Trapping In Local Minima Research Articles

Learning in Sinusoidal Spaces With Physics-Informed Neural Networks

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws. However, it turns out to be difficult to train an accurate PINN model for many problems in practice. In this paper, we present a novel perspective of the merits of learning in sinusoidal spaces with PINNs. By analyzing behavior at model initialization, we first show that a PINN of increasing expressiveness induces an initial bias around flat output functions. Notably, this initial solution can be very close to satisfying many physics PDEs, i.e., falling into a local minimum of the PINN loss that only minimizes PDE residuals, while still being far from the true solution that jointly minimizes PDE residuals and the initial and/or boundary conditions. It is difficult for gradient descent optimization to escape from such a local minimum trap, often causing the training to stall. We then prove that the sinusoidal mapping of inputs, in an architecture we label as sf-PINN, is effective to increase input gradient variability, thus avoiding being trapped in such deceptive local minimum. The level of variability can be effectively modulated to match high-frequency patterns in the problem at hand. A key facet of this paper is the comprehensive empirical study that demonstrates the efficacy of learning in sinusoidal spaces with PINNs for a wide range of forward and inverse modelling problems spanning multiple physics domains.

A Hybrid DL Architecture for Improved Generalizability with Self-Adaptive Jaya Optimizer for Diabetic Retinopathy

Anomalies such as microaneurysms, exudates, and hemorrhages are diagnosed by retinal vessel segmentation to identify different phases of Diabetic Retinopathy (DR); several typical ways to detect Hard Exudates (HE) in retinal images have been used to determine the severity of diabetes. This work proposes a hybrid approach to better segment such abnormal cells. It optimizes the learning parameters of a Convolutional Neural Network (CNN) with a nature-inspired optimizer, the Self-Adaptive Jaya Optimization Algorithm (SAJOA). The SAJOA helps in avoiding trapping in local minima. It uses the SAJOA to steer the search for obtaining near-optimal parameter values for the CNN training. We choose the learning parameters such as batch size, dropout rate, learning rate, etc. The batch size affects the batch normalization performance, and the dropout rate involves the regularization property of the model. The near-optimal values of these two parameters help improve the generalization ability of the deep learning architecture. Thus, this hybrid approach improves the CNN performance and generalizability, leading to precise segmentation of unseen data, which aids in diagnosing diabetic retinopathy. The results of many trials were evaluated against the DRIVE dataset; the proposed method achieved accuracy and F1 score on average, higher by 7 to 8% than the state-of-the-art methods.

An evolutionary crow search algorithm equipped with interactive memory mechanism to optimize artificial neural network for disease diagnosis

Artificial neural network (ANN) is an information processing paradigm that loosely models the thinking patterns of the human brain with specifications such as real-time learning, self-adaption, and self-organization. The learning process of ANNs is complex and tackles shortcomings such as a slow convergence rate, learning time-consuming, and local minimum trapping, especially when using gradient-based optimization techniques. Although many metaheuristics have been proposed to arm ANN and solve these weaknesses, ANN learning still needs solution quality. Therefore, this study proposes an evolutionary crow search algorithm (ECSA) to optimize the hyperparameters of ANNs for diagnosing chronic diseases. ECSA introduces an evolutionary search strategy, self-adaptive adaptive flight length, and an interactive memory mechanism to alleviate the canonical crow search algorithm's shortcomings. The evolutionary search strategy and self-adaptive flight length provide a meaningful search strategy in which crows effectively explore and exploit problem spaces by maintaining population diversity. During the search process, the interactive memory mechanism records the best solution obtained during optimization. The performance of ECSA was evaluated and compared with well-known metaheuristic algorithms in terms of local and global search abilities, local optima avoidance, and convergence speed towards the promising area. Then, the results were statistically analyzed. Ultimately, the effectiveness of an adaptation of ECSA named ECSA-MLP for optimizing hyperparameters of the multilayer perceptron network for diagnosing diseases including coronavirus, breast cancer, diabetes, cardiovascular, cervical cancer, Parkinson's, mammography, and acute inflammation was compared with state-of-the-art competitor algorithms. The experimental results indicated the superiority of ECSA over competitor algorithms in optimizing the network.

