Covariance Matrix Adaptation Research Articles

Prioritization of model smell refactoring using a covariance matrix-based adaptive evolution algorithm

The refactoring process enhances the software design by modifying the structure of design parts impaired with model smells without altering the overall software behavior. However, handling these smells without proper prioritization will not produce the anticipated effects. In this paper, we solve the prioritization of the model smell refactoring using a multi-objective optimization (MOO) algorithm called the multi-objective (MO) covariance matrix adaptation evolution strategy (MO CMA-ES). Our formulation relies on the refactoring of unified modeling language (UML) class diagrams to mitigate the negative effect of design smells. We treat the prioritization problem as a real-valued MOO where we propose novel data encoding procedures. We use two conflicting objectives, quality, and maintainability , to balance the refactoring. We first build a new solution representation that guarantees smell fixing and eliminates the rejection limitation. Furthermore, we suggest a custom mapping scheme to properly encode real-valued quantities using unique representations. For performance evaluation purposes, we developed a large custom dataset with more than 30,000 class records, using seven popular open-source software projects. A novel relative coverage metric is proposed to mitigate the limitations associated with the standard coverage. For benchmarking purposes, we also consider an improved version of the nondominated sorting genetic algorithm (NSGA-II(. The reported performance scores confirm the superiority of the MO CMA-ES algorithm over NSGA-II. The former successfully identified the refactoring sequences that lead to the best improvements in software quality and maintainability while it is able to fix all identified design smells. These improvements are quantified in terms of hypervolume, coverage, spacing metrics, and execution time. The MO CMA-ES attained the highest average maximum quality score of 1149 while keeping the average maintainability at the lowest score of 13.8. In all experiment settings, the proposed solution leads to longer refactoring sequences at no additional computational cost.

Global Linear Convergence of Evolution Strategies on More than Smooth Strongly Convex Functions

Evolution strategies (ESs) are zeroth-order stochastic black-box optimization heuristics invariant to monotonic transformations of the objective function. They evolve a multivariate normal distribution, from which candidate solutions are generated. Among different variants, CMA-ES is nowadays recognized as one of the state-of-the-art zeroth-order optimizers for difficult problems. Despite ample empirical evidence that ESs with a step-size control mechanism converge linearly, theoretical guarantees of linear convergence of ESs have been established only on limited classes of functions. In particular, theoretical results on convex functions are missing, where zeroth-order and also first-order optimization methods are often analyzed. In this paper, we establish almost sure linear convergence and a bound on the expected hitting time of an ES family, namely, the $(1+1)_\kappa$-ES, which includes the (1+1)-ES with (generalized) one-fifth success rule and an abstract covariance matrix adaptation with bounded condition number, on a broad class of functions. The analysis holds for monotonic transformations of positively homogeneous functions and of quadratically bounded functions, the latter of which particularly includes monotonic transformation of strongly convex functions with Lipschitz continuous gradient. As far as the authors know, this is the first work that proves linear convergence of ES on such a broad class of functions.

Data-driven adaptive predictive control of hydrocracking process using a covariance matrix adaption evolution strategy

In this paper, a new data-driven adaptive predictive control architecture to the reactor temperature control problem in hydrocracking process is proposed with completely unknown system dynamics. Specifically, the nonlinear relationship between the reactor temperature and conversion is established using echo state networks (ESNs) with an intrinsic plasticity rule, and a covariance matrix adaption evolution strategy (CMA-ES) is used to optimize the reactor temperature iteratively using the input and state information. Besides, the prescribed performance function is introduced to guarantee the transient and steady performance of the system. In addition, the input constraints and external disturbance are simultaneously considered. Numerical simulation results and industrial application prove the efficacy of the proposed method.

