmark, we set up the radar-based SNN gesture recognition model with 2,048 input neurons, 20 hidden neurons, four output neurons, and four delays. This model is similar to the study in Gerhards et al.  and HuanFor the Echelon Reorder optimization algorithm with only MAC as the processor, the densified weight-delay map  can be split and deployed into two Subordinate PEs as depicted on the right part of m and row number are calculated to be 4 and 5,500. According to the analysis in Section 3.2.3, the mixed optimization is expected to outperform the pure MAC regarding memory footprint but be inferior concerning execution time. The experiment data from Analyzing the performance data reported on the bottom left of The balanced random cortex-like network, commonly used to benchmark and map to neuromorphic systems  than the balanced random cortex-like network (800), as shown in In addition to the distinction in pre-neuron number, these two benchmark models structure different weight connection densities  and post-neuron numbers . The formula 2 indicates the model with smaller weight connection densities, and post-neuron numbers deserve a better memory optimization effect for weight-delay map. The blue bars of two echelon algorithms relative to the original MAC in the memory cost comparison of In addition, we introduce a definition of “memory alignment rate of column” to account for the reason for a sharper drop of the blue bar from echelon (MAC) to echelon (MAC + ARM). The memory alignment rate of the column presents the impact of memory alignment along the column of the weight-delay map for the size of the whole memory aligned weight-delay map, that is, the rate of the right side white rectangle area to the whole area in m is the reminder of post-neuron number npost divided by 16. With the increase of the post-neuron number, the memory alignment rate decreases. This means that the extra area brought by column memory alignment is a decreasing share of the total weight-delay map. As a result, the echelon (MAC + ARM) algorithm, functioning as optimizing this extra area as mentioned in Section 3.2.2 and 3.2.3, behaves much better in the radar gesture recognition model than in the balanced random cortex-like network. Similarly, the different ratios  in comparison of serial ARM and original MAC  are caused by memory alignment along the row and column of weight matrices of delay x shown in where This study describes the processing chain for accelerating SNN inference with multi-core MAC arrays, including Echelon Reorder information densification algorithm, Multi-core two-stage splitting and multi-core authorization deployment strategies. These algorithms and strategies alleviate the intrinsic memory issue of excessive usage originating from memory alignment and data sparsity. They also realize the multi-core spatial-temporal load balancing for the large SNN layer. We benchmark with constructed and actual SNN models. The former explores how model feature and algorithm selection affect the spatial-temporal optimization performance, and the latter demonstrates two actual SNN models  on SpiNNaker 2 hardware. They prove the feasibility of the whole optimization process and achieves performance increase. Based on the theoretical analysis and the experiment result, we found those as follows:The proposed algorithms and strategies are applicable to various densities of matrix multiplication operands, and the memory optimization degree increases with the weight operand getting sparse.In addition to the weight sparsity, the memory optimization rate is also positively correlated with delay range.The number of post-neurons periodically affects the memory optimization rate, and the overall trend is downward.The number of pre-neuron is generally independent of the memory optimization performance but has intense correlation with running time.The echelon mixed processor algorithm behaves better regarding memory but has less temporal efficiency than the echelon pure MAC solution.The proposed algorithms not only provide a concrete solution for accelerating SNN on the multi-core MAC arrays of SpiNNaker 2 but also has a referential value for hardware systems embedded with multi-core MAC arrays that intend to solve the SpGEMM issue.Some researchers have introduced the parallel computing concept into SNN inference to tackle the problems caused by CPU-based parallel processing. One of the representative works of parallel processors accelerating SNN computation is GeNN , carried out the experiment of constructed SNN models (supported by DS), and performed the actual SNN models mapping and emulating on SpiNNaker 2, based on the low-level hardware design and communication library from FKe. BV helped JH with the basic structure of SNN middle-ware development. KK and CM supervised the findings of this study. All authors discussed the results and contributed to the final manuscript.


A robust optimal scheduling method driven by multi-objects is proposed for the collaborative optimization problem between dynamic scheduling, preventive maintenance of equipment, and robustness of scheduling schemes in a complex manufacturing system. Firstly, the equipment maintenance task is mapped to the process level, and composite dispatching rules with weight parameters are designed, which flexibly consider equipment maintenance and system processing status. Secondly, the performance-driven ideology is analyzed through two models based on the IWOA-MLP algorithm. Thirdly, the feedback mechanism ideology facilitates adaptive closed-loop optimizations. Finally, a series of experiments were carried out on the simulation platform of a semiconductor manufacturing enterprise in Shanghai. The experimental results show that the proposed robust optimal scheduling system can effectively deal with mixed uncertainty, improve production performances, and maintain highly robust measures. As manufacturing systems are complex, random, multi-constraint, and multi-objective, their scheduling problems involve several factors, such as tasks, resources, and the amount of time it takes to perform a task. In traditional scheduling theory, all problem parameters are assumed to be fixed, but there are many types of random disturbances in the actual production process, such as unexpected equipment failures, order changes, differences among workers, and changes in dispatching rules. The manufacturing system is often unable to implement production according to the established initial scheduling scheme due to these uncertain factors in the actual production process, or the initial scheduling scheme needs to be adjusted, which will have a significant impact on production processes and outcomes. Scheduling schemes are usually required to be capable of accommodating a certain degree of random disturbance in order to ensure that the production task is successfully completed and the production effect is achieved. By slightly adjusting the scheduling scheme to make it implementable and produce satisfactory scheduling results, the scheduling scheme has a certain degree of robustness.The production scheduling of complex manufacturing systems involves allocating limited resources  according to time series to achieve one or several target valuesTherefore, the purpose of this paper is to study the adaptive closed-loop optimization approach to the multi-objective driven robust optimal scheduling of complex manufacturing systems. Specifically, this paper discusses dynamic dispatching, equipment maintenance, and robustness of scheduling schemes for complex manufacturing systems based on CT (cycle time), ODR (on-time delivery rate), EA (equipment unavailability), and RM (robustness measure). By integrating intelligent manufacturing dynamic operation optimization theory, this paper systematically solves the adaptive closed-loop optimal scheduling problem in manufacturing systems.The arrangement of this paper is as follows. Section "2. The academic community has only recently begun to focus on both topics: fault maintenance are comprehensively considered in workshop management, and equipment maintenance is considered as a decision variable or constraint as part of production scheduling. By integrating optimization, production costs can be reduced, equipment life can be extended, and product quality can be improved.Among all uncertain factors in production, machine failure is the most common. Preventive maintenance is more practical and reasonable than maintenance following machine failure and can reduce the impact of machine failure on the entire manufacturing process to a considerable extent. Maintenance scheduling in the production process refers to determining the start and duration time of each equipment maintenance task, which often takes into consideration the equipment load factor and the urgency of the maintenance task. The maintenance of production equipment and the scheduling of manufacturing processes are interrelated and interactive, but they are often studied separately3 investigated the integration of production scheduling and preventive maintenance in a two-stage hybrid flow shop, which was able to optimize both the manufacturing cycle and the availability of machines in the first stage. A strategy of scheduling preventive maintenance has been adopted by Dai et al.4: when reliability is reduced to the threshold value, the integrated optimization of flexible job-shop scheduling problem (FJSP) and preventive maintenance is studied. Zandieh et al.5 conducted an integrated optimization study on shop scheduling and preventive maintenance in FJSP by focusing on maximum completion time and system unavailability as optimization objectives. Considering the single-machine system problem, Wang et al.6 designed a multi-objective evolutionary algorithm based on the support vector regression proxy index to determine the processing order of a workpiece and the input of equipment maintenance resources. The flow shop scheduling problem with random failures was studied by Zhang et al.7. They developed two nested optimization algorithms based on the comprehensive index of quality robustness and robustness as the optimization objective. An integrated optimization model for equipment preventive maintenance and production scheduling was established by Wang et al.8 using discrete flow shops as the background, which improved the equipment reliability and reduced the impact of equipment failures on workpiece processing.Hu et al.The existing literature indicates that production scheduling considering equipment maintenance is primarily based on single-machine systems (no tight forward or backward relationship between workpieces) and flow shops (subject to the same failure probability distribution), which are inconsistent with the actual manufacturing system. Different types of equipment often fail at different rates in complex manufacturing systems. Moreover, there are timing constraints and resource constraints between jobs, and interruptions may directly or indirectly affect the start time of other jobs via the network. Consequently, integrated scheduling optimization of complex manufacturing systems is required under uncertain random factors.10. Various uncertain factors have led scholars to conduct a robust scheduling study of the FJSP to promote the seamless connection between production organization and equipment maintenance12.Although research on preventive maintenance of equipment is becoming more and more sophisticated, most studies still only consider the random event of equipment failure. Other unpredictable random events occur during the production process, preventing preventive maintenance from being able to prevent all machine failures13 measured robustness by comparing the actual scheduling goal with the initial scheduling goal, and provided a method to measure initial scheduling robustness. For scheduling problems with interval processing times, Zheng et al.14 used the maximum regret value of the actual scheduling target for initial scheduling under the disturbance of uncertain factors to express robustness. A decomposition method based on graph theory was proposed by Kutanoglu et al.15 to achieve scheduling robustness using expected average weighted tardiness as the robustness index. A dual objective Pareto optimization method was used by Xiong et al.16 to simultaneously optimize the performance of the FJSP scheduling and the scheduling robustness under the influence of random machine failures.Robust scheduling consists of defining the robustness of scheduling, specifying the robustness index and the method for measuring it. Based on this, it is also necessary to select the appropriate robust scheduling method according to the characteristics of the problem and the available information to solve the robust scheduling problem. Ba et al.In the above documents, robustness indicators and corresponding measurement methods have been provided in part. Even so, they generally represent the ability of scheduling to maintain the original state or performance in the face of uncertainty. Only a few documents explain the criteria and basis for the design of its measurement method as well as its application and role in robust scheduling research. To make the situation more suitable for practical engineering applications, it is usually necessary to optimize the equipment maintenance centrally and dynamic dispatching as well as the robustness of the scheduling scheme to ensure that the scheduling scheme considering equipment maintenance is adaptable to dynamic processing environments, that is, robust enough to handle dynamic processing environments.17.The manufacturing industry has put forward high demands for universality, adaptability, and robustness of scheduling schemes due to the rapid development of personalized customization. Consequently, closed-loop optimal scheduling based on data-driven approaches has gradually gained a great deal of interest in academia as well as industry. It is impossible to establish a strict optimization model for the production scheduling problem, which is NP-hard, due to the impact of random factors on the robustness of the scheduling scheme. To assist in the decision-making optimization of production scheduling, a simulation system is necessary18 proposed a production scheduling optimization method based on an intelligent factory multi-level simulation system, combining the scheduling optimization and simulation modules. Feng et al.19 introduced a closed loop optimization mechanism in the simulation-based hierarchical optimization modeling framework to solve the problems of scheduling implementation delay, incomplete utilization of equipment, and waste of production resources caused by the open loop implementation of traditional scheduling optimization based on the static optimization model. To adapt the scheduling rules to the characteristics of the semiconductor production line, Yu et al.20 proposed a self-organized scheduling method, which means that the equipment in the production line can automatically call the most effective scheduling rules that will match the optimization goal according to the current production state at any decision-making time. According to the semiconductor production line characteristics, Qiao et al.21 designed a combined scheduling rule. The response surface method is used to optimize the weight parameters in the scheduling rules, to improve the regulations' applicability to other production states.Feng et al.Although scholars have done a lot of research on the data-based closed-loop optimal scheduling problem, the existing methods usually address specific production processes and rarely consider scheduling optimization, control integration, model consistency, and other issues. Although some methods adopt the idea of "closed loop optimization", they do not consider the universality and robustness of