Improved Tuna Swarm Optimization Algorithm for Engineering Design Problems

Tuna Swarm Optimization (TSO) which is developed by being inspired by the hunting strategies of the tuna fish is a metaheuristic optimization algorithm (MHA). TSO is able to solve some optimization problems successfully. However, TSO has the handicap of having premature convergence and being caught by local minimum trap. This study proposes a mathematical model aiming to eliminate these disadvantages and to increase the performance of TSO. The basic philosophy of the proposed method is not to focus on the best solution but on the best ones. The Proposed algorithm has been compared to six current and popular MHAs in the literature. Using classical test functions to have a preliminary evaluation is a frequently preferred method in the field of optimization. Therefore, first, all the algorithms were applied to ten classical test functions and the results were interpreted through the Wilcoxon statistical test. The results indicate that the proposed algorithm is successful. Following that, all the algorithms were applied to three engineering design problems, which is the main purpose of this article. The original TSO has a weak performance on design problems. With optimal costs like 1.74 in welded beam design problem, 1581.47 in speed reducer design problem, and 38.455 in I-beam design problem, the proposed algorithm has been the most successful one. Such a case leads us to the idea that the proposed method of this article is successful for improving the performance of TSO.

A bio-medical snake optimizer system driven by logarithmic surviving global search for optimizing feature selection and its application for disorder recognition

Abstract It is of paramount importance to enhance medical practices, given how important it is to protect human life. Medical therapy can be accelerated by automating patient prediction using machine learning techniques. To double the efficiency of classifiers, several preprocessing strategies must be adopted for their crucial duty in this field. Feature Selection (FS) is one tool that has been used frequently to modify data and enhance classification outcomes by lowering the dimensionality of datasets. Excluded features are those that have a poor correlation coefficient with the label class, i.e., they have no meaningful correlation with classification and do not indicate where the instance belongs. Along with the recurring features, which show a strong association with the remainder of the features. Contrarily, the model being produced during training is harmed, and the classifier is misled by their presence. This causes overfitting and increases algorithm complexity and processing time. The pattern is made clearer by FS, which also creates a broader classification model with a lower chance of overfitting in an acceptable amount of time and algorithmic complexity. To optimize the FS process, building wrappers must employ metaheuristic algorithms as search algorithms. The best solution, which reflects the best subset of features within a particular medical dataset that aids in patient diagnosis, is sought in this study using the Snake Optimizer (SO). The swarm-based approaches that SO is founded on have left it with several general flaws, like local minimum trapping, early convergence, uneven exploration and exploitation, and early convergence. By employing the cosine function to calculate the separation between the present solution and the ideal solution, the logarithm operator was paired with SO to better the exploitation process and get over these restrictions. In order to get the best overall answer, this forces the solutions to spiral downward. Additionally, SO is employed to put the evolutionary algorithms’ preservation of the best premise into practice. This is accomplished by utilizing three alternative selection systems – tournament, proportional, and linear – to improve the exploration phase. These are used in exploration to allow solutions to be found more thoroughly and in relation to a chosen solution than at random. These are Tournament Logarithmic Snake Optimizer (TLSO), Proportional Logarithmic Snake Optimizer, and Linear Order Logarithmic Snake Optimizer. A number of 22 reference medical datasets were used in experiments. The findings indicate that, among 86% of the datasets, TLSO attained the best accuracy, and among 82% of the datasets, the best feature reduction. In terms of the standard deviation, the TLSO also attained noteworthy reliability and stability. On the basis of running duration, it is, nonetheless, quite effective.

Enhanced Grey Wolf Optimization based Hyper-parameter optimized Convolution Neural Network for Kidney Image Classification

Over the last few years, Convolution Neural Networks (CNN) have shown dominant performance over real world applications due to their ability to find good solutions and deal with image data. However their performance is highly dependent on the network architecture and methods for optimizing their hyper parameters especially number and size of filters. Designing a good CNN architecture requires human expertise and domain knowledge. So, it is difficult in CNN to find sufficient number and size of filters for classification problems. The standard GWO algorithm used for any optimization purpose suffers from some issues such as slow convergence speed, trapping in local minima and unable to maintain balance between exploration and exploitation. In order to have proper balance between these phases, two modifications in GWO are introduced in this paper. A technique for finding optimum CNN architecture using methods based on Enhanced Grey Wolf Optimization (E-GWO) is proposed. The paper presents optimization of hyper parameters (numbers and size of filters in convolution layer) of CNN using E-GWO to improve the performance of the model. Kidney ultrasound images dataset collected from ultrasound centre is used to evaluate the performance of the proposed algorithm. Experimental results showed that optimization of CNN with E-GWO outperformed CNN optimized with traditional GA, PSO and GWO and conventional CNN yielding 97.01% accuracy. At last, the obtained results are statistically validated using t-test.

