PGA: A new particle swarm optimization algorithm based on genetic operators for the global optimization of clusters.

We have developed a global optimization program named PGA based on particle swarm optimization algorithm coupled with genetic operators for the structures of atomic clusters. The effectiveness and efficiency of the PGA program can be demonstrated by efficiently obtaining the tetrahedral Au20 and double-ring tubular B20, and identifying the ground state ZrSi 17 - 20 - $$ {\mathrm{ZrSi}}_{17\hbox{--} 20}^{-} $$ clusters through the comparison between the simulated and the experimental photoelectron spectra (PESs). Then, the PGA was applied to search for the global minimum structures of Mg n - $$ {\mathrm{Mg}}_n^{-} $$ (n = 3-30) clusters, new structures have been found for sizes n = 6, 7, 12, 14, and medium-sized 21-30 were first determined. The high consistency between the simulated spectra and the experimental ones once again demonstrates the efficiency of the PGA program. Based on the ground-state structures of these Mg n - $$ {\mathrm{Mg}}_n^{-} $$ (n = 3-30) clusters, their structural evolution and electronic properties were subsequently explored. The performance on Au20, B20, ZrSi 17 - 20 - $$ {\mathrm{ZrSi}}_{17\hbox{--} 20}^{-} $$ , and Mg n - $$ {\mathrm{Mg}}_n^{-} $$ (n = 3-30) clusters indicates the promising potential of the PGA program for exploring the global minima of other clusters. The code is available for free upon request.

Active-learning for global optimization of Ni-Ceria nanoparticles: The case of Ce4-xNixO8- x (x = 1, 2, 3).

Ni-CeO2 nanoparticles (NPs) are promising nanocatalysts for water splitting and water gas shift reactions due to the ability of ceria to temporarily donate oxygen to the catalytic reaction and accept oxygen after the reaction is completed. Therefore, elucidating how different properties of the Ni-Ceria NPs relate to the activity and selectivity of the catalytic reaction, is of crucial importance for the development of novel catalysts. In this work the active learning (AL) method based on machine learning regression and its uncertainty is used for the global optimization of Ce(4-x)NixO(8-x) (x = 1, 2, 3) nanoparticles, employing density functional theory calculations. Additionally, further investigation of the NPs by mass-scaled parallel-tempering Born-Oppenheimer molecular dynamics resulted in the same putative global minimum structures found by AL, demonstrating the robustness of our AL search to learn from small datasets and assist in the global optimization of complex electronic structure systems.

Multi-Adaptive Strategies-Based Higher-Order Quantum Genetic Algorithm for Agile Remote Sensing Satellite Scheduling Problem.

The agile remote sensing satellite scheduling problem (ARSSSP) for large-scale tasks needs to simultaneously address the difficulties of complex constraints and a huge solution space. Taking inspiration from the quantum genetic algorithm (QGA), a multi-adaptive strategies-based higher-order quantum genetic algorithm (MAS-HOQGA) is proposed for solving the agile remote sensing satellites scheduling problem in this paper. In order to adapt to the requirements of engineering applications, this study combines the total task number and the total task priority as the optimization goal of the scheduling scheme. Firstly, we comprehensively considered the time-dependent characteristics of agile remote sensing satellites, attitude maneuverability, energy balance, and data storage constraints and established a satellite scheduling model that integrates multiple constraints. Then, quantum register operators, adaptive evolution operations, and adaptive mutation transfer operations were introduced to ensure global optimization while reducing time consumption. Finally, this paper demonstrated, through computational experiments, that the MAS-HOQGA exhibits high computational efficiency and excellent global optimization ability in the scheduling process of agile remote sensing satellites for large-scale tasks, while effectively avoiding the problem that the traditional QGA has, namely low solution efficiency and the tendency to easily fall into local optima. This method can be considered for application to the engineering practice of agile remote sensing satellite scheduling for large-scale tasks.

FaSS-MVS: Fast Multi-View Stereo with Surface-Aware Semi-Global Matching from UAV-Borne Monocular Imagery.

