Test Scheduling and Test Time Minimization of System-on-Chip Using Modified BAT Algorithm

System-on-Chip (SoC) is a structure in which semiconductor components are integrated into a single die. As a result, testing time should be reduced to achieve a low cost for each chip. Effective test scheduling can reduce the SoC testing time, which is more challenging due to its complexity. In this paper, the modified BAT algorithm-based test scheduling is proposed. Testing is carried out on the SoC ITC’02 benchmark circuits. The Modified Bat method is a recently heuristic algorithm that performs global optimization by imitating bat echolocation. Compared to other state-of-the-art algorithms, the Modified BAT Optimization method reduces testing time on SoCs. This paper improves the algorithm’s exploration process by adjusting the equation for bat loudness (A0) and pulse emission rate (r). The modified BAT algorithm converges to the optimal solution faster. It has been used in 14 international standard test functions. The test results indicate that the modified BAT algorithm has a fast convergence speed, which minimizes the testing time compared to other evolutionary algorithms on the ITC’02 SoC benchmark circuits.


I. INTRODUCTION
According to Moore's law, the integration level doubles every 1.5 years because of the improvement in semiconductor technology. Complex functional electronic products at the micro-level are developed due to this advancement in IC design. The SoC contains over a million gates, memory, cores, and analog and digital blocks on a single chip. On a larger scale, IC design and manufacturing present significant challenges such as power consumption and thermal issues. Because testing requires a lot of switching, the test mode requires more thought than the standard model. In SoC testing, modular testing is an effective strategy for embedded cores [1], [2].
The transmission of test data to cores is a significant problem at the system level. The test wrappers isolate the The associate editor coordinating the review of this manuscript and approving it for publication was Zhenzhou Tang . cores by adapting the Test Access Mechanism (TAM) width to the inputs-outputs of wrappers. Figure 1 shows the SoC testing block diagram. The wrapper and TAM optimization are critical since test time varies with wrappers and TAM width design. It also depends on how TAM wires are attached to the wrapper chains. CPU, memory, DSP, and mixed-signal modules are some of the cores that are used. To reduce test time, multiple cores are tested concurrently. All requirements must be approachedwith caution. The major constraint in the core-based design is the interface between TAM and cores. Test responses and stimuli are stored and analyzed [3].
There are different description levels for hardware in which cores can be categorized and used as hard, soft, and firm cores. In soft cores, more implementation is performed by the designer. They are independent of the process and also flexible. The hard cores are developed for expectable performance, but are not flexible. The firm core characteristics lie between soft and hardcore. Each core is tested as a separate VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ unit in the modular core-based design. The system integrator located the cores on the die to test with their test data. These cores cannot be accessed directly from the SoC pins. Test resources and cores are accessed through the design of the test architecture. So,the test schedule is the major challenge of the modular test approach. In test scheduling, the main operation is accessing the testing order of data where the testing of each core consumes less time. Cores are arranged in various ways in a test schedule called an NP-hard problem. While performing test scheduling, the maximum value must not be reached for the core's power and TAM width. There are three scheduling techniques for the core: partitioned, non-partitioned, and pre-emptive techniques for scheduling. The core is immediately scheduled in partitioned scheduling after testing the previous core.
No new core will be tested in a non-partitioned schedule till all the core tests are carried out during the session. Core testing may be interrupted in a pre-emptive technique and resumed later, but all the cores must be tested. The major challenge leading to considerable test time in the scheduling process is the occurrence of test data volume in an enormous amount. Simultaneous core testing in a modular fashion is done to overcome this challenge. The cores are depicted in Figure 2. The bin region that has not been filled is referred to as idle time.
The benchmark circuits are a collection of benchmarks proposed at the International IEEE Test Conference [4]. Table 1 details the ITC'02 benchmarks. Tables 2 and 3 provide details of the D695 and P22810 benchmarks. Under various load conditions of the SoC benchmark circuits, the role of the optimization techniques in testing is to reduce the testing time taken as the objective function shown in equation (1) below. where S o and S i are the scan chain length of the output and input, and t pi is the core i test pattern for the benchmark circuit for optimization. This research suggests optimal test scheduling algorithms for reducing test time. The proposed strategy can lower test costs by indirectly reducing test time.