the scheduling scheme, let alone the integrated optimization of equipment maintenance, scheduling scheme robustness, and manufacturing system performance.22. In expression prediction problems, artificial neural network is an effective method to make data modeling and is capable of fitting and representing the canonical correlation between input and output23.Deep learning has been counted in the most popular research fields since it was proposed. Being capable of extracting potentially valuable knowledge from complex systems secures the irreplaceable important role of deep learning in big data solutions24. Theoretically, if the layers of the neural network are "deep" enough and numeric quantities of single perceptions in the hidden layer, MLP can approach arbitrary nonlinear functions even if the data distribution is very complex25. However, a network too deep may not be effective. Deep neural network is prone to the phenomenon of gradient appearance, and a network whose hidden layers are too more would lead to overfitting when the amount of data is not significant. Therefore, it is necessary to use some methods to train and optimize the parameters of MLP to make it more consistent with the current problem26.As a typical artificial neural network, multilayer perceptron (MLP) is widely used for remote sensing and prediction of meteorological and natural data, including the combination of MLP and CNN models for atmospheric research and geological survey27. Therefore, the whale optimization algorithm can be used to optimize the algorithm parameters of MLP.With the development of computer science and technology, new meta-heuristic algorithms are emerging, such as the gray wolf optimization algorithm, artificial bee colony algorithm, etc. The whale optimization algorithm is a population-based meta-heuristic algorithm, which has a unique search mechanism: (1) fast convergence speed; (2) strong global search ability; (3) simple and easy to implement; (4) high stability. It has been successfully applied to model prediction and parameter optimizationCombined with the current research status, this paper will propose a joint decision-making method for production scheduling and equipment maintenance and use the multi-objective optimization method based on IWOA-MLP to build an integrated optimization system for robust scheduling and equipment maintenance, to simultaneously optimize the CT ODR, EA, and RM of scheduling schemes. Then the scheduling parameters are adaptively adjusted based on the idea of closed-loop optimization so that the scheduling rules can adapt to the current working conditions, thus effectively improving production efficiency, maintaining the availability of production equipment, avoiding the deterioration of actual scheduling performance, and maintaining the robustness of the scheduling scheme.The scheduling problem of the specification The variables involved in this paper are defined as Table The setting time of equipment, the processing preparation time, and the transportation time of the job are not considered.Equipment maintenance and processing are not allowed simultaneously.n workpieces go through All equipment faults can be maintained, and the processing can continue to work after repair.Processing tasks interrupted due to equipment failure can be continued after equipment maintenance.There is no inherent priority between machines.There is a specific process route between operations of the same job.According to the scheduling problems of this study, the following assumptions are made:The scheduling problem solved in this research has the following constraints:Formula  indicatenstraint  ensures (1) Performances of the manufacturing system.This paper chooses the cycle time and on-time delivery rate as the optimization objectives at the scheduling level. So, the first kind of objective function is as follows:where, (2) Equipment availability.22. Based on the above assumptions, the availability of equipment At the level of preventive maintenance, it is assumed that all machine failures will follow the same exponential distribution, and the failure rate is n in Eq. :10\documIf then Eq.  can be uMake mentclasspt{minimaEquation  can indiThe availability  formula :14\documThen the third optimization objective function is shown in formula :15\docum(3) Robustness of scheduling scheme.Robust scheduling is a scheduling method with a robustness index as the optimization objective. The higher the robustness, the closer the actual scheduling scheme is to the pre-scheduling scheme. The measurement method of the robustness index depends on uncertain factors and preferences. For the uncertain factors of discrete scenarios, the scheduling performance robustness measure 28. Therefore, for the same scheduling problem, the robustness of different scheduling can be qualitatively compared by using relaxation time, and this can be used as a measure of scheduling robustness.The relaxation time between jobs can absorb the disturbance of uncertain factors in the scheduling implementation process, reduce the impact of uncertain factors on the initial scheduling, and improve the robustness of scheduling. Experiments show that scheduling robustness has a strong correlation with the average relaxation time between jobsThis study uses a relaxation-time based measurement method to describe the scheduling robustness index. For scheduling scheme  formula :16\documStandardize  formula :17\documThen the fourth optimization objective of this research is shown in Eq. :18\documTherefore, the multi-objective driven robust optimal scheduling scheme proposed in this paper is to take formula , formulaIn complex manufacturing systems, if the current scheduling scheme is no longer than the optimal scheme due to disturbance factors, it is usually necessary to adopt a dynamic scheduling method to generate a new scheduling scheme to obtain better performance indicators of the production line. To solve the above problems, this paper proposes a multi-performance driven closed-loop adaptive optimal scheduling framework as shown in Fig. As shown in Fig. The dispatching rule embedded in the simulation model is a combined dispatching rule, which integrates many factors, such as equipment maintenance, process constraints, workpiece priority, and urgency of workpiece delivery. Based on the simulation model, we can obtain many sample data and store them in the database. Before establishing the performance prediction model and scheduling parameter optimization model, the feature selection algorithm based on an improved immune algorithm is used to reduce the attributes of the manufacturing system, decreasing redundant features and computing time. The performance prediction model and the scheduling parameter optimization model are implemented based on IWOA-MLP. The former outputs the expected performance according to the operation state of the manufacturing system; the latter can output a combination of scheduling parameters based on the processing status and expected performance data corresponding to excellent samples. The newly generated scheduling parameter combination is updated to the combined scheduling rules to achieve optimal adaptive scheduling.The traditional heuristic dispatching rule does not consider process constraints, which makes the satisfaction rate of process constraints of the production line low. Then leads to the reduction of the ODR of the workpiece. This paper designs a semiconductor production line scheduling rule that comprehensively considers flexible maintenance of equipment, process constraints, and dynamic dispatching. It will consider multiple factors related to process constraints and factors related to flexible maintenance of equipment and job dispatching, such as downstream equipment load, equipment maintenance urgency, job delivery urgency, and equipment availability. The scheduling rule process is shown in Fig. Step 1: Judge whether the workpiece meets the process constraint according to formula . If yes,Step 2: Calculate the process constraint urgency g to Eq. .20\documFormula  means thStep 3: Calculate the delivery urgency of the workpiece according to Eq. .21\documStep 4: Calculate the work piece dispatching priority according to Formula .22\documStep 5: Determine whether the current time is in the maintenance period of the equipment according to formula . If the Step 6: Calculate the emergency degree  formula .24\documStep 7: Calculate the load degree g to Eq. .25\documStep 8: Calculate the unavailability of equipment according to Formula  and FormStep 9: Calculate equipment maintenance priority  formula .27\documStep 10: Normalize the dispatching priority of the workpiece Step 11: Compare the normalized job scheduling priority The whale optimization algorithm is a swarm intelligence optimization algorithm developed by simulating humpback whales' bubble net foraging mode. The algorithm mainly consists of two stages: shrink and surround and position update.