Blood flow and diameter effect in the navigation process of magnetic nanocarriers inside the carotid artery

Background and objective: Serious side effects are occurred during the cancer therapy. Magnetic driving of nanoparticles is a novel method for the elimination of these effects by supplying with anticancer drug or increase the temperature of the infected area. For this reason, a numerical model for optimal guidance of nanoparticles, through the gradient magnetic field, inside the human artery system is presented in this study. Methods: The present method couples Computational Fluid Dynamics (CFD) and Discrete Element Method (DEM) techniques. In addition, the optimum magnetic intensity each time is evaluated by using the covariance matrix adaptation evolution strategy (CMA-ES). Under five feature blood flow velocities in cardiac cycle, the developed method evaluate and select the optimum gradient magnetic field in order to eliminate the deviation of the guided nanoparticles from a pre-described trajectory. Results: Results of the simulations indicate both the influence of the blood flow and the volume of nanocarriers in the magnetic driving process in real conditions. Specifically, the blood flow and the volume of particles are inversely proportional parameters in the magnetic navigation process. As the blood flow is decreased, the deviation of nanoparticles compared to the desired path is minimized. On the contrary, the decrease of the volume of nanocarriers increase the distance of particles from the described trajectory. However, greater magnetic gradient values are needed as the blood flow is increased. Furthermore, the imposed gradient magnetic values are strongly connected with the position of the nanoparticles and the blood blow velocity. Conclusions: Based on the results of the present study, the most important parameter in the navigation process is the magnetic volume of particles. Under real conditions, the effect of the blood flow is insignificant compared to the volume of particles in the navigation process. In addition, great differences in the optimized magnetic sequence are presented both among the different blood flows and the volume of particles.

Through-focus EUV multilayer defect compensation considering optical proximity correction.

Extreme ultraviolet (EUV) multilayer defects result in the degradation of through-focus imaging quality. The optical proximity effect is another crucial factor that degrades the imaging quality. Both the impacts of the defects and the optical proximity effects could be mitigated by modifying the original mask patterns. A heuristic-based defect compensation method considering optical proximity correction and through-focus optimization is proposed in this paper. The edge of the mask pattern and the insertion of sub-resolution assist features (SRAFs) are optimized by covariance matrix adaptation evolution strategy (CMA-ES) to compensate for the degradation of the imaging quality with a certain defocus range. New encoding strategies for the edge pixels of the mask pattern and the SRAFs are proposed and utilized in this paper to ensure the manufacturability of the mask and the efficiency of the optimization at the same time. The rigorous database approach based on the scattering matrix is adopted to simulate the mask diffraction spectrum efficiently. Simulations verify that the through-focus imaging quality of both the defective masks with bump defects and pit defects could be obviously improved by the proposed defect compensation method.

A novel belief rule base expert system with interval-valued references

As an essential parameter in the belief rule base (BRB), referential values refer to evaluation criteria for describing attributes using quantitative data or linguistic terms, the rationality and preciseness of which are important to the modeling accuracy. At present, the studies on referential values of BRB are mainly related to single-valued data. However, due to the inherent uncertainty, ambiguity, and vagueness of expert knowledge, the single-valued references provided by experts cannot represent qualitative information adequately. In this paper, a novel BRB with interval-valued references (BRB-IR) is proposed, in which qualitative knowledge and quantitative data can be integrated to construct models. First, the interval-valued referential values provided by experts are optimized by a nonlinear optimization algorithm to obtain the optimal referential values. Furthermore, other model parameters are optimized by the projection covariance matrix adaptation evolutionary strategy (P-CMA-ES) algorithm. Finally, a case study for pipeline leak detection is constructed to verify the model's effectiveness, and the results show that the proposed BRB-IR is more effective and characterizes expert knowledge better than the classical BRB using single-valued references.

Multirobot Adaptive Task Allocation of Intelligent Warehouse Based on Evolutionary Strategy

To solve the dynamic and real-time problem of multirobot task allocation in intelligent warehouse system under parts-to-picker mode, this paper presents a combined solution based on adaptive task pool strategy and Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) algorithm. In the first stage of the solution, a variable task pool is used to store dynamically added tasks, which can dynamically divide continuous and large-scale task allocation problems into small-scale subproblems to solve them to meet dynamic requirements. And an adaptive control strategy is used to automatically adjust the total number of tasks in the task pool to achieve a trade-off among throughput, energy consumption, and waiting time, which has better adaptability than manually adjusting the size of the task pool. In the second stage of the solution, when the task pool is full, tasks in the task pool will be assigned to robots. For the task allocation problem, this paper regards it as an optimization problem and uses the CMA-ES algorithm to find the optimal task assignment solution for all the robots. By comparing with fixed threshold method under 56 different task pool sizes, the experimental results show that the throughput can be close to reaching the optimal level, and the average distance traveled by robots to handle each unit is lower using adaptive threshold method; so, adaptive task pool solution has better adaptability and can find the optimal task pool size by itself. This method can satisfy the dynamic and real-time requirements and can be effectively applied to the intelligent warehouse system.