With FaSS-MVS, we present a fast, surface-aware semi-global optimization approach for multi-view stereo that allows for rapid depth and normal map estimation from monocular aerial video data captured by unmanned aerial vehicles (UAVs). The data estimated by FaSS-MVS, in turn, facilitate online 3D mapping, meaning that a 3D map of the scene is immediately and incrementally generated as the image data are acquired or being received. FaSS-MVS is composed of a hierarchical processing scheme in which depth and normal data, as well as corresponding confidence scores, are estimated in a coarse-to-fine manner, allowing efficient processing of large scene depths, such as those inherent in oblique images acquired by UAVs flying at low altitudes. The actual depth estimation uses a plane-sweep algorithm for dense multi-image matching to produce depth hypotheses from which the actual depth map is extracted by means of a surface-aware semi-global optimization, reducing the fronto-parallel bias of Semi-Global Matching (SGM). Given the estimated depth map, the pixel-wise surface normal information is then computed by reprojecting the depth map into a point cloud and computing the normal vectors within a confined local neighborhood. In a thorough quantitative and ablative study, we show that the accuracy of the 3D information computed by FaSS-MVS is close to that of state-of-the-art offline multi-view stereo approaches, with the error not even an order of magnitude higher than that of COLMAP. At the same time, however, the average runtime of FaSS-MVS for estimating a single depth and normal map is less than 14% of that of COLMAP, allowing us to perform online and incremental processing of full HD images at 1-2 Hz.

GAMaterial-A genetic-algorithm software for material design and discovery.

Genetic algorithms (GAs) are stochastic global search methods inspired by biological evolution. They have been used extensively in chemistry and materials science coupled with theoretical methods, ranging from force-fields to high-throughput first-principles methods. The methodology allows an accurate and automated structural determination for molecules, atomic clusters, nanoparticles, and solid surfaces, fundamental to understanding chemical processes in catalysis and environmental sciences, for instance. In this work, we propose a new genetic algorithm software, GAMaterial, implemented in Python3.x, that performs global searches to elucidate the structures of atomic clusters, doped clusters or materials and atomic clusters on surfaces. For all these applications, it is possible to accelerate the GA search by using machine learning (ML), the ML@GA method, to build subsequent populations. Results for ML@GA applied for the dopant distributions in atomic clusters are presented. The GAMaterial software was applied for the automatic structural search for the Ti6 O12 cluster, doping Al in Si11 (4Al@Si11 ) and Na10 supported on graphene (Na10 @graphene), where DFTB calculations were used to sample the complex search surfaces with reasonably low computational cost. Finally, the global search by GA of the Mo8 C4 cluster was considered, where DFT calculations were made with the deMon2k code, which is interfaced with GAMaterial.

Application of conformational space annealing to the protein structure modeling using cryo-EM maps.

Conformational space annealing (CSA), a global optimization method, has been applied to various protein structure modeling tasks. In this paper, we applied CSA to the cryo-EM structure modeling task by combining the python subroutine of CSA (PyCSA) and the fast relax (FastRelax) protocol of PyRosetta. Refinement of initial structures generated from two methods, rigid fitting of predicted structures to the Cryo-EM map and de novo protein modeling by tracing the Cryo-EM map, was performed by CSA. In the refinement of the rigid-fitted structures, the final models showed that CSA can generate reliable atomic structures of proteins, even when large movements of protein domains were required. In the de novo modeling case, although the overall structural qualities of the final models were rather dependent on the initial models, the final models generated by CSA showed improved MolProbity scores and cross-correlation coefficients to the maps. These results suggest that CSA can accomplish flexible fitting and refinement together by sampling diverse conformations effectively and thus can be utilized for cryo-EM structure modeling.

Global deep learning optimization of chemical exchange saturation transfer magnetic resonance fingerprinting acquisition schedule.

Chemical exchange saturation transfer (CEST) MRI is a promising molecular imaging technique but suffers from long scan times and complicated processing. CEST was recently combined with magnetic resonance fingerprinting (MRF) to address these shortcomings. However, the CEST-MRF signal depends on multiple acquisition and tissue parameters so selecting an optimal acquisition schedule is challenging. In this work, we propose a novel dual-network deep learning framework to optimize the CEST-MRF acquisition schedule. The quality of the optimized schedule was assessed in a digital brain phantom and compared with alternate deep learning optimization approaches. The effect of schedule length on the reconstruction error was also investigated. A healthy subject was scanned with optimized and random schedules and with a conventional CEST sequence for comparison. The optimized schedule was also tested in a subject with metastatic renal cell carcinoma. Reproducibility was assessed via test-retest experiments and the concordance correlation coefficient calculated for white matter (WM) and grey matter (GM). The optimized schedule was 12% shorter but yielded equal or lower normalized root mean square error for all parameters. The proposed optimization also provided a lower error compared with alternate methodologies. Longer schedules generally yielded lower error. In vivo maps obtained with the optimized schedule showed reduced noise and improved delineation of GM and WM. CEST curves synthesized from the optimized parameters were highly correlated (r = 0.99) with measured conventional CEST. The mean concordance correlation coefficient in WM/GM for all tissue parameters was 0.990/0.978 for the optimized schedule but only 0.979/0.975 for the random schedule. The proposed schedule optimization is widely applicable to MRF pulse sequences and provides accurate and reproducible tissue maps with reduced noise at a shorter scan time than a randomly generated schedule.