(1) Shrink surround.Whales can sense and surround their prey. Because the position of the optimal design in the hunting or search space is inconsistent with the previous position, the WOA optimization algorithm assumes that the current optimal candidate solution is the target prey or close to the optimal solution. In this case, the whale defines the best search agent; then, other search agents will try to change their positions and move closer to the best search agent. The hunting behavior of shrinking enclosure is described by the following formula:The calculation formula of (2) Location update.There are two ways to explore and update whale position, one is spiral position update, the other is random search. To simulate the position update mode of whales at a certain time, ensure that whales have equal probability to choose spiral position update or random search mode at the same time. Set the random number When When  formula  to surroWhen  in Eqs.  and 38)\documentThe initial population position of the algorithm is randomly generated by chaotic Tent mapping to make the population distribution more uniform and accelerate the convergence speed of the algorithm.A new nonlinear parameter The fitness control mechanism is introduced to prevent the stagnation of update and improve the ability of the algorithm to jump out of the local optimum by controlling the population position update.Introducing the Harris Hawk siege mechanism to speed up the hunting of whales.At the end of each whale hunting iteration, the position control mechanism of Gaussian detection is added to increase the optimization accuracy of the algorithm.In the basic whale optimization algorithm, the whale position update process is through the random selection of position update mechanism, so there is a problem that the most effective update method cannot be selected in the whale position update; Moreover, in the search process of the algorithm, there is a problem that multiple iterations do not change the leader Multilayer perceptron, known as Deep Neural Network (DNN), is the simplest neural network structure, which is composed of input layer, hidden layer, and output layer. Each layer consists of multiple neurons. Although its structure is simple, it can learn the deeper nonlinear characteristics of data. And it is suitable for such a huge nonlinear system, i.e., a complex manufacturing system.As shown in Fig. The output layer neurons are responsible for the computer's cognition of the input information. The hidden layer to the output layer can be regarded as a multi category logical regression , more than 800 equipment, 10 processing zones, hundreds of products, and thousands of processes flow. The monthly output of 5-inch chips is up to 28,000 pieces, and the monthly output of 6-inch chips is up to 51,000 pieces.30. To analyze the effectiveness of the scheduling system proposed in this paper, we design simulation experiments from multiple dimensions. The experimental design mainly includes the following three parts.Combined with the actual situation of the semiconductor production line and the needs of the enterprise, this paper selects four performance indicators as the objectives of scheduling optimization: average CT of the workpiece, ODR of the workpiece, EA, and RM of the scheduling scheme(1) Comparison of compound scheduling rules with heuristic rules and other dispatch rules.29.In this paper, we improve the scheduling rules for the two bottleneck processing areas, the photolithography area, and the oxidation area, and adopt the combined scheduling rules that comprehensively consider the equipment and the workpiece. The average CT, ODR, EA, and RM of the scheduling scheme is counted. To evaluate the advantages and disadvantages of combined dispatching rules more intuitively, a variety of comparison experiments are set up for comparison: FIFO, EDD, SPT and the adaptive dispatching rules mentioned in the literature(2) Closed-loop optimization verification based on IWOA-MLP algorithm.To test the effectiveness of the designed "closed-loop optimization based on IWOA-MLP algorithm" link, we conducted simulation experiments and comparisons between the combined scheduling rules and the entire scheduling system. As shown in Fig. (3) Comparison of this scheduling system with the self-organizing scheduling system.20 and the predictive scheduling system proposed in work31 respectively. Analyze and compare the average CT of workpieces, ODR, EA, and RM of scheduling schemes.Also based on the simulation platform of a semiconductor manufacturing enterprise in Shanghai, simulation experiments were conducted on the scheduling system proposed in this paper, the self-organizing scheduling system proposed in workCorresponding to the experimental description part, this part will analyze the results of simulation experiments from three aspects: "combined scheduling rules", "closed-loop optimization", and "scheduling system". Before this, we first make a brief analysis of the attribute selection results of offline work. The production status attribute of the manufacturing system can describe the processing status of the workpiece and the running status of the equipment in the processing area, which can well reflect the real-time running status of the semiconductor production line. This paper selects the attribute selection method based on the improved immune algorithm to screen the attributes of the manufacturing system and selects the 11 attributes that strongly correspond to the performance indicators from the 67 attributes of the manufacturing system. The results are shown in Table To further verify the effectiveness of the combined dispatching rules proposed in this chapter, the combined dispatching rules are compared with FIFO, SPT, EDD, and adaptive dispatching rules. The statistics of average CT, ODR, EA, and RM of scheduling rules are respectively made, and the results are shown in Table 29 is 1. Because these four scheduling rules do not consider predictive maintenance of equipment, the equipment failure rate is 0, so the EA index is 1.The EA index of FIFO, SPT, EDD, and the scheduling rules inThe CT, ODR, and RM of the combined dispatching rule are better than FIFO, because FIFO is first come first processing, which can only reduce the waiting time of the workpiece globally and has poor optimization effect on the overall performance of the system.The ODR and RM of the combined dispatching rule are better than SPT, but the average CT is lower than SPT. This is because SPT preferentially selects the workpieces with short processing time, which can shorten the average CT of the workpieces, but at the same time, it will make the queue length of the workpieces exceed the expectation and may increase the rework rate of the workpieces.The average CT and RM of the combined dispatching rule are better than EDD, but the ODR is lower than EDD. This is because