The underground explosion point high precision measurement method based on multidimensional information fusion of vibration sensors

PurposeThe purpose of this paper is to solve the problem that the location of the initiation point cannot be measured accurately in the shallow underground space, this paper proposes a method, which is based on fusion of multidimensional vibration sensor information, to locate single shallow underground sources.Design/methodology/approachFirst, in this paper, using the characteristics of low multipath interference and good P-wave polarization in the near field, the adaptive covariance matrix algorithm is used to extract the polarization angle information of the P-wave and the short term averaging/long term averaging algorithm is used to extract the first break travel time information. Second, a hybrid positioning model based on travel time and polarization angle is constructed. Third, the positioning model is taken as the particle update fitness function of quantum-behaved particle swarm optimization and calculation is performed in the hybrid positioning model. Finally, the experiment verification is carried out in the field.FindingsThe experimental results show that, with root mean square error, spherical error probable and fitness value as evaluation indicators, the positioning performance of this method is better than that without speed prediction. And the positioning accuracy of this method has been improved by nearly 30%, giving all of the three tests a positioning error within 0.5 m and a fitness less than 1.Originality/valueThis method provides a new idea for high-precision positioning of shallow underground single source. It has a certain engineering application value in the fields of directional demolition of engineering blasting, water inrush and burst mud prediction, fuze position measurement, underground initiation point positioning of ammunition, mine blasting monitoring and so on.

Prediction and optimization of emission in an agricultural harvest engine with biodiesel-diesel blends by a method of ANN and CMA-ES

To address the current problems of high exhaust emission level of domestic agricultural equipments and serious human and environmental hazards of agricultural machinery engine emissions, in this study, an agricultural harvester diesel engine test platform was firstly built to conduct a biodiesel-diesel combustion emission test and collect data. In addition, an Artificial Neural Network high-precision model was designed and constructed for training and prediction of the outputs such as nitrogen oxides (NOx), hydrocarbons (HC), carbon monoxide (CO), opaque smoke, and post-turbo emission temperatures at different engine operating conditions and various biodiesel-diesel blend ratios, speed and engine load. The type of neural network selected is a feed-forward multi-layer perceptron network because of its advantage of reflecting the correlations between input and output. The model's regression coefficients of NOx, HC, CO, opaque smoke, and post-turbo emission temperatures R2 = 0.9822, 0.9934, 0.9937, 0.9967 0.9970, were close to 1; mean square error (MSE) = 9.79%, 7.73%, 6.48%, 9.58% 2.27%, root mean square error (RMSE) = 18.41 ppm, 3.21 ppm, 16.48 ppm, 0.39 m−1, 10.86 °C. The results show that the established models have high confidence and can be used for high-precision agricultural machinery engine emission prediction and calculation. Covariance Matrix Adaptation-Evolutionary Strategy (CMA-ES) was applied to obtain the best matching parameters for the optimum engine operating conditions with optimized emissions. The biodiesel-diesel blend ratio, engine speed, and engine load were optimized with different single-target emissions as the objective function, respectively. In addition, with multi-target emissions as the objective function, the values of the three optimization variables are 5%, 1850 rpm, 25% respectively. The error rate between the experimental data and predicted values is around 3%-10%, and thereby the method is considered practicable through experimental validation. The experimental results show that ANN supported by CMA-ES is a good method for predicting and optimizing emissions of diesel engines burning biodiesel-diesel blends in agricultural machinery.

Covariance matrix adapted grey wolf optimizer tuned eXtreme gradient boost for bi-directional modelling of direct metal deposition process

The process of direct metal deposition for cladding has become extremely popular. Online condition monitoring of the process is necessary to obtain a desired clad geometry. The aforementioned fact has necessitated the development of accurate predictive models for establishing relationships between the input and the output parameters of the process in a bi-directional fashion. The present study attempts to build both forward and backward models of a direct deposition process of austenitic steel utilizing the extreme gradient boost technique. Inspired by the successful application of grey wolf optimization algorithm in solving real life problems, the authors further propose a novel modification of the same and use it to tune the parameters of the model with an aim to improve its performance. The improvement has been accomplished by changing the initial perspective prey location guided by the covariance matrix adaptation and recombination. The new optimization algorithm has been tested and compared with the original algorithm along with some of its variants and several other state-of-the-art meta-heuristics on 23 benchmark objective functions from literature and 5 from CEC 2017. The new optimizer has been further validated on some real engineering case studies. The developed hybrid models for bi-directional mappings using different optimizer turn-by-turn have been trained and tested using statistically augmented experimental data-set. The overall mean absolute percentage errors in testing forward mapping and backward mapping using the model with new optimizer have been found within 10%, which is quite satisfactory. The adequacy of the developed models has also been found acceptable.