Efficient Bayesian automatic calibration of a functional-structural wheat model using an adaptive design and a metamodelling approach.

Functional-structural plant models are increasingly being used by plant scientists to address a wide variety of questions. However, the calibration of these complex models is often challenging, mainly because of their high computational cost, and, as a result, error propagation is usually ignored. Here we applied an automatic method to the calibration of WALTer: a functional-structural wheat model that simulates the plasticity of tillering in response to competition for light. We used a Bayesian calibration method to jointly estimate the values of five parameters and quantify their uncertainty by fitting the model outputs to tillering dynamics data. We made recourse to Gaussian process metamodels in order to alleviate the computational cost of WALTer. These metamodels are built from an adaptive design that consists of successive runs of WALTer chosen by an efficient global optimization algorithm specifically adapted to this particular calibration task. The method presented here performed well on both synthetic and experimental data. It is an efficient approach for the calibration of WALTer and should be of interest for the calibration of other functional-structural plant models.

Trihydrogen Cation Helium Clusters: A New Potential Energy Surface.

We present a new analytical potential energy surface (PES) for the interaction between the trihydrogen cation and a He atom, H 3 + - H e ${{H}_{3}^{+}-He}$ , in its electronic ground state. The proposed PES has been built as a sum of two contributions: a polarization energy term due to the electric field generated by the molecular cation at the position of the polarizable He atom, and an exchange-repulsion and dispersion interactions represented by a sum of "atom-bond" potentials between the three bonds of H 3 + ${{H}_{3}^{+}}$ and the He atom. All parameters of this new PES have been chosen and fitted from data obtained from high-level ab-initio calculations. Using this new PES plus the Aziz-Slaman potential for the interaction between Helium atoms and assuming pair-wise interactions, we carry out classical Basin-Hopping (BH) global optimization, semiclassical BH with Zero Point Energy corrections, and quantum Diffusion Monte Carlo simulations. We have found the minimum energy configurations of small He clusters doped with H 3 + ${{H}_{3}^{+}}$ , H 3 + H e N ${{H}_{3}^{+}{\left(He\right)}_{N}}$ , with N=1-16. The study of the energies of these clusters allows us to find a pronounced anomaly for N=12, in perfect agreement with previous experimental findings, which we relate to a greater relative stability of this aggregate.

Adaptive Aquila Optimizer Combining Niche Thought with Dispersed Chaotic Swarm.

The Aquila Optimizer (AO) is a new bio-inspired meta-heuristic algorithm inspired by Aquila's hunting behavior. Adaptive Aquila Optimizer Combining Niche Thought with Dispersed Chaotic Swarm (NCAAO) is proposed to address the problem that although the Aquila Optimizer (AO) has a strong global exploration capability, it has an insufficient local exploitation capability and a slow convergence rate. First, to improve the diversity of populations in the algorithm and the uniformity of distribution in the search space, DLCS chaotic mapping is used to generate the initial populations so that the algorithm is in a better exploration state. Then, to improve the search accuracy of the algorithm, an adaptive adjustment strategy of de-searching preferences is proposed. The exploration and development phases of the NCAAO algorithm are effectively balanced by changing the search threshold and introducing the position weight parameter to adaptively adjust the search process. Finally, the idea of small habitats is effectively used to promote the exchange of information between groups and accelerate the rapid convergence of groups to the optimal solution. To verify the optimization performance of the NCAAO algorithm, the improved algorithm was tested on 15 standard benchmark functions, the Wilcoxon rank sum test, and engineering optimization problems to test the optimization-seeking ability of the improved algorithm. The experimental results show that the NCAAO algorithm has better search performance and faster convergence speed compared with other intelligent algorithms.