The contributions to the paper are as follows: 1. The Modified BAT algorithm is used for the test schedule to achieve the optimal testing time of the System-on-Chip.
2. The efficiency of heuristic algorithms is evaluated by computing their performance over a range of TAM widths on the two ITC'02 benchmarks, D695 and P22810.
The proposed Modified BAT algorithm is compared to seven state-of-the-art algorithms for SoC test scheduling. Based on the results from MATLAB simulations, the proposed algorithm is evaluated under various TAM widths, reducing the test time than the other heuristic algorithms.

II. MOTIVATION
Test application time increases with an increase in the complexity of the system. This paper, uses various optimization approaches such as GOA, MFO, MVO, CPSOGA, BBO, SCA, and Modified BAT algorithms to optimize the test time for d695 and p22810 circuits. The given cost function is minimized by solving the SoC test planning problem to minimize the test time. The motivation of this research is to reduce testing time analysis for various TAM widths.

III. LITERATURE REVIEW
Darwin's evolutionary algorithms, which rely on the survival of the most important principle, could be considered optimization techniques. According to Darwin's theory, the fittest individuals are more likely to survive in nature [5]. Genetic Algorithms (GA) work on solution representation in binary format, whereas evolution strategies and differential evolution support solutions with absolute values [6]. The GA implementation methodology is of two levels. The initial solution is provided at the first level for GA. This method can improve efficiency and throughput in the second level with only a tiny amount of increased design space-PSO-based non-preemptive test scheduling proposed by Xu et al. [7]. Ant Colony algorithm has been applied to many optimization areas. ABC performs better in large-scale global, numerical, and combinational optimization.
The BAT algorithm improves outcomes for optimizing lower-dimensional problems, whereas it is difficult for higher-dimensional problems since the BAT algorithm converges faster. The differential evolution algorithm uses selection, crossover, and mutation to apply to continuous function optimization. Genetic Algorithm (GA), Harmony Search Method (HSM), ACO, Simulated Annealing (SA), and PSO are meta-heuristic approaches applied to resolve optimization problems identified by researchers. The algorithms described above deal with continuous and discrete variables that do not need any objective function gradient and handle both continuous and discrete variables. The issue of SoC hierarchy is discussed in the hierarchical awareness of the test planning system used for TAM optimization. Table 4 shows various recent heuristic optimization algorithms. In Ant Colony Optimization (ACO) [8], [9], at each iteration, when the test core number reduces, the test time increases, leading to an ineffective output, but the count remains constant. This problem is solved by the Modified ACO technique [10]. The Modified ACO examines the ant count will decrease if the core count decreases.
The Grasshopper Optimization Algorithm (GOA) [11] algorithm's optimization process is inspired by the movement of a grasshopper colony. Their actions resemble the solution to the optimization problem. The Moth Flame Optimization (MFO) [12] is the simulation of moths' unique ability to navigate at night. The moth navigated at night using a process known as transverse orientation. The Multi-Verse Optimizer (MVO) algorithm [13] is based on three cosmological ideas: wormholes, white holes, and black holes. Exploitation and exploration are carried out with the help of mathematical models of these three concepts. In the CPSOGSA [14], [15] algorithm, the diversification strength of GSA is combined with the high exploitation capabilities of PSO. The ability of the CPSOGSA to avoid local minima stagnation and accelerate convergence will be tested.  The ecological distribution of organisms inspires the BBO algorithm [16] in a specific ecosystem. The Sine Cosine Algorithm (SCA) [17] generates several fluctuating and random solutions. SCA has a fast convergence speed, which helps to avoid local optima.
Rohini et al. [39] proposed DVFS-based SoC test scheduling solutions for optimization through selecting clock frequency and supply voltages election. Marrouche et al. [40] proposed the Process Algebra (PA) algorithm. To save time, Karaboga et al. [41] proposed the Fuzzy and PA algorithms. Test scheduling is concurrent, and various constraints are to be considered. In Strength Pareto Evolutionary Algorithm (SPEA) [42], the mutation and crossover operators are used every generation.