EDD preferentially selects the workpieces with urgent delivery for processing, which can maximize the ODR. However, EDD does not consider the overall status of the production line, so it may not be the most suitable dispatching rule for the current production line status and cannot reflect real-time and dynamic nature.29 in terms of CT and ODR, it can more effectively deal with uncertain events in the production process, so as to more effectively improve production efficiency, maintain machine availability, and avoid deterioration of actual scheduling performance; The scheduling rules described in literature29 do not consider equipment failure and preventive maintenance, and cannot reflect the authenticity of the actual scheduling problem.Although the combined scheduling rule is slightly inferior to the scheduling rule described in the literatureThe following conclusions can be obtained by analyzing Table The simulation experiment compares the scheduling system based IWOA-MLP with the compound dispatching rules. As different scheduling parameter combinations will lead to different performance index values, the experimental results are shown in Table Compared with the "combined scheduling rules", the "four performance driven closed-loop optimal scheduling system" can improve the CT, ODR, EA and RM performance of the system by 5.357%, 2.319%, 8.491%, and 9.537% respectively. The effectiveness of the "performance driven" and "closed-loop optimization" links are illustrated.Compared with the "combined scheduling rules", the closed-loop optimal scheduling system based on machining cycle drive can improve the CT, ODR, EA, and RM performance of the system by 7.872%, 1.912%, 3.066%, and 5.450%, respectively. The method based on machining cycle drive can greatly improve the machining cycle index of the system, indicating the effectiveness of "performance driven".Similar to conclusion 2), compared with the "combined scheduling rule", the closed loop optimal scheduling system based on ODR drive can greatly improve the ODR performance of the system, while the improvement of other performance is small; The EA driven closed-loop optimal scheduling system can greatly reduce the EA performance of the system; The closed loop optimal scheduling system based on RM drive can greatly improve the RM performance of the system.This part of experiment can show the effectiveness of "performance driven" and "closed-loop optimization" in this method at the same time.Based on Table 29 and the predictive scheduling system based on MLP algorithm proposed in literature31. The experimental results are shown in Table To test the effectiveness of the whole system of "Robust Optimal Scheduling System Based on IWOA-MLP Algorithm" proposed in this paper, it will be compared with the self-organized scheduling system proposed in literatureThis dispatching system integrates equipment failure and equipment preventive maintenance. The other two dispatching systems believe that the equipment is always available. Based on this, the CT and ODR generated by the three scheduling systems are comparable, which is sufficient to illustrate the superiority of the scheduling system.Compared with the self-organized scheduling system and the predictive scheduling system, the robust optimal scheduling system based on IWOA-MLP algorithm can improve the RM of the system by 16.931% and 25.568%, respectively. It shows that the robust optimal scheduling system proposed in this paper has high RM while improving the system performance.The proposed method combines MLP and IWOA and belongs to the deep neural network method, which does require longer execution time. So, compared with the other two scheduling methods, this method requires more time to generate new scheduling schemes. Although there are differences in the execution-time of the three methods, they are all within the real-time requirements of industrial scheduling problems.Based on Table In this research, to improve the performances of the semiconductor manufacturing system, we proposed an IWOA-MLP-based scheduling method with a performance-driven and a feedback-mechanism. We designed a dynamic dispatching rule which integrated equipment maintenance, and process constraints, and correlated the real-time status of the manufacturing system. We used numerous samples obtained from a virtual simulation model of an industrial semiconductor manufacturing system to construct a performance prediction model which can output performance estimation according to 11 processing statuses, which were selected through a feature selection method. In addition, we built a parameter optimization model which can output optimized dispatching parameters according to the 11 processing statuses and four predicted performances. Using the parameter optimization model, we could obtain the most suitable dispatching parameters which can update the dispatching rule to adaptively acclimatize to a new production environment.The simulation results of this study indicated that the proposed IWOA-MLP-based scheduling method outperformed other several conventional scheduling policies in average cycle time (CT), equipment availability (EA), on-time delivery rate (ODR), and robustness measure (RM). Moreover, it can self-adaptively satisfy the dynamic environment of the manufacturing system and improve the overall performance of the semiconductor manufacturing system.


This work is mainly intended to investigate the flysch landslide reinforcement measures used in the Smokovac-Mateševo section of the North-South Expressway project in Montenegro. Bentley’s Plaxis software is used for a numerical analysis of sliding surface parameters of flysch strata in the limit equilibrium state. This study analyzes the slope safety factor for rreinforcement measures such as rock bolts, retaining walls, anti-sliding piles, slope unloading and bolt anchoring and obtains an optimal combination of reinforcement application for the flysch landslide. The effects of seismic action on complex stress and the discontinuous stress boundary conditions arising from various reinforcement measures on landslide stability are also examined. The measures applied in this paper can be used as a reference for flysch landslide reinforcement or other similar slope engineering measures. Flysch, a sedimentary structure primarily composed of sandstone, shale, mudstone, and other rock masses, is predominantly found in semi-deep and deep-sea environments . This tyOur study focuses on the complex topography of the Smokovac-Mateševo section of the North-South Expressway construction project in Montenegro, where the flysch stratum is a dominant feature. Comprising of inter-bedded sandstone and thin layers of sandy marl and shale, the flysch formation is especially vulnerable to brittleness, weathering, and softening when exposed to water and air. The area is characterized by a high content of weak rock mass, particularly argillaceous rock along the highway, rendering the flysch formation relatively susceptible to degradation, failure, and in-situ landslides. The details on the region’s geological survey data, including the bulk weight, angle of internal friction, and cohesion, are presented in Despite significant advances in geotechnical slope research, flysch slopes and their corresponding protection technologies remain inadequately studied. Some scholars have examined the effect of geological slope evolution and sliding mechanisms in large flysch formations –23, whilThe construction of roads in flysch regions presents landslide risks when the naturally occurring slopes are disrupted, necessitating comprehensive research into the treatment and protection of unstable flysch formations. The disruption of naturally occurring slopes poses landslide risks for the construction of roads in flysch regions, thus entailing comprehensive research into the treatment and protection of unstable flysch formations. Arbanas et al.  