Thermal Sensor Allocation for Effective and Efficient Heat Transfer Measurements in Transportation Systems.

Power plants, electric generators, high-frequency controllers, battery storage, and control units are essential in current transportation and energy distribution networks. To improve the performance and guarantee the endurance of such systems, it is critical to control their operational temperature within certain regimes. Under standard working conditions, those elements become heat sources either during their entire operational envelope or during given phases of it. Consequently, in order to maintain a reasonable working temperature, active cooling is required. The refrigeration may consist of the activation of internal cooling systems relying on fluid circulation or air suction and circulation pulled from the environment. However, in both scenarios pulling surrounding air or making use of coolant pumps increases the power demand. The augmented power demand has a direct impact on the power plant or electric generator autonomy, while instigating higher power demand and substandard performance from the power electronics and batteries' compounds. In this manuscript, we present a methodology to efficiently estimate the heat flux load generated by internal heat sources. By accurately and inexpensively computing the heat flux, it is possible to identify the coolant requirements to optimize the use of the available resources. Based on local thermal measurements fed into a Kriging interpolator, we can accurately compute the heat flux minimizing the number of sensors required. Considering the need for effective thermal load description toward efficient cooling scheduling. This manuscript presents a procedure based on temperature distribution reconstruction via a Kriging interpolator to monitor the surface temperature using a minimal number of sensors. The sensors are allocated by means of a global optimization that minimizes the reconstruction error. The surface temperature distribution is then fed into a heat conduction solver that processes the heat flux of the proposed casing, providing an affordable and efficient way of controlling the thermal load. Conjugate URANS simulations are used to simulate the performance of an aluminum casing and demonstrate the effectiveness of the proposed method.

Research on Global Optimization Algorithm of Integrated Energy and Thermal Management for Plug-In Hybrid Electric Vehicles.

Power distribution and battery thermal management are important technologies for improving the energy efficiency of plug-in hybrid electric vehicles (PHEVs). In response to the global optimization of integrated energy thermal management strategy (IETMS) for PHEVs, a dynamic programming algorithm based on adaptive grid optimization (AGO-DP) is proposed in this paper to improve optimization performance by reducing the optimization range of SOC and battery temperature, and adaptively adjusting the grid distribution of state variables according to the actual feasible region. The simulation results indicate that through AGO-DP optimization, the reduction ratio of the state feasible region is more than 30% under different driving conditions. Meanwhile, the algorithm can obtain better global optimal driving costs more rapidly and accurately than traditional dynamic programming algorithms (DP). The computation time is reduced by 33.29-84.67%, and the accuracy of the global optimal solution is improved by 0.94-16.85% compared to DP. The optimal control of the engine and air conditioning system is also more efficient and reasonable. Furthermore, AGO-DP is applied to explore IETMS energy-saving potential for PHEVs. It is found that the IETMS energy-saving potential range is 3.68-23.74% under various driving conditions, which increases the energy-saving potential by 0.55-3.26% compared to just doing the energy management.

Exploring the Potential Energy Surface of Pt6 Sub-Nano Clusters Deposited over Graphene.

Catalytic systems based on sub-nanoclusters deposited over different supports are promising for very relevant chemical transformations such as many electrocatalytic processes as the ORR. These systems have been demonstrated to be very fluxional, as they are able to change shape and interconvert between each other either alone or in the presence of adsorbates. In addition, an accurate representation of their catalytic activity requires the consideration of ensemble effects and not a single structure alone. In this sense, a reliable theoretical methodology should assure an accurate and extensive exploration of the potential energy surface to include all the relevant structures and with correct relative energies. In this context, we applied DFT in conjunction with global optimization techniques to obtain and analyze the characteristics of the many local minima of Pt6 sub-nanoclusters over a carbon-based support (graphene)-a system with electrocatalytic relevance. We also analyzed the magnetism and the charge transfer between the clusters and the support and paid special attention to the dependence of dispersion effects on the ensemble characteristics. We found that the ensembles computed with and without dispersion corrections are qualitatively similar, especially for the lowest-in-energy clusters, which we attribute to a (mainly) covalent binding to the surface. However, there are some significant variations in the relative stability of some clusters, which would significantly affect their population in the ensemble composition.

Automated and Efficient Generation of General Molecular Aggregate Structures.