A solution is found by swarm-based optimization algorithms using the trial-and-error method. The most effective swarm-based optimization technique is the behavior of peerto-peer learning. The recent count of this category is the ABC optimization algorithm. It contains a group of probable solutions similar to other optimization techniques dependent on population. The food source of a honey bee indicates potential solutions. The amount of nectar (food source quality) determines fitness. In modified ABC population's average fitness value helps to converge faster and prevents premature convergence [43]. The firefly algorithm simulates the natural behavior of fireflies.
The intensity of light or brightness is found using the objective problem function of the firefly's attractiveness β.
Test time is minimized by exchanging and compressing tests in one system. When the difficulty (i.e. the number of test alternatives) increases, the optimization time increases. The research presents a testing approach in SoC that combines test wrapper, test access design, test data compression, and testing schedule.

IV. PROPOSED WORK A. BAT ALGORITHM
BAT algorithm is an approach focused on the behaviour of bat echolocation. Bats can discriminate the various types of insects and find their prey even in complete darkness. Bats employ a variety of sonar to sense echolocation techniques to prey. They trace their staying splits and evade difficulties in the dark. During prey search, bats fly with the velocity vi at the frequency f min , changing their loudness A0 and wavelength λ. They emit pulse wavelength, which can be adjusted automatically. This pulse emission rate is dependent on the target proximity. Most bats employ echolocation only to a particular degree. Microbats use echolocation extensively, and this behavior makes them famous [45], [46]. Figure 3 represents the Testing Time vs. Input data's of D695 SoC. When micro bats release a loud sound pulse, they observe its echo, which bounces from the things around them. Based on the vibrations, species differ in properties associated with the hunting strategy. Depending on the type of species, the bandwidth of their signals varies and gets improved by added harmonics. Each pulse exists only up to 8 to 10ms, but it has a frequency of 20-150 kHz, which is constant. When the prey is hunted, the pulse emission rate speeds up to 200 pulses per second. The emitted pulse intensity is at a maximum of 110dB, which is in the ultrasonic region. The intensity is high while the bat searches for its prey, whereas the intensity is lesser while coming towards the prey. Microbats avoid small obstacles like human hair. They build up a three-dimensional surroundings situation using time variance among two ears. They can sense the prey's moving speed, orientation, and target distance. The wing flap rate of target insects induces a Doppler effect that helps the bats discriminate the targets. These bats are susceptible to smell and also have good eyesight. Bats employ a mixture of all the senses for smooth navigation and effectual prey recognition.
Necessary steps in BAT algorithm: STEP 1: Parameters are initiated by setting the original values.  STEP 2: Generation of the random initial population where the initial position 'x 0 ', initial velocity 'v 0 ', and initial frequency 'f i ' is considered a solution.
STEP 3: For every solution, objective function is calculated, and the original population is evaluated. The values of r i and A i are initialized by fine-tuning the velocity 'v i ' and position 'x i ' so that the generation of the population is made.
where β is a random number following a uniform distribution. STEP 4: The target function is measured. STEP 5: The local search iteration method is used every time. Therefore, the best-found solution can be improved. STEP 6: A new solution is created randomly and accepted by a parameter with certain proximity. Whenever the volume of pulse emission increases, the loudness decreases. As given below, A i and r i values get updated.
where γ and α are constants. STEP 7: The best solution is selected. Repeat the process until the criteria for termination are satisfied, and the complete solution is obtained. The BAT algorithm uses the echolocation techniques of the bats where obstacles are detected and prevented with the help of sonar rays. The pulse rate varies from 0 to 1, where 0 refers to the maximum emission rate.

B. MODIFIED BAT ALGORITHM
The BAT algorithm's exploration process is enhanced by adjusting r and A [47], [48], [49], [50], [51], [52]. The proposed modified BAT algorithm explores search space more effectively by enhancing the exploration component. In the BAT algorithm, the bat searches the space and possesses only one loudness and pulse emission rate.