discusseIn response, this paper employs numerical simulation to investigate the stability of flysch slopes and the effect of various landslide reinforcement measures  on the slope safety factor. We used PLAXIS, a widely accepted numerical simulation software, to analyse the stress superposition and discontinuous boundary conditions brought about by seismic events and reinforcement support structures, as well as the subsequent changes in slope safety factors and their impact on slope stability. Given the limited research on the combined effects of flysch landslide reinforcement technologies, this study aspires to offer valuable data on the efficacy of slope protection measures for similar rock formations, in an attempt to provide a reference for future works.The structural analysis in this paper was carried out using Plaxis software. Here, the calculation models comprised the following four types of elements: continuum elements, beam elements, geogrid elements and anchors, numerical simulation network model established is shown in The model design and the calculation process is according to the following five steps: defining the soil materials, creating the geometry, applying the boundary conditions, generating the mesh and performing the analysis.σv = γ·h and σh = K0·σv respectively , with ϕ being the friction angle of the soil).Defining the soil (supporting structures) materials: the parameters for the rock strata and supporting structures are defined using values shown in Tables Creating the geometry: The slope’s dimensions, layers, and any other relevant features, such as retaining walls or anchors are defined and modeled.Applying the boundary conditions: Since the flysch and anti-sliding pile have different stiffness values, it is essential to consider the boundary conditions between rock-soil mass and anti-sliding pile elements. For "Discontinuous boundary conditions," the element stress value at the contact point between the flysch boundary plane and anti-sliding pile should be equal so as to satisfy boundary conditions.Generating the mesh: Automatic mesh generation tool is used to create a customized mesh to ensure that the mesh is fine enough to accurately capture the slope’s behaviour.Performing the analysis: Construction stages are defined for the model, and the analysis is run.The seismicity of the system is considered in the "Inconsistent Boundary Conditions and Seismicity" section. The applied seismic loads correspond to the historic maximum of the project area. In all numerical simulations presented in this paper, slope instability is assumed to be reached when the Factor of Safety (FOS) approaches 1.ϕ = 32.5°, which are the cohesion parameter and internal friction angle of the slope sliding surface, respectively. In the limit equilibrium state, numerical simulation method is used to analyse the relationship between reinforcement measures such as retaining walls, anti-sliding piles, anchor bolts and the safety factor of the slope. Sliding plane strength parameters determined in this step were used for all calculations in the following steps.Since slope failure is determined by the strength of the potentially sliding plane, rather than the strength of the rock mass, we use back analysis to gradually reduce the applied sliding plane strength parameters to reach a Factor of Safety (FOS) near 1.0 , and to As the first measure of treatment, fixing of gravity retaining wall is introduced. The wall is fixed with prestressed anchors, anchored in RC frame cast on the surface and bonded to the rock category E, and partially to the rock behind the fault line. The model shows an increase in global stability. The slope FOS is shown in After applying prestressed anchors on the retaining wall, two rows anti-sliding piles, 1.50 m in diameter, are constructed at the bottom of the slope. The model’s global stability is checked, as well as the contribution of the anti-sliding piles. As shown in Unloading refers to the removal of the upper sliding body on top of the slope. This step involves dividing the upper portion into four parts, showing the changes on global FOS. For calculation, the effect of the anchors with steel mesh was neglected, the mesh structure was adopted for local protection of the slope above the retaining wall, and further, the mesh structure has no effect on global stability. The models and simulation results from the first to the fourth unloading of sliding body upper part are shown in Figs The additional prestressed anchors with bonding part extending through the sliding body were introduced. Global FOS and sliding surface did not change from previous steps as shown in H  and FV , acting on the ground mass are introduced. W is the weight of the sliding mass . The seismic wave is bound to decay when propagating through the heterogeneous flysch layers, but the maximum distance of the flysch layers is relatively small (<50m). The attenuation and reduction of seismic waves is, therefore, not considered in the numerical simulation. Calculation shows that seismicity exhibits a local effect after the introduction of the seismic loads. However, global FOS still stands at a high level of 2.038, as shown in Seismic loading was then introduced based on the previous step for the permanent structure design. The design seismic forces FAccording to the assumption of the above theoretical slope model, the displacement and deformation between the reinforcement structure and the rock and soil mass are discontinuous. The anti-sliding piles are the most effective protection measure. There is a discontinuous boundary of displacement and deformation between the reinforcement and surrounding materials. In this step, the numerical simulation analysis will consider the effect of discontinuous boundary conditions between the anti-sliding pile and the rock and soil mass on the safety factor of the slope. This analysis follows the step where the new anchor bolts are applied.In the numerical analysis, discontinuous boundary conditions are modelled by setting a discontinuous interface between the anti-sliding pile and the rock-soil mass in front of the pile. The stress states of the contacting surfaces of the anti-sliding pile and the rock-soil mass are equal on this discontinuous surface. The safety factor of the slope model is calculated, as shown in The introduction of the described changes in the model reduced the global FOS from 2.262 to 2.081, but the critical sliding surface did not show any change because it is more affected by the local properties. Fu  used theThe stiffness equation of the rock mass is “condensed” on to the stiffness equation of the pile, and the resulting displacement of the rock mass is smaller than when the discontinuous boundary is considered. Moreover, the numerical analysis of this step considers the discontinuous boundary conditions of displacement and deformation between the rock-soil mass and the anti-sliding pile. The calculation shows the displacement is large, which caused a decline in slope stability and the slope’s FOS.H and FV) is consistent with the "result of slope seismic stability" mentioned earlier. Here, the complex stress changes and discontinuous stress boundary conditions are investigated for slope reinforcement. As shown in In this step, seismicity is introduced on top of the previous step for permanent structure design case. The magnitude of earthquake inertia force . Slopes generally slide during the construction of anti-sliding piles at the lower part of the slope and the compression of the pile finally comes into effect to stop further sliding. If anti-sliding piles are adopted first, the unstable slope will not have the support of anti-sliding piles’ anchoring force. The disturbance from construction at the lower part of the slope will then cause serious landslide of the slope. The order of reinforcement measures in this paper can be used as reference in similar projects in the future.