Using Density Functional Theory for Testing the Robustness of Mobile-Proton Molecular Dynamics Simulations on Electrosprayed Ions: Structural Implications for Gaseous Proteins.

Current experiments only provide low-resolution information on gaseous protein ions generated by electrospray ionization (ESI). Molecular dynamics (MD) simulations can yield complementary insights. Unfortunately, conventional MD does not capture the mobile nature of protons in gaseous proteins. Mobile-proton MD (MPMD) overcomes this limitation. Earlier MPMD data at 300 K indicated that protein ions generated by "native" ESI retain solution-like structures with a hydrophobic core and zwitterionic exterior [Bakhtiari, M.; Konermann, L. J. Phys. Chem. B 2019, 123, 1784-1796]. MPMD redistributes protons using electrostatic and proton affinity calculations. The robustness of this approach has never been scrutinized. Here, we close this gap by benchmarking MPMD against density functional theory (DFT) at the B3LYP/6-31G* level, which is well suited for predicting proton affinities. The computational cost of DFT necessitated the use of small peptides. The MPMD energetic ranking of proton configurations was found to be consistent with DFT single-point energies, implying that MPMD can reliably identify favorable protonation sites. Peptide MPMD runs converged to DFT-optimized structures only when applying 300-500 K temperature cycling, which was necessary to prevent trapping in local minima. Temperature cycling MPMD was then applied to gaseous protein ions. Native ubiquitin converted to slightly expanded structures with a zwitterionic core and a nonpolar exterior. Our data suggest that such inside-out protein structures are intrinsically preferred in the gas phase, and that they form in ESI experiments after moderate collisional excitation. This is in contrast to native ESI (with minimal collisional excitation, simulated by MPMD at 300 K), where kinetic trapping promotes the survival of solution-like structures. In summary, this work validates the MPMD approach for simulations on gaseous peptides and proteins.

A Novel MPPT Controller Based on Mud Ring Optimization Algorithm for Centralized Thermoelectric Generator under Dynamic Thermal Gradients

Most industrial processes generate raw heat. To enhance the efficiency of industrial operations, this raw heat is recovered. Thermoelectric generators (TEG), as solid state devices, provide an excellent application of heat recovery in the form of most manageable electrical power. This work presents a novel MPPT controller based on the Mud Ring Optimization algorithm for a centralized Thermoelectric Generator (TEG) under dynamic thermal gradients. The existing stochastic optimization algorithm for Maximum Power Point Tracking (MPPT) control in renewable energy systems exhibits several limitations that affect its performance in MPPT control. The convergence speed, local minima trap, hyper parameters’ sensitivity toward the population size, acceleration coefficients, and the stopping criterion all impact the convergence stability. In addition to these limitations, sensor noise sensitivity in measurement fluctuates the control system leading to reduced performance. Therefore, the careful design and implementation of the MRO algorithm is crucial to overcome these limitations and achieve a satisfactory performance in MPPT control. The results of this study contribute to developing more efficient MPPT control of TEG systems and implementing renewable energy technologies. The algorithm effectively tracks the maximum power point in dynamic thermal environments and increases the power output compared to conventional MPPT methods. The findings illustrate the efficacy of the proposed controller providing a higher power output (Avg. 99.95%) and faster response time (220 ms) under dynamic thermal conditions achieving 38–70% faster tracking of the GM in dynamic operating conditions.

Retrieval of Subsurface Resistivity from Magnetotelluric Data Using a Deep-Learning-Based Inversion Technique

Inversion is a fundamental step in magnetotelluric (MT) data routine analysis to retrieve a subsurface geoelectrical model that can be used to inform geological interpretations. To reduce the effect of non-uniqueness and local minimum trapping problems and improve calculation speeds, a data-driven mathematical method with a deep neural network was developed to estimate the subsurface resistivity. In this study, a deep learning (DL) inversion technique using a revised multi-head convolutional neural network (CNN) architecture was investigated for MT data analysis. We created synthetic datasets consisting of 100,000 random samples of resistivity layers to train the network’s parameters. The trained model was validated with independent noised datasets, and the predicted results displayed reasonable accuracy and reliability, which demonstrates the potential application of DL inversion for real-world MT data. The trained model was used to analyze MT data collected in the southwestern Athabasca Basin, Canada. The calculated results from the DL method displayed a detailed subsurface resistivity distribution compared to traditional iterative inversion. Since this approach can predict a resistivity model without multiple forward modeling operations after the CNN model is created, this framework is suitable to speed up the computation of multidimensional MT inversion for subsurface resistivity.