Modeling intermolecular interactions of complex non-covalent structures is important in many areas of chemistry. To facilitate the generation of reasonable dimer, oligomer, and general aggregate geometries, we introduce an automated computational interaction site screening (aISS) workflow. This easy-to-use tool combines a genetic algorithm employing the intermolecular force-field xTB-IFF for initial search steps with the general force-field GFN-FF and the semi-empirical GFN2-xTB method for geometry optimizations. Compared with the alternative CREST program, aISS yields similar results but with computer time savings of 1-3 orders of magnitude. This allows for the treatment of systems with thousands of atoms composed of elements up to radon, e.g., metal-organic complexes, or even polyhedra and zeolite cut-outs which were not accessible before. Moreover, aISS can identify reactive sites and provides options like site-directed (user-guided) screening.

Restructuring and Activation of Cu(111) under Electrocatalytic Reduction Conditions.

The dynamic restructuring of Cu surfaces in electroreduction conditions is of fundamental interest in electrocatalysis. We decode the structural dynamics of a Cu(111) electrode under reduction conditions by joint first-principles calculations and operando electrochemical scanning tunneling microscopy (ECSTM) experiments. Combining global optimization and grand canonical density functional theory, we unravel the potential- and pH-dependent restructuring of Cu(111) in acidic electrolyte. At reductive potential, Cu(111) is covered by a high density of H atoms and, below a threshold potential, Cu adatoms are formed on the surface in a (4×4) superstructure, a restructuring unfavorable in vacuum. The strong H adsorption is the driving force for the restructuring, itself induced by the electrode potential. On the restructured surface, barriers for hydrogen evolution reaction steps are low. Restructuring in electroreduction conditions creates highly active Cu adatom sites not present on Cu(111).

MLAGO: machine learning-aided global optimization for Michaelis constant estimation of kinetic modeling.

BACKGROUND: Kinetic modeling is a powerful tool for understanding the dynamic behavior of biochemical systems. For kinetic modeling, determination of a number of kinetic parameters, such as the Michaelis constant (Km), is necessary, and global optimization algorithms have long been used for parameter estimation. However, the conventional global optimization approach has three problems: (i) It is computationally demanding. (ii) It often yields unrealistic parameter values because it simply seeks a better model fitting to experimentally observed behaviors. (iii) It has difficulty in identifying a unique solution because multiple parameter sets can allow a kinetic model to fit experimental data equally well (the non-identifiability problem). RESULTS: To solve these problems, we propose the Machine Learning-Aided Global Optimization (MLAGO) method for Km estimation of kinetic modeling. First, we use a machine learning-based Km predictor based only on three factors: EC number, KEGG Compound ID, and Organism ID, then conduct a constrained global optimization-based parameter estimation by using the machine learning-predicted Km values as the reference values. The machine learning model achieved relatively good prediction scores: RMSE = 0.795 and R2 = 0.536, making the subsequent global optimization easy and practical. The MLAGO approach reduced the error between simulation and experimental data while keeping Km values close to the machine learning-predicted values. As a result, the MLAGO approach successfully estimated Km values with less computational cost than the conventional method. Moreover, the MLAGO approach uniquely estimated Km values, which were close to the measured values. CONCLUSIONS: MLAGO overcomes the major problems in parameter estimation, accelerates kinetic modeling, and thus ultimately leads to better understanding of complex cellular systems. The web application for our machine learning-based Km predictor is accessible at https://sites.google.com/view/kazuhiro-maeda/software-tools-web-apps , which helps modelers perform MLAGO on their own parameter estimation tasks.

Estimating the optimal linear combination of predictors using spherically constrained optimization.

BACKGROUND: In the context of a binary classification problem, the optimal linear combination of continuous predictors can be estimated by maximizing the area under the receiver operating characteristic curve. For ordinal responses, the optimal predictor combination can similarly be obtained by maximization of the hypervolume under the manifold (HUM). Since the empirical HUM is discontinuous, non-differentiable, and possibly multi-modal, solving this maximization problem requires a global optimization technique. Estimation of the optimal coefficient vector using existing global optimization techniques is computationally expensive, becoming prohibitive as the number of predictors and the number of outcome categories increases. RESULTS: We propose an efficient derivative-free black-box optimization technique based on pattern search to solve this problem, which we refer to as Spherically Constrained Optimization Routine (SCOR). Through extensive simulation studies, we demonstrate that the proposed method achieves better performance than existing methods including the step-down algorithm. Finally, we illustrate the proposed method to predict the severity of swallowing difficulty after radiation therapy for oropharyngeal cancer based on radiation dose to various structures in the head and neck. CONCLUSIONS: Our proposed method addresses an important challenge in combining multiple biomarkers to predict an ordinal outcome. This problem is particularly relevant to medical research, where it may be of interest to diagnose a disease with various stages of progression or a toxicity with multiple grades of severity. We provide the implementation of our proposed SCOR method as an R package, available online at https://CRAN.R-project.org/package=SCOR .