Transport properties are one of the most crucial assets of hydrogel samples, influencing their main application potential, i.e., as drug carriers. Depending on the type of drug or the application itself, it is very important to be able to control these transport properties in an appropriate manner. This study seeks to modify these properties by adding amphiphiles, specifically lecithin. Through its self-assembly, lecithin modifies the inner structure of the hydrogel, which affects its properties, especially the transport ones. In the proposed paper, these properties are studied mainly using various probes (organic dyes) to effectively simulate drugs in simple release diffusion experiments controlled by UV-Vis spectrophotometry. Scanning electron microscopy was used to help characterize the diffusion systems. The effects of lecithin and its concentrations, as well as the effects of variously charged model drugs, were discussed. Lecithin decreases the values of the diffusion coefficient independently of the dye used and the type of crosslinking. The ability to influence transport properties is better observed in xerogel samples. The results, complementing previously published conclusions, showed that lecithin can alter a hydrogel’s structure and therefore its transport properties. Hydrogels are hydrophilic polymeric materials with a three-dimensional structure (or 3D networks of hydrophilic polymers) capable of swelling in aqueous solutions or biological fluids and also possessing unique properties, such as biocompatibility, biodegradability, superabsorbency, viscoelasticity, softness, and responsiveness to external stimuli (pH and temperature) ,2,3. TheIn the case of designing systems for the controlled release and delivery of drugs, special attention should be given to the mechanism of transportation and its correlation with the microstructure of hydrogels. The physical and mechanical properties of such systems can easily be improved (1) by adding a structure modifier; (2) by means of binary systems composed of two or more mixed polymers, such as interpenetrating polymer networks; (3) by using self-reinforced composite materials composed of fibers embedded in a matrix of the same polymer; and (4) by means of the sol-gel reaction to produce silica reinforcement . AnotherThe characterization of hydrogels with a modified internal structure is often based on the analysis of their mechanical properties as well as their biocompatibility and biodegradability. In our previous paper , we provTransport properties generally include viscosity, thermal conductivity, and the diffusion coefficient (diffusivity), which indicates the rate at which specific (per unit volume) momentum, heat, or mass are transferred . StudyinIn this article, we present a study of the transport properties of hydrogel and xerogel systems determined on the basis of the given release experiments. In general, we investigated the diffusion of organic dyes  and calculated the diffusion coefficients for hydrogel systems with different weight concentrations of lecithin as a structure modifier.According to previously published data and to extend the results obtained in the previous article , the samFor each type of crosslinking, samples differing in lecithin concentration were investigated. Lecithin concentrations were selected according to a previous study, and the samples were labeled according to these concentrations ; the reference sample without lecithin addition was marked as “R”.−1) and the negatively-charged dyes eosin B (580.09 g·mol−1) and amido black 10B (616.50 g·mol−1).The probes that were chosen to study the transport properties of the hydrogel samples differed in some of their physicochemical properties (electric charge and molecular weight) as well as in some of their visual properties, such as their absorption maximum. Specifically, the probes chosen were the positively charged rhodamine 6G . The supporting method was scanning electron microscopy (SEM), from which images of the studied hydrogels were obtained and further compared with previously published xerogel images.To characterize the transport properties of the physically crosslinked hydrogel matrix, agarose hydrogels modified by different additions of lecithin were studied. Agarose was chosen because, in the context of amphiphilic modifications, we try to approach the functionality and properties of extracellular matrix (ECM), and agarose hydrogels are frequently used in vitro models across numerous disciplines . HydrogeDeff) was the crucial transport parameter that provided us with information about the transport properties of the studied hydrogels. Specifically, it is a value that describes how each individual dye is released from the hydrogel. The procedure for obtaining Deff and the method to calculate it are described in The effective diffusion coefficient  and previous experience with this organic dye . The resWhat happens to the hydrogel after evaporation of the dispersion medium, and how does this affect the other substances in the gel? To answer this key question, the same hydrogel samples as used in the previous experiment were dried prior to characterization. In this case, however, the dye release from agarose was very quick, and it was not possible to measure the release over longer intervals as was performed for the dye release from non-dried hydrogel samples. For this reason, a fiber UV-Vis spectrometer was used, allowing the measurement of UV-Vis spectra every twenty seconds. In this setup, the absorbance was measured for approximately the first hour, which, for agarose xerogel samples, was enough time for around twenty percent of the dye to be released from the sample . As staThe images obtained from SEM show differences in hydrogel structures between samples with different lecithin concentrations  and how 2+ ions. Alginate has been extensively used as a hydrogel-synthetic ECM and thus is an ideal representative of an ionically crosslinked hydrogel for this study [As an example of an ionically crosslinked hydrogel matrix, sodium alginate crosslinked by calcium ions (2:1 wt. ratio) was studied. Bond formation resulted from the interaction of negatively charged poly(guluronic) acid units of alginate with divalent Cais study . StructuThe first studied model dye was positively charged rhodamine 6G, which was released from an ionically crosslinked alginate hydrogel. Lecithin, which acts as an internal structure modifier, was added to the hydrogel systems in different concentrations. The amount was the key factor that influenced both the hydrogel and xerogel structures and their related transport properties, which can be seen in Deff) was the highest for the reference sample and decreased with increasing lecithin concentration. The differences in Deff values for the samples with distinct additions of lecithin were negligible and thus confirmed the insignificant influence of lecithin concentration on the final value of the diffusion coefficient (in comparison with the reference sample).The amount of released dye was the highest for the reference sample, as this hydrogel did not contain any structures or artifacts that would serve as obstacles or as storage moieties for the dye, and since the alginate hydrogel complex should act as a neutral system , the dyeXerogel samples for ionically crosslinked alginate yielded very similar results to those for physically crosslinked agarose samples. In the case of lecithin additions, the concentration of dye was undetectable, probably because of the blockage of positively charged dye release caused by lecithin throughout the whole duration of the experiment. The time of development of the dye release a was almNegatively charged dyes were also studied. As is obvious from The results for ionically crosslinked xerogels with negatively charged eosin B followed those for physically crosslinked xerogels with the same dye, showing that the reference sample had a much bigger diffusion coefficient than the other samples, their lower coefficients resulting from lecithin addition. According to this, it could be concluded that crosslinking does not have a considerable influence on the diffusion coefficients of xerogels for this type of model drug (dye). The timing of the release of this dye indicates that lecithin slowed down the release since alginate does not interact with eosin B . As mentThe release of the second negatively charged dye, amido black 10B, from ionically crosslinked alginate was significantly slowed down by lecithin additions. The associated diffusion coefficient increased with increasing concentration up to the 1 wt.