Optimization Test Functions Research Articles

Optimization test function synthesis with generative adversarial networks and adaptive neuro-fuzzy systems

This paper presents an approach to synthesizing optimization test functions that couples generative adversarial networks and adaptive neuro-fuzzy systems. A generative adversarial network produces optimization landscapes from a database of known optimization test functions, and an adaptive neuro-fuzzy system performs regression on the generated landscapes to provide closed-form expressions. These expressions can be implemented as fuzzy basis function expansions. Eight databases of two-dimensional optimization landscapes reported in the literature are used to train the generative network. Exploratory landscape analysis over the generated samples reveals that the network can lead to new optimization landscapes with features of interest. In addition, fuzzy basis function expansions provide the best approximation results when compared against two symbolic regression frameworks over several selected landscapes. Examples are used to illustrate the ability of these functions to model complex surface artifacts such as plateaus. The proposed approach can be used as a mathematical collaboration tool that couples generative artificial and computational intelligence techniques to formulate high-dimensional optimization test problems from two-dimensional synthesized functions.

Correction of nonmonotone trust region algorithm based on a modified diagonal regularized quasi-Newton method

In this paper, a new appropriate diagonal matrix estimation of the Hessian is introduced by minimizing the Byrd and Nocedal function subject to the weak secant equation. The Hessian estimate is used to correct the framework of a nonmonotone trust region algorithm with the regularized quasi-Newton method. Moreover, to counteract the adverse effect of monotonicity, we introduce a new nonmonotone strategy. The global and superlinear convergence of the suggested algorithm is established under some standard conditions. The numerical experiments on unconstrained optimization test functions show that the new algorithm is efficient and robust.

Quantum Chimp Optimization Algorithm: A Novel Integration of Quantum Mechanics Into the Chimp Optimization Framework for Enhanced Performance

Abstract This research introduces the Quantum Chimp Optimization Algorithm (QChOA), a pioneering methodology that integrates quantum mechanics principles into the Chimp Optimization Algorithm (ChOA). By incorporating non-linearity and uncertainty, the QChOA significantly improves the ChOA’s exploration and exploitation capabilities. A distinctive feature of the QChOA is its ability to displace a ’chimp,’ representing a potential solution, leading to heightened fitness levels compared to the current top search agent. Our comprehensive evaluation includes twenty- nine standard optimization test functions, thirty CEC-BC functions, the CEC06 test suite, ten real-world engineering challenges, and the IEEE CEC 2022 competition’s dynamic optimization problems. Comparative analyses involve four ChOA variants, three leading quantum-behaved algorithms, three state-ofthe-art algorithms, and eighteen benchmarks. Employing three non-parametric statistical tests (Wilcoxon rank-sum, Holm-Bonferroni, and Friedman average rank tests), results show that the QChOA outperforms counterparts in 51 out of 70 scenarios, exhibiting performance on par with SHADE and CMA-ES, and statistical equivalence to jDE100 and DISHchain1e+12. The study underscores the QChOA’s reliability and adaptability, positioning it as a valuable technique for diverse and intricate optimization challenges in the field.

Research on hybrid reservoir scheduling optimization based on improved walrus optimization algorithm with coupling adaptive ε constraint and multi-strategy optimization