Optimized levy flight model for heart disease prediction using CNN framework in big data application

Cardiac disease is one of the most complex diseases globally. It affects the lives of humans critically. It is essential for accurate and timely diagnosis to treat heart failure and prevent the disease. In most aspects, it was not so successful with the traditional method, which uses past medical history. Many existing models had several types of the loss function in traditional CNN can lead to misidentification of the model. To solve this problem, so many scholars have used the swarm intelligence algorithm, but most of these techniques are stuck in the local minima and suffer from premature convergence. In the proposed method, we build up the Levy Flight – Convolutional Neural Network (LV-CNN) depending on the diagnostic system using heart disease image data set for heart disease assessment. Initially, the input Big Data images are resized to reduce the computational complexity of the system. Then, those resized images are subject to the proposed LV-CNN model. Therefore, the LV approach is integrated with the Sunflower Optimization Algorithm (SFO) to reduce loss function occurring in the CNN architecture. Such a combination helps the SFO algorithm avoid trapping in local minima due to the random walk of the levy flight. The proposed algorithm will be simulated using the MATLAB tool and tested experimentally in terms of accuracy is 95.74%, specificity is 0.96%, the error rate is 0.35, and time consumption is 9.71 s. This comparative analysis revealed that the excellence of the proposed model.

Robot path planning based on artificial potential field with deterministic annealing

In the context of motion planning in robotics, the problem of path planning based on artificial potential fields has been examined using different algorithms to avoid trapping in local minima. With this objective, this paper proposes a novel method based on a deterministic annealing strategy to improve the potential field function by introducing a temperature parameter to increase the robot’s obstacle avoidance efficiency. The annealing and tempering strategies prevent the robot from being trapped at the local minima and allow it to continue towards its destination. The initial path is optimised using an annealing algorithm to enhance the overall performance. The time, length and success rate of the planned path measures the quality of the solution. Simulation results and comparative experiments demonstrate that the proposed algorithm can solve path planning in different environments. The proposed algorithm is suitable for complex environments with convex or non-convex polygon obstacles.

Piecewise-potential-field-based path planning method for fixed-wing UAV formation

The multi-UAV path planning method based on artificial potential field (APF) has the advantage of rapid processing speed and the ability to deal with dynamic obstacles, though some problems remain—such as a lack of consideration of the initial heading constraint of the UAVs, making it easy to fall into a local minimum trap, and the path not being sufficiently smooth. Consequently, a fixed-wing UAV formation path planning method based on piecewise potential field (PPF) is proposed, where the problem of UAV formation flight path planning in different states can be solved by suitable design of the PPF function. Firstly, the potential field vector can be used to represent the potential field functions of obstacles and target points to meet the kinematic constraints of the UAV. Secondly, the local minimum region can be detected, the additional potential field vector being set to break away from this region. Finally, the change rules of the potential field vector of a UAV in the formation reconstruction scene can be designed, a smooth formation flight track being assured by adjusting the corresponding speed of each UAV track point. Considering the path planning of a five-UAV formation as an example, we conducted simulation experiments. The results showed that—compared with the existing methods based on APF—the results obtained using the PPF-based method considered the initial heading limits of the UAVs, the planned path being considerably smoother. Moreover, the proposed method could plan multiple UAV tracks, satisfying the known constraints without conflict in complex scenarios.

A Rayleigh Wave Globally Optimal Full Waveform Inversion Framework Based on GPU Parallel Computing

Conventional gradient-based full waveform inversion (FWI) is a local optimization, which is highly dependent on the initial model and prone to trapping in local minima. Globally optimal FWI that can overcome this limitation is particularly attractive, but is currently limited by the huge amount of calculation. In this paper, we propose a globally optimal FWI framework based on GPU parallel computing, which greatly improves the efficiency, and is expected to make globally optimal FWI more widely used. In this framework, we simplify and recombine the model parameters, and optimize the model iteratively. Each iteration contains hundreds of individuals, each individual is independent of the other, and each individual contains forward modeling and cost function calculation. The framework is suitable for a variety of globally optimal algorithms, and we test the framework with particle swarm optimization algorithm for example. Both the synthetic and field examples achieve good results, indicating the effectiveness of the framework.