% sample. During the experiment, the dye release from the samples with the two highest lecithin concentrations was either immeasurable or exhibited big deviations. This was caused by disintegration, which led to the release of both the dye and the lecithin. A similar order of magnitude for the diffusion coefficients  can be oOn the other hand, ionically crosslinked xerogels with negatively charged amido black 10B show the exact same trend as physically crosslinked agarose hydrogels. The value of the diffusion coefficient decreases with increasing lecithin concentration. The results of FTIR analysis using PCA showed that the main differences between the alginate gels without and with lecithin spectrally correspond to the characteristic bands of lecithin .Prior to SEM observation, ionically crosslinked alginate hydrogels were shock-frozen in liquid nitrogen and subsequently lyophilized, as were the agarose hydrogels. As stated before, this procedure was used to minimize the alteration of hydrogel structure; however, for these types of hydrogels, it was not effective. As can be seen from A mixture of PVA ) with chitosan crosslinked by epichlorohydrin was studied as an example of a chemically crosslinked hydrogel. As well as other types of crosslinking, the internal structure and subsequent transport properties of samples were modified by the addition of different amounts of amphiphilic lecithin. Chemically crosslinked samples were studied only in their xerogel form since the preparation method finishes with mixtures in their dried state; thus, rehydrated samples would yield the same results . The onlThe main evaluated parameters were the diffusion coefficients and the amount of released dye. Three different dyes were used to study the transport properties of chemically crosslinked PVA-chitosan samples: positively charged rhodamine 6G, negatively charged eosin B, and amido black 10B. The negatively charged dyes were held inside the gel very strongly, which was because of the small pores in the highly organized structure of the chemically crosslinked gel as well as the interaction of the positively charged chitosan with the negatively charged dye. The only dye that was measurable outside the gel was released immediately after the experiment started; neither long nor short experiments, the latter focused on the first hour of the experiment, were able to provide results that could be analyzed. Only a residual amount of both of these dyes was released from the xerogels; therefore, no diffusion coefficient values could be calculated.Only experiments with the positively charged dye, rhodamine 6G, yielded results sufficient for analyses and for obtaining information about diffusion coefficients. As can be seen in The chemically crosslinked hydrogels were used in their native (hydrated) form for the preparation of samples for morphological study. The prepared xerogels were left to swell in water and were subsequently shock-frozen in liquid nitrogen and freeze-dried. The images obtained using SEM show the layered structure of the hydrogels. The only observable difference between each sample is the smoothness of the cross-sectional view. With increasing lecithin content, the interlayer roughness increases .These results correspond with already-published data for xerogels of these chemically crosslinked hydrogels . Since tThis work focused on the description of the transport properties of differently crosslinked hydrogels and xerogels , which were altered with different concentrations of amphiphilic lecithin as a structure modifier to influence the transport properties of the gels. For characterization of the transport properties of the above-mentioned hydrogel systems, various model probes with different charges were used .The positively charged dye interacted with the lecithin modifier, which meant that for the physically and ionically crosslinked hydrogels, the dye was held within the hydrogel and released very little dye or none at all, regardless of the quantity of the modifier. When the charge of the dyes did not interact with the modifier (in the case of negatively charged dyes), the quantity of lecithin had a significant impact on the speed and amount of dye release. Which meant that the diffusion coefficient was lower for the xerogel samples with lecithin compared to the reference samples. In summary, therefore, we can state that the addition of lecithin to physically or ionically crosslinked hydrogels slows down the release of the model drug and affects the amount of drug released. Chemically crosslinked hydrogels appear to be a system that is also affected by lecithin, but not as significantly as in other types of crosslinking.This work closely follows already-published results dealing mainly with the mechanical properties of the same types of hydrogels and modifications used in this work. Together with our former work, it is possible to compare different morphological characterizations of gels in their hydrogel and xerogel forms.Differently crosslinked hydrogel matrices and the effect of lecithin on their properties were studied. Three different crosslinking mechanisms were studied: physical, ionic, and chemical. Agarose E was purchased from Condalab , calcium chloride from Lach-Ner , and sodium alginate, poly, chitosan, epichlorohydrin, and L-α-Phosphatidylcholine (lecithin) were all purchased from Sigma-Aldrich . Dyes used for diffusion experiments differed in charge: positively charged rhodamine 6G , negatively charged amido black 10B , and eosin B  were used.−1, eosin B—0.015 g·l−1, or amido black 10B—0.01 g·l−1). The sample thus prepared was mixed and dissolved at an elevated temperature. It was then left to stand for 24 h to gel prior to further study [Physically crosslinked hydrogels were prepared using agarose. For every sample, a mixture of agarose (1 wt.%) and lecithin  was weighed in a container. A liquid dispersion medium was then added to the mixture. The dispersion medium was either pure deionized water  or, if needed, a solution of appropriate dye (rhodamine 6G—0.01 g·ler study .3) at a two-to-one weight ratio. Lecithin was added to the alginate solution and stirred for 24 h. A solution of calcium chloride  was sprayed on the layer of sodium alginate with lecithin in order to create a homogeneous hydrogel [Ionically-crosslinked hydrogels were prepared by sodium alginate (2 wt.%) crosslinked by calcium ions of calcium chloride  which was constantly stirred. The water was then routinely measured in a UV/Vis spectrophotometer every ten minutes to obtain the absorbance value for the released dye. The experiment ended when all the dye was released, the amount led to a constant weight, or the sample was damaged or destroyed.2∙s−1.The most fundamental parameter that can express (and consequently be used to compare) the transport properties of hydrogels with inner structural changes resulting from the addition of a modifier, such as lecithin, is the effective diffusion coefficient, expressed as the amount of dye released from the gel per mIt must be noted that calculated diffusion coefficients are not absolute values but only relative (or effective) ones. This means that porosity and tortuosity are hidden in the values of diffusion coefficients. The determination of absolute values of diffusion coefficients requires deeper research focused specifically on the diffusion phenomena of each specific hydrogel. This was not the principal aim of this publication. Therefore, we used effective values for the diffusion coefficients as proxies for comparing the transport properties of the studied hydrogels as a function of the additive concentration and/or type of crosslinking.The time of development of the mass of released dye can be expressed as follows:nt) divided by the amount of substance at equilibrium (nrov). The effective diffusion coefficients were calculated from the slope of the linear regression of this ratio of the amount of substance as a function of the square root of time. The dimensions of the releasing medium  were considered as circles of diameter (δ). From this simple calculation, it is obvious that the release experiments must be performed until the equilibrium state is achieved (when the concentration of released dye does not change over time) [The total amount of released dye at a specific time is expressed as the ratio of the amount of substance at a given time (er time) .During the measurements as well as after evaluation of the results from UV-Vis spectrophotometry, it was found that the release of the dyes from the xerogel samples was too fast for the experimental setup. For this reason, the xerogels were measured again using optical probes and OceanView 2.0 software , which allowed us to obtain UV-Vis absorbance every 20 s for the first hour of the experiment.Morphological characterization of the structures of all prepared hydrogel samples was performed using a ZEISS EVO LS 10  scanning electron microscope. The samples in their native  form were shock-frozen in liquid nitrogen and then immediately freeze-dried. A few small specimens were taken from each studied hydrogel to maintain objective observation. Before observation, the specimens were gold-coated in a sputtering device .The surface morphologies of every sample were recorded. Observations were realized in secondary electron mode, and the accelerating voltage was set to 5 kV to avoid charging the sample.