Dissecting the 2015 Chinese stock market crash

AbstractWe perform a novel analysis of the 2015 Chinese stock market crash by calibrating the log‐periodic power law singularity (LPPLS) model to two important Chinese stock indices, SSEC and SZSC, from early 2014 to June 2015. Our analysis indicates that the LPPLS model can readily detect the bubble behaviour of the faster‐than‐exponential increase corrected by the accelerating logarithm‐periodic oscillations in the crash. The existence of the log‐periodicity is identified by applying the Lomb spectral analysis on the detrended residuals. The Ornstein–Uhlenbeck property and the stationarity of the LPPLS fitting residuals are confirmed by the Phillips–Perron test and the Dickey–Fuller test. We find that the actual critical day of bubble crash can be well predicted by the LPPLS model as far back as 2 months before the actual crash. We have shown that the covariance matrix adaptation evolution strategy (CMA‐ES) can be used as an alternative optimization algorithm for the LPPLS model fit. Furthermore, the change rate of the prediction end time gap ( ) can be used as an additional indicator along with the key indicator to improve the prediction of bubble burst.

Systematic in-depth study on material constitutive parameter identification for numerical cutting simulation on 16MnCr5 comparing temperature-coupled and uncoupled Split Hopkinson pressure bars

A comprehensive systematic comparative study on high-strain-rate tests (Split Hopkinson Pressure Bar), with and without in-situ heating of the specimens and their respective influence on the quality of empirical material models is presented. The determination of material constitutive model parameters is one of the most challenging aspects of the modelling and simulation of machining processes. Chip formation and process forces show a significant dependence on the actual constitutive model and its parameters as well as on the testing method. Typically, the influences of strain, strain rate, and temperature are investigated in separate experiments of quasi-static compression tests and tests, because the most widespread phenomenological constitutive material models (e.g. Johnson–Cook model) neglect interactions between temperature and strain rate. In contrast, the presented work demonstrates, that a coupled experimental approach of strain rate and temperature in the same test increases the quality of such uncoupled material models as well. The authors compared both approaches (separated and in situ temperature-dependent experiments) by determining the constitutive model parameters for AISI 5115 steel samples taken from a single material batch. The parameters are calculated based on a covariance matrix adaptation evolution strategy and applied in identical two-dimensional orthogonal FEM cutting simulations. Process forces and chip thickness values were used for comparison with the machining experiments. The work therefore gives new aspects to decide for a suitable experimental approach when calibrating a constitutive equation.

Generative Design of Structured Materials for Controlled Frequency Responses.

Spatially varying material properties allow the dynamic response of structural systems to be almost arbitrarily tailored, far beyond the first or fundamental natural frequency. Continuing advances in manufacturing technology are making it possible to achieve the necessary range of stiffness and density variations, but the design of these property distributions is a challenging task because of the complex multidimensional nature of the problem. Generative design methods based on evolutionary optimization algorithms have been successfully used to obtain solutions based on multi-material distributions. However, the applicability of these solutions is limited by their reliance on multi-material additive manufacturing (AM), which currently only offers digitally mixed acrylic polymer options that are generally unsuitable to produce functional parts. A novel structured material solution is proposed here, in which the problem domain is divided into several volume elements (voxels), each of which contains a structure whose geometrical form is altered to adjust its effective properties to desired values. The single material structural solution will be amenable for ready fabrication by the powder-based selective laser sintering and melting processes with real engineering polymer and metal systems, thereby allowing for the realization of the benefits in real-world applications. The resulting continuous design spaces are searched using a modern evolutionary algorithm, the covariance matrix adaptation evolution strategy (CMA-ES). A MATLAB implementation of this evolutionary design method, in conjunction with finite element simulations for fitness evaluation, showed good convergence for several different cantilever beam test cases when tested against several different sets of target natural frequencies. Correlations with the multi-material solutions show that the single structured material approach is on par or even better in some cases, even though the test domain was discretized into 80% fewer voxels than for the multi-material case. Furthermore, the voxel structures can be realized using current AM technologies.