Tree Parzen estimator for global geometry optimization: A benchmark and database of experimental gas-phase structures of organic molecules.

Finding global and local minima on the potential energy surface is a key task for most studies in computational chemistry. Having a set of possible conformations for chemical structures and their corresponding energies, one can judge their chemical activity, understand the mechanisms of reactions, describe the formation of metal-ligand and ligand-protein complexes, and so forth. Despite the fact that the interest in various minima search algorithms in computational chemistry arose a while ago (during the formation of this science), new methods are still emerging. These methods allow to perform conformational analysis and geometry optimization faster, more accurately, or for more specific tasks. This article presents the application of a novel global geometry optimization approach based on the Tree Parzen Estimator method. For benchmarking, a database of small organic molecule geometries in the global minimum conformation was created, as well as a software package to perform the tests.

Application of Combined Local and Global Optimization Algorithms in Joint Interpretation of Direct Current Resistivity and Seismic Refraction Data: A Case Study of Dammam Dome, Eastern Saudi Arabia.

The main geological structures in the Dammam Dome are defined by integrating geophysical measurements and applying new methodological approaches. Dammam Dome is characterized by a well-developed fracture/joints system; thus, high complexity of the subsurface is expected. Direct Current Resistivity (DCR) and Seismic Refraction (SR) geophysical survey aimed to map the Dammam Dome's near-surface features. The geophysical data were acquired along two profiles in the northern part of Dammam Dome. To maximize the results from conducting DCR and SR measurements over a complex area, a combined local and global optimization algorithm was used to obtain high-resolution near-surface images in resistivity and velocity models. The local optimization technique involves individual and joint inversion of the DCR and SR data incorporating appropriate regularization parameters, while the global optimization uses single and multi-objective genetic algorithms in model parameter estimation. The combined algorithm uses the output from the local optimization method to define a search space for the global optimization algorithm. The results show that the local optimization produces satisfactory inverted models, and that the global optimization algorithm improves the local optimization results. The joint inversion and processing of the acquired data identified two major faults and a deformed zone with an almost N-S direction that corresponds with an outcrop were mapped in profile one, while profile two shows similar anomalies in both the resistivity and velocity models with the main E-W direction. This study not only demonstrates the capability of using the combined local and global optimization multi-objectives techniques to estimate model parameters of large datasets (i.e., 2D DCR and SR data), but also provides high-resolution subsurface images that can be used to study structural features of the Dammam Dome.

Parallel Cooperative Coevolutionary Grey Wolf Optimizer for Path Planning Problem of Unmanned Aerial Vehicles.

The path planning of Unmanned Aerial Vehicles (UAVs) is a complex and hard task that can be formulated as a Large-Scale Global Optimization (LSGO) problem. A higher partition of the flight environment leads to an increase in route's accuracy but at the expense of greater planning complexity. In this paper, a new Parallel Cooperative Coevolutionary Grey Wolf Optimizer (PCCGWO) is proposed to solve such a planning problem. The proposed PCCGWO metaheuristic applies cooperative coevolutionary concepts to ensure an efficient partition of the original search space into multiple sub-spaces with reduced dimensions. The decomposition of the decision variables vector into several sub-components is achieved and multi-swarms are created from the initial population. Each sub-swarm is then assigned to optimize a part of the LSGO problem. To form the complete solution, the representatives from each sub-swarm are combined. To reduce the computation time, an efficient parallel master-slave model is introduced in the proposed parameters-free PCCGWO. The master will be responsible for decomposing the original problem and constructing the context vector which contains the complete solution. Each slave is designed to evolve a sub-component and will send the best individual as its representative to the master after each evolutionary cycle. Demonstrative results show the effectiveness and superiority of the proposed PCCGWO-based planning technique in terms of several metrics of performance and nonparametric statistical analyses. These results show that the increase in the number of slaves leads to a more efficient result as well as a further improved computational time.