In the modified BAT algorithm based on the problem's dimension, pulse rate and loudness are balanced to an equal number. BAT can search the space effectively using this modified BAT approach. Echolocation is the mechanism employed by bats for hunting. Depending on echolocation capability, bats may locate their food and differentiate insects even in darkness. The Modified BAT algorithm can be applied for various benchmarks like multimodal, unimodal, and shifted types with different dimensions by considering upper and lower boundaries from the real-valued vectors with the number 'n' and the dimension 'd'.
where i = 1, 2 . . . n, and j = 1, 2 . . . d; x max j , x min j are the dimension j th upper and lower boundaries. The frequency, position, and velocity of BAT for future iterations are evaluated using the equations 3, 4 and 5.
β ∈ [0, 1], x * denotes the solution of BAT having the best fitness value. β represent a randomly generated number. Among the best solution, one of the existing solutions is selected, and hence a new candidate solution is made using the random walk.
Pulse emission rate and loudness are initialized to generate the population by adjusting velocity and position given in the form of the equations 6 and 7.

V. RESULTS AND DISCUSSIONS
The Modified BAT algorithm is tested on 14 benchmark functions (f 1 to f 14 ) with varying dimensions, as shown in  Figures 3 and 4 show the D695 SoC benchmark data. The input data are the internal scan chain, inputs and test patterns, minimum chain length, number of outputs, and maximum chain length. Figure 4 represents a 3D model of the test function. The algorithm's performance is measured using Standard deviation, Mean and Best. A common approach for measuring the algorithm's effectiveness is the Mean Value Test (MV), which characterizes the algorithm's convergence accuracy and optimization capabilities by providing the data set's mean value. Standard Deviation (SD), which displays the SD of the data set and demonstrates the stability of the improved algorithm, is another good technique for evaluating the algorithm's performance.
Before running the algorithms GOA, MFO, MVO, CPSOGA, BBO, SCA, and Modified BAT, several parameters must be set. Table 5 shows the initial values of the parameters for GOA, MFO, MVO, CPSOGA, BBO, SCA, and Modified BAT algorithms.
The seven algorithms use the same experimental parameters during the testing process: the particle is 60, the number of iterations is 100, and the F1-F14 dimensions are 100. A 500GB memory Intel(R) Core(TM) i3 -7100T processor running at 3.40GHz powers the experimental test environment. The MATLAB version is MATLAB (2019b). The optimization results of the seven algorithms are compared in Table 6.
, m = 10 (23) VOLUME 10, 2022 To validate the modified BAT algorithm performance, this section compares it to the performance of GOA, MFO, MVO, CPSOGA, BBO, and SCA. Figure 6 depicts the simulation results of the f1 to f14 test functions. Figure 4 is the pictorial Explanation of 3D model of 14 various test function which adapted in this research work. Figure 6 is concern about Comparison of Convergence curve for f1 to f14 test functions. Correlation test that we've done both in this segment and in the Examination Test for Improper Integrals, that it won't generally be the denominator that is driving the assembly or disparity. Some of the time the numerator will decide whether something will merge or wander so don't get excessively locked. The examination tests are utilized to decide union or disparity of series with positive terms. If each term in one series is not exactly the relating term in some concurrent series, it should unite as well. In request for a series to join the series terms should go to focus in the breaking point. On the off chance that the series terms don't go to focus in the cutoff then it is absolutely impossible that the series can meet since this would violate the hypothesis Wilcoxon's rank-sum test [X] determines whether the Modified BAT results were statistically VOLUME 10, 2022    significant (5% significance level). Table 6 shows the p values for Modified BAT across all benchmark functions f 1 through f 14 . In this table 6, NA stands for ''not applicable,'' indicating that the related method could not be statistically compared in this test.  The algorithms convergence curves on f 1 to f 14 functions are depicted in Figure 5. The Modified BAT method has a faster convergence rate, as shown in the diagram. Based on VOLUME 10, 2022  According to all test results, the improved BAT method improves convergence speed in most cases and shows a good optimization effect in convergence accuracy. When the algorithm's convergence speed and optimization correctness are guaranteed, the algorithm's robustness is enhanced.      