Effect of uncertainty on dynamic damping and stiffness of spherical hollow rubber isolators based on harmonic experiment

This study aims to identify the effect of uncertainty on the dynamic characteristics of a thin-walled hollow spherical rubber isolator. Firstly, the nonlinearity and uncertainties of the spherical rubber isolator were obtained by swept-sine experiments. The relationship between dynamic stiffness and damping against relative displacement amplitude was established. Then, a high-order polynomial function with uncertain parameters introduced was used for simulation. The uncertain parameters were quantified using the singular value decomposition and Monte Carlo simulations. Furthermore, the dynamic stiffness and damping of the experimental data were optimized using the Covariance Matrix Adaptation and Evolution Strategy. Finally, the high consistency between the simulation results and experimental results were demonstrated. Overall, the nonlinear model established according to the uncertain parameter quantization is feasible. This method can predict the nonlinear characteristics of the rubber isolator well and also may be applied to other nonlinear models.

Towards an efficient validation of dynamical whole-brain models

Simulating the resting-state brain dynamics via mathematical whole-brain models requires an optimal selection of parameters, which determine the model’s capability to replicate empirical data. Since the parameter optimization via a grid search (GS) becomes unfeasible for high-dimensional models, we evaluate several alternative approaches to maximize the correspondence between simulated and empirical functional connectivity. A dense GS serves as a benchmark to assess the performance of four optimization schemes: Nelder-Mead Algorithm (NMA), Particle Swarm Optimization (PSO), Covariance Matrix Adaptation Evolution Strategy (CMAES) and Bayesian Optimization (BO). To compare them, we employ an ensemble of coupled phase oscillators built upon individual empirical structural connectivity of 105 healthy subjects. We determine optimal model parameters from two- and three-dimensional parameter spaces and show that the overall fitting quality of the tested methods can compete with the GS. There are, however, marked differences in the required computational resources and stability properties, which we also investigate before proposing CMAES and BO as efficient alternatives to a high-dimensional GS. For the three-dimensional case, these methods generated similar results as the GS, but within less than 6% of the computation time. Our results contribute to an efficient validation of models for personalized simulations of brain dynamics.

Optimal stochastic scheduling in microgrids under managed risk

This paper addresses the stochastic optimal day-ahead microgrid (MG) energy resources scheduling, considering the uncertain load, price of electricity, and generated electrical power by wind and solar units. Moreover, the vehicle-to-grid (V2G) implementation, load curtailment cost, and spinning reserve requirements are modeled to make the results more practical and applicable. Furthermore, the price elasticity of supply is considered to explore the relation between V2G capability and the optimization process. The stochastic energy resources scheduling problem is formulated in a two-level optimization framework. The unit commitment of dispatchable resources is analyzed in the upper level, and the lower level is formulated as a scenario-based two-stage stochastic programming problem that minimizes the operation cost of MG considering all the constraints. The risk of attaining unfavorable high costs of MG scheduling is considered using the variance approach. The generated scenarios are reduced by using the backward reduction method for each uncertain variable at each hour, independently. The artificial intelligent-based methods, including differential evolution algorithm (DEA), particle swarm optimization (PSO), and covariance matrix adaptation evolution strategy (CMAES) are applied to solve the problem. The effectiveness of the proposed approaches is confirmed by simulations on a modified 13-bus IEEE test system, in two cases of neglecting the risk and including the managed risk by applying the real-world data. The results confirmed the better performance of CMAES for solving such optimization problems.

Horse herd optimization algorithm for economic dispatch problems

This article applies the horse herd optimization (HHO) algorithm to convoluted economic dispatch (ED) problems. HHO mimics the social behaviour of horses of different ages using six significant traits: grazing, hierarchy, sociability, imitation, defence mechanism and roam. The efficacy of the HHO method is demonstrated on five different ED problems, namely, valve-point effects, prohibited feasible area, ramp rate limits and multiple fuels. The simulated outcomes of the recommended method are comparable to those obtained by established artificial intelligence methods. Comparative and statistical analyses demonstrate that the proposed HHO algorithm performs well and can produce superior results to some other well-known and established algorithms, namely, differential evolution (DE), success-history based adaptive differential evolution with linear population size reduction (L-SHADE) and covariance matrix adaptation–evolution strategy (CMA-ES).