Bayesian Seismic Source Inversion With a 3‐D Earth Model of the Japanese Islands

AbstractWe present probabilistic centroid‐moment tensor solutions inferred from the combination of Hamiltonian Monte Carlo sampling and a 3‐D full‐waveform inversion Earth model of the Japanese islands. While the former provides complete posterior probability densities, the latter allows us to exploit waveform data with periods as low as 15 s. For the computation of Green's functions, we employ spectral‐element simulations through the radially anisotropic and visco‐elastic model, leading to substantial improvements of data fit compared to layered models. Focusing on 13 Mw 4.8–Mw 5.3 offshore earthquakes with a significant non‐double‐couple (non‐DC) component, we simultaneously infer the centroid location, time and moment tensor without any a priori constraints on the faulting mechanism. Furthermore, we perform the inversions across several period bands, varying the minimum period between 15 and 50 s. Accounting for 3‐D Earth structure at shorter periods can increase the double‐couple (DC) component of an event, compared to the GCMT solution, by tens of percent. This suggests that non‐DC events in the GCMT catalog may result from unmodeled Earth structure and the related limitation to longer‐period data. We also observe that significant changes in source parameters, and the DC component in particular, may be related to only small waveform changes, thereby accentuating the importance of a reliable Earth model. Posterior probability density distributions become increasingly multimodal for shorter‐period data that provide tighter constraints on source parameters. This implies, in our specific case, that stochastic approaches to the source inversion problem are required for periods below ∼20 s to avoid trapping in local minima.

A Review on Path Planning and Obstacle Avoidance Algorithms for Autonomous Mobile Robots

Mobile robots have been widely used in various sectors in the last decade. A mobile robot could autonomously navigate in any environment, both static and dynamic. As a result, researchers in the robotics field have offered a variety of techniques. This paper reviews the mobile robot navigation approaches and obstacle avoidance used so far in various environmental conditions to recognize the improvement of path planning strategists. Taking into consideration commonly used classical approaches such as Dijkstra algorithm (DA), artificial potential field (APF), probabilistic road map (PRM), cell decomposition (CD), and meta-heuristic techniques such as fuzzy logic (FL), neutral network (NN), particle swarm optimization (PSO), genetic algorithm (GA), cuckoo search algorithm (CSO), and artificial bee colony (ABC). Classical approaches have limitations of trapping in local minima, failure to handle uncertainty, and many more. On the other hand, it is observed that heuristic approaches can solve most real-world problems and perform well after some modification and hybridization with classical techniques. As a result, many methods have been established worldwide for the path planning strategy for mobile robots. The most often utilized approaches, on the other hand, are offered below for further study.

A combined GA and DLS parallel algorithm for multimode Rayleigh wave inversion

Multichannel analysis of surface waves (MASW) is a vital method in near-surface exploration. Linear algorithms, such as damped least square method (DLS), are highly dependent on the initial model and are prone to trapping in local minima. While nonlinear algorithms such as genetic algorithm (GA) are globally optimal but inefficient, they are not very practical for complex calculations.In this paper, we propose a combined GA and DLS parallel algorithm (GA-DLS), which has a global search capability due to the GA framework, and has a quick local search capability due to the DLS parallel computing. To simulate the earth model in complex near-surface conditions, we set a low-velocity layer among a layered earth model (LVL) and a high-velocity layer among a layered earth model (HVL), we perform the inversion with DLS, GA, and GA-DLS, respectively. The comparison shows that the GA-DLS inversion gets an efficient and accurate result. Finally, we use the GA-DLS algorithm to invert the field data and achieve good results, verifying the effectiveness of the algorithm.

A Nonlinear Multigrid Method for the Parameter Identification Problem of Partial Differential Equations with Constraints

In this paper, we consider the parameter identification problem of partial differential equations with constraints. A nonlinear multigrid method is introduced to the process of parameter inversion. By keeping the objective functions on coarse grids consistent with those on fine grids, the proposed method reduces the dimensions of objective functions enormously and mitigates the risk of trapping in local minima effectively. Furthermore, constraints significantly improve the convergence ability of the method. We performed the numerical simulation based on the porosity identification of elastic wave equations in the fluid-saturated porous media, which suggests that the nonlinear multigrid method with constraints decreases the computational expenditure, suppresses the noise, and improves the inversion results.