Reservoir flood control scheduling is a challenging optimization task, particularly due to the complexity of various constraints. This paper proposes an innovative algorithm design approach to address this challenge. Combining the basic walrus optimization algorithm with the adaptive ε-constraint method and introducing the SPM chaotic mapping for population initialization, spiral search strategy, and local enhancement search strategy based on Cauchy mutation and reverse learning significantly enhances the algorithm's optimization performance. On this basis, innovate an adaptive approach ε A New Algorithm for Constraints and Multi Strategy Optimization Improvement (ε-IWOA). To validate the performance of the ε-IWOA algorithm, 24 constrained optimization test functions are used to test its optimization capabilities and effectiveness in solving constrained optimization problems. Experimental results demonstrate that the ε-IWOA algorithm exhibits excellent optimization ability and stable performance. Taking the Taolinkou Reservoir, Daheiting Reservoir, and Panjiakou Reservoir in the middle and lower reaches of the Luanhe River Basin as a case study, this paper applies the ε-IWOA algorithm to practical reservoir scheduling problems by constructing a three-reservoir flood control scheduling system with Luanxian as the control point. A comparative analysis is conducted with the ε-WOA, ε-DE and ε-PSO (particle swarm optimization) algorithms.The experimental results indicate that ε-IWOA algorithm performs the best in optimization, with the occupied flood control capacity of the three reservoirs reaching 89.32%, 90.02%, and 80.95%, respectively. The control points in Luan County can reduce the peak by 49%.This provides a practical and effective solution method for reservoir optimization scheduling models. This study offers new ideas and solutions for flood control optimization scheduling of reservoir groups, contributing to the optimization and development of reservoir scheduling work.

Cross-channel color image encryption through 2D hyperchaotic hybrid map of optimization test functions

The security of chaos-based Image Encryption (IE) algorithms inherently depends on the permutation and diffusion strategy of the algorithm and the dynamic performance of chaotic maps. However, the existing studies suffer from low disordering capability, poor dynamic performance, and lack of sensitivity of the chaotic maps. In order to address these limitations, a Cross-Channel Color IE (CCC-IE) algorithm is presented, which has high shuffling ability with diagonal permutation and bi-directional sequential diffusion through a novel 2D hyperchaotic hybrid map of optimization test functions. The proposed 2D hyperchaotic map, namely 2D-RG map, is designed by hybridizing the Rastrigin and Griewank functions. Their chaotic nature, such as high complexity and fluctuation, makes them suitable for design of chaotic map. The 2D-RG map-based CCC-IE algorithm diagonally scrambles the pixels of the image across RGB channels and sequentially manipulates the pixel values in bi-direction for improving resistance of the algorithm to the cyberthreats. The dynamic performance of the 2D-RG map and the reliability of the CCC-IE algorithm are separately investigated and validated through a detailed comparison with the state of the art. The results manifest that the CCC-IE not only visually but also numerically is the more reliable algorithm thanks to the superior chaotic characteristics of the 2D-RG map.

A New Gradient-Accelerated Two-Stage Multiobjective Optimization Method for CO2-Alternating-Water Injection in an Oil Reservoir

Summary CO2-water-alternating-gas (CO2-WAG) is a reservoir development method that can simultaneously enhance oil recovery and achieve CO2 storage. However, improperly designed parameters for CO2 injection and oil production may significantly reduce the oil displacement efficiency and CO2 storage. Furthermore, optimizing the injection parameters is computationally expensive due to the high computational cost of the compositional simulation. This work aims to propose an efficient optimization method to obtain a series of well-control schemes that balance maximizing net present value (NPV) and CO2 storage for decision-makers. Given the number of CO2-WAG cycles and the duration of each cycle, we optimize the water injection rate, gas injection rate, and half-cycle for the injection well and the bottomhole pressure (BHP) for the production well. In this paper, a two-stage optimization strategy is proposed to enhance the optimization efficiency. The first stage performs the surrogate-assisted single-objective optimizations of each considered objective. It is designed to find the endpoints of the Pareto front that connect all solutions of the multiobjective optimization; this stage not only provides important search directions for the subsequent multiobjective optimization but also improves the accuracy of the surrogate model near the Pareto front. The second stage is the surrogate-assisted multiobjective optimization, which aims to find all the solutions along the Pareto front based on the Pareto endpoints obtained from the first stage. In addition, this study successfully combines the gradient of the objective functions with the meta-heuristic algorithm during the multiobjective optimization, which ensures a faster convergence to the global optimum. The proposed multiobjective optimization algorithm shows faster convergence than the conventional optimization methods when applied to the three multiobjective optimization test functions. Finally, a comparison with the conventional multiobjective optimization is conducted based on one test function and two benchmark reservoir simulation models to verify the correctness and efficiency of the proposed method. It is confirmed that the proposed method outperforms the conventional ones for the optimization of CO2-WAG injection.

A Multi-Strategy Improved Sooty Tern Optimization Algorithm for Concrete Dam Parameter Inversion

A original strategy for optimizing the inversion of concrete dam parameters based on the multi-strategy improved Sooty Tern Optimization algorithm (MSSTOA) is proposed to address the issues of low efficiency, low accuracy, and poor optimizing performance. First, computational strategies to improve the traditional Sooty tern algorithm, such as chaos mapping to improve the initial position of the population, a new nonlinear convergence factor, the LIMIT threshold method, and Gaussian perturbation to update the optimal individual position, are adopted to enhance its algorithmic optimization seeking ability. Then, the measured and finite element data are combined to create the optimization inversion fitness function. Based on the MSSTOA, the intelligent optimization inversion model is constructed, the inversion efficiency is improved by parallel strategy, and the optimal parameter inversion is searched. The inversion strategy is validated through test functions, hypothetical arithmetic examples, and concrete dam engineering examples and compared with the inversion results of the traditional STOA and other optimization algorithms. The results show that the MSSTOA is feasible and practical, the test function optimization results and computational time are better than the STOA and other algorithms, the example inversion of the elastic modulus is more accurate than the traditional STOA calculation, and the results of the MSSSTOA inversion are reasonable in the engineering example. Compared with other algorithms, the local extremes are skipped, and the time consumption is reduced by at least 48%. The finite element hydrostatic components calculated from the inversion results are well-fitted to the statistical model with minor errors. The intelligent inversion strategy has good application in concrete dam inverse analysis.

A Deep Learning Neural Network Method Using Linear Eigenvalue Statistics for Schizophrenic EEG Data Classification

Electroencephalography (EEG) signals can be used as a neuroimaging indicator to analyze brain-related diseases and mental states, such as schizophrenia, which is a common and serious mental disorder. However, the main limiting factor of using EEG data to support clinical schizophrenia diagnosis lies in the inadequacy of both objective characteristics and effective data analysis techniques. Random matrix theory (RMT) and its linear eigenvalue statistics (LES) can provide an effective mathematical modeling method for exploring the statistical properties of non-stationary nonlinear systems, such as EEG signals. To obtain an accurate classification and diagnosis of schizophrenia, this paper proposes a LES-based deep learning network scheme in which a series of random matrixes, consisting of EEG data sliding window sampling and their eigenvalues, are employed as features for deep learning. Due to the fact that the performance of the LES-based scheme is sensitive to the LES’s test function, the proposed LES-based deep learning network is embedded with two ways of combining LES’s test functions with learning techniques: the first is to have the LES’s test function assigned, while, using the second way, the optimal LES’s test function should be solved in a functional optimization problem. In this paper, various test functions and different optimal learning methods were coupled in experiments. Our results revealed a binary classification accuracy of nearly 90% in distinguishing between healthy controls (HC) and patients experiencing the first episode of schizophrenia (FES). Additionally, we achieved a ternary classification accuracy of approximately 70% by including clinical high risk for psychosis (CHR). The LES-embedded approach yielded notably higher classification accuracy compared to conventional machine learning methods and standard convolutional neural networks. As the performance of schizophrenia classification is strongly influenced by test functions, a functional optimization problem was proposed to identify an optimized test function, and an approximated parameter optimization problem was introduced to limit the search area of suitable basis functions. Furthermore, the parameterization test function optimization problem and the deep learning network were coupled to be synchronously optimized during the training process. The proposal approach achieved higher classification accuracy rates of 96.87% between HC and FES, with an additional 89.06% accuracy when CHR was included. The experimental studies demonstrated that the proposed LES-based method was significantly effective for schizophrenic EEG data classification.

Multi-objective Adaptive Fuzzy Campus Placement based Optimization Algorithm for optimal integration of DERs and DSTATCOMs

The novel Adaptive Fuzzy Campus Placement based Optimization Algorithm (AFCPOA) presented in this paper is expected to solve the issue of single objective and multi objective optimal optimization problems. AFCPOA’s performance was evaluated on 25 benchmark optimization test functions and compared to other existing methods. Optimal location and sizing of Distributed Generation (DG), Distribution STATtic COMpensator (DSTATCOM), DGs and DSTATCOMs, Battery Energy Storage Systems (BESS) in the presence of PVDGs, and BESS in the presence of PVDGs and DSTATCOMs were integrated into Radial Distribution System (RDS) to fulfil the objectives. Technical advantages of DG include active power losses reduction and control of voltage dips. DSTATCOM functions as a capacitor, injecting reactive power to improve the consistency and quality of power flow and sustain voltage against any imbalance and distortion on load side or supply side. The appropriate location and capacity for BESS present a significant barrier for the integration of BESS and renewable DGs with distribution networks. The objective functions in this problem are to minimize total real power losses, reactive power losses, and voltage deviation. Additionally, the improvement of voltage profile was taken into consideration as a constraint while choosing the best location. Finally, the suggested algorithm is evaluated on IEEE 33 bus RDS and PG & E 69 bus RDS. Simulation results show the proposed method’s excellent performance and applicability.

Meerkat optimization algorithm: A new meta-heuristic optimization algorithm for solving constrained engineering problems

In this paper, we proposed a meerkat optimization algorithm(MOA) by simulating the behavior pattern of meerkats in nature. MOA is mainly inspired by the survival strategies of meerkat populations, whose sentinel mechanism controls meerkats to switch between different behavior patterns. Some mathematical properties of meerkat optimization algorithm are proved, and the advantages of MOA are verified with classical optimization test functions. MOA is applied to solve real-world engineering problems with constraints, which proves the effectiveness and superiority of MOA in solving such problems.

Improved BAT Algorithm Using Density-Based Clustering

BAT algorithm is a nature-inspired metaheuristic algorithm that depends on the principle of the echolocation behavior of bats. However, the algorithm suffers from being stuck in the local optima early due to its poor exploration. An improved BAT algorithm based on the density-based clustering technique is proposed to enhance the algorithm’s performance.
 In this paper, the initial population is improved by generating two populations, randomly and depending on the clusters’ center information, and by getting the fittest individuals from these two populations, the initial improved one is generated. The random walk function is improved using chaotic maps instead of the fixed-size movement, and so the local search is improved as well as the global search abilities by diversifying the solutions. Another improvement is to deal with stagnation by partitioning the search space into two parts depending on the generated clusters’ information to obtain the newly generated solution and comparing their quality with the previously generated solution and choosing the best.
 The performance of the proposed improved BAT algorithm is evaluated by comparing it with the original BAT algorithm over ten benchmark optimization test functions. Depending on the results, the improved BAT outperforms the original BAT by obtaining the optimal global solutions for most of the benchmark test functions.

Optimal power flow analysis considering renewable energy resources uncertainty based on an improved wild horse optimizer

AbstractIn recent years, electricity networks across the globe have undergone rapid development, especially with the incorporation of various renewable energy sources (RES). The goal is to increase the penetration level of RES in the power grid to maximize energy efficiency. However, the optimal power flow (OPF) problem for conventional power generation with RES integration is highly complex, non‐linear, and non‐convex, and this complexity is further compounded when stochastic RES is integrated into the network. To address this problem, this article proposes an elite evolutionary strategy (EES) based on evolutionary approaches to improve the Wild Horse Optimizer (WHO), creating an enhanced hybrid technique called EESWHO. The proposed technique's effectiveness and robustness were tested on 23 numerical optimization test functions, including seven unimodal, six multimodal, and ten composite test