Comparative study on metaheuristic algorithms for optimising wave energy converters

The optimisation of WECs is a focus current research. With the increase in optimisation variables, traditional optimisation methods are insufficient to find the best design in a wide and complex solution space, and more advanced algorithms are required. In addition, the iterative optimisation of the WEC requires a reliable and accurate WEC simulation method to ensure the effectiveness of optimisation. Therefore, a MATLAB-APDL-AQWA united simulation system (MAA-system) is developed to calculate the WEC generation power accurately. Then, a memory mechanism is designed to avoid calculating the fitness of duplicate individuals in the search process by creating a memory base to store individual coding information and fitness information. Seven metaheuristic algorithms — the genetic algorithm, differential evolution, immune algorithm (IA), covariance matrix adaptation evolution strategy (CMA-ES), particle swarm optimisation, ant colony optimisation, and simulated annealing — with memory mechanisms are utilised to optimise the draft, power take-off parameter, and layout of WEC globally in random wave conditions. The performances of these algorithms in different search spaces are analysed. The results show CMA-ES is the best choice for solving the unimodal optimisation problem of WEC, and IA is more suitable for multimodal optimisation such as the WEC array layout.

Learning Competitive Swarm Optimization.

Particle swarm optimization (PSO) is a popular method widely used in solving different optimization problems. Unfortunately, in the case of complex multidimensional problems, PSO encounters some troubles associated with the excessive loss of population diversity and exploration ability. This leads to a deterioration in the effectiveness of the method and premature convergence. In order to prevent these inconveniences, in this paper, a learning competitive swarm optimization algorithm (LCSO) based on the particle swarm optimization method and the competition mechanism is proposed. In the first phase of LCSO, the swarm is divided into sub-swarms, each of which can work in parallel. In each sub-swarm, particles participate in the tournament. The participants of the tournament update their knowledge by learning from their competitors. In the second phase, information is exchanged between sub-swarms. The new algorithm was examined on a set of test functions. To evaluate the effectiveness of the proposed LCSO, the test results were compared with those achieved through the competitive swarm optimizer (CSO), comprehensive particle swarm optimizer (CLPSO), PSO, fully informed particle swarm (FIPS), covariance matrix adaptation evolution strategy (CMA-ES) and heterogeneous comprehensive learning particle swarm optimization (HCLPSO). The experimental results indicate that the proposed approach enhances the entropy of the particle swarm and improves the search process. Moreover, the LCSO algorithm is statistically and significantly more efficient than the other tested methods.

Snake Optimizer: A novel meta-heuristic optimization algorithm

In recent years, several metaheuristic algorithms have been introduced in engineering and scientific fields to address real-life optimization problems. In this study, a novel nature-inspired metaheuristics algorithm named as Snake Optimizer (SO) is proposed to tackle a various set of optimization tasks which imitates the special mating behavior of snakes. Each snake (male/female) fights to have the best partner if the existed quantity of food is enough and the temperature is low. This study mathematically mimics and models such foraging and reproduction behaviors and patterns to present a simple and efficient optimization algorithm. To verify the validity and superiority of the proposed method, SO is tested on 29 unconstrained Congress on Evolutionary Computation (CEC) 2017 benchmark functions and four constrained real-world engineering problems. SO is compared with other 9 well-known and newly developed algorithms such as Linear population size reduction-Success-History Adaptation for Differential Evolution (L-SHADE), Ensemble Sinusoidal incorporated with L-SHADE (LSHADE-EpSin), Covariance matrix adaptation evolution strategy (CMAES), Coyote Optimization Algorithm (COA), Moth-flame Optimization, Harris Hawks Optimizer, Thermal Exchange optimization, Grasshopper Optimization Algorithm, and Whale Optimization Algorithm. Experimental results and statistical comparisons prove the effectiveness and efficiency of SO on different landscapes with respect to exploration–exploitation balance and convergence curve speed. The source code is currently available for public from: https://se.mathworks.com/matlabcentral/fileexchange/106465-snake-optimizer