Adaptive simulated annealing with greedy search for the circle bin packing problem

We introduce a new bin packing problem, termed the circle bin packing problem with circular items (CBPP-CI). The problem involves packing all the circular items into multiple identical circle bins as compact as possible with the objective of minimizing the number of used bins. We first define the tangent occupying action (TOA) and propose a constructive greedy algorithm that sequentially packs the items into places tangent to the packed items or the bin boundaries. Moreover, to avoid falling into a local minimum trap and efficiently judge whether an optimal solution has been established, we continue to present an adaptive simulated annealing with greedy search (ASA-GS) algorithm that explores and exploits the search space efficiently. Specifically, we offer two novel local perturbation strategies to jump out of the local optimum and incorporate the greedy search to achieve faster convergence. The parameters of ASA-GS are adaptive according to the number of items so that they can be size-agnostic across the problem scale. We design two sets of new benchmark instances, and the empirical results show that ASA-GS completely outperforms the constructive greedy algorithm. Moreover, for the problem of packing unequal circles to a fixed size circular container to maximize the area of circles packed, ASA-GS outperforms the advanced formulation space search (FSS) algorithm in terms of solution quality and computational cost, inferring that our approach is not only adapted to CBPP-CI but also works well when the number of bins is reduced to one to become a typical circle packing problem.

A Hybrid Approach of Spotted Hyena Optimization Integrated with Quadratic Approximation for Training Wavelet Neural Network.

Spotted hyena optimization (SHO) is one of the newly evolved swarm-based metaheuristic optimization methods based on the social life cycle of hyenas. In recent times SHO is being applied to various engineering applications as well as to solve real-life complications. In this paper, we have hybridized SHO with quadratic approximation operator (QAO), termed as QASHO. The proposed QASHO has been scrutinized to enhance the exploitation ability, aiming to achieve global optimum, as QAO performs better within the local confinement region. Furthermore, the proposed approach shows improved strength in terms of escaping from the local minima trap, as in each iteration we discard some of the worst individuals by some suitable ones. To validate the proficiency of the proposed QASHO approach, 28 standard problems have been preferred in connection with IEEE-CEC-2017. The outcome observed from the suggested method has also equated with contemporary metaheuristic approaches. To prove the statistical significance, a nonparametric test has also been accomplished. Additionally as a real-life application, the suggested approach QASHO has utilized to train wavelet higher-order neural networks (HONN) by choosing datasets from the UCI store. The above correlations reveal that QASHO can deal with complex optimization tasks.

МЕТАЭВРИСТИКА НА ОСНОВЕ ПОВЕДЕНИЯ КОЛОНИИ БЕЛЫХ КРОТОВ

Optimization algorithms inspired by the natural world have turned into powerful tools for solvingcomplex problems. However, they still have some disadvantages that require the study of new andmore advanced optimization algorithms. In this regard, when solving NP complete problems, there isa need to develop new methods for solving this class of problems. One of these methods can bemetaheuristics based on the behavior of a colony of white moles. This paper proposes a newmetaheuristic algorithm called the blind white moles algorithm. This algorithm was developed basedon the social behavior of blind moles in search of food and protecting the colony from intruders. Theproposed solution will be able to overcome many disadvantages of conventional optimization algorithms,including falling into the trap of local minima or a low convergence rate. The purpose of thiswork is to develop an algorithm for optimizing a complex objective function. The scientific noveltylies in the development of a genetic algorithm based on the behavior of a colony of white moles forsolving NP complete problems. The problem statement in this paper is as follows: to optimize thesearch for solutions to complex functions by applying an algorithm based on the behavior of a colonyof white moles. The practical value of the work lies in the creation of a new search architecture thatallows using the developed algorithm for the effective solution of NP complete problems, as well asconducting a comparative analysis with existing analogues. The fundamental difference from theknown approaches is in the application of a new bioinspired search structure based on the behaviorof a colony of white moles, which will allow to exclude falling into a local minimum or a low convergencerate. The presented results of the computational experiment showed the advantages of the proposedmultidimensional approach to solving the problems of placing VLSI elements in comparisonwith existing analogues. Thus, the problem of creating methods, algorithms and software for solvingNP complete problems is currently of particular relevance.