8 and 9 show the box plot of test time and TAM width of Modified BAT for D695 and P22810. In this container plot, The case length gives a sign of the example fluctuation and the line across the crate shows where the example is focused. The place of the case in its bristles and the place of the line in the container additionally lets us know whether the example is symmetric or slanted, either to one side or left long tell n box implies that values are slanted towards one side of the information or the other. Presently information can be emphatically or adversely slanted in the event that it's not balanced. In information that is emphatically slanted, the long tail is in the positive course. Figures 10 and 11 show a three-dimensional plot of Modified BAT test time and TAM width for D695 and P22810. This part presents an illustration of ongoing revolution of a 3D surface plot. The information utilized are from the Tests dataset. it is useful to see both the wires of the model and the 3D radiation plot at the equivalent time.plot3( X, Y, Z ) plots arranges in three dimensional space. To plot a bunch of directions associated by line fragments, determine X, Y, and Z as vectors of a similar length. To plot numerous arrangements of directions on similar arrangement of tomahawks, determine something like one of X, Y, or Z as a network and the others as vectors. Threelayered (3D) impacts can be utilized to give profundity and add visual effect on diagrams in paginated reports.3D Representation is a significant piece of the plan cycle. It makes the plan cycle simpler for the architects and the clients. It permits the client to see a visual presentation of their home, even before the end result is done. This makes the plan cycle quicker and more straightforward. Figures 12 and 13 provide the test time for the different proposed algorithms for the two benchmarks.
The results show that the Modified BAT algorithm reduces testing time by a certain percentage when compared to the other algorithm. In comparison to GOA, MFO, MVO, CPSOGA, BBO, and SCA algorithms, the Modified BAT optimization algorithm reduces testing time by 15%, 9%, 7%, 5%, 10%, and 13% for d695 SoC and 14%, 8%, 7%, 5%, 9%, and 12% for p22810 SoC. As the TAM width increases, the testing time decreases due to the increased number of partitions.

VI. CONCLUSION
This paper solved the TAM optimization and test scheduling problems using a meta-heuristic approach. The proposed optimization algorithm is tested in SOCs D695 and P22810. Testing time of GOA, MFO, MVO, CPSOGA, BBO, SCA, and Modified BAT algorithms are estimated. Among the algorithms, the modified BAT algorithm performs better than the others. When compared with GOA, MFO, MVO, CPSOGA, BBO, and SCA algorithms, the test time of the Modified BAT Algorithm has been reduced to 15%, 9%, 7%, 5%, 10%, and 13% for d695 SoC and 14%, 8%, 7%, 5%, 9% and 12% for p22810. The proposed method outperforms the competition in terms of exploiting the optimum and provides advantages in terms of exploration, according to the findings. More research is required to develop an optimal list schedule and find the optimal number of partitions and partition locations. In the ITC'02 circuits, the Modified BAT algorithm outperformed other algorithms in finding optimal results in most cases. Algorithms such as Hybrid WOA-SA, Artificial Fish Swarm Algorithm, and Dragonfly Algorithm may be used in the future to reduce test time. BHEKISIPHO TWALA (Senior Member, IEEE) is working as a Research Scientist at Digital Transformation Portfolio, Tshwane University of Technology, Pretoria West, Pretoria, South Africa, with over 20 years experience in putting mathematics to scientific use in the form of data comparison, inference, analysis, and presentation to design, collect, and interpret data experiments surrounding the fields of transport, medical, artificial intelligence, software engineering, robotics and most recently in electrical and electronic engineering science. A track record of publications in conferences and journals and the ability to communicate scientific ideas to an informed lay audience. Plans for future research work will, of course, be influenced by the ideas and opportunities which present themselves at my employer, but the intention is to continue exploring problems in the areas of machine learning (artificial intelligence) and statistics and be committed to the highest levels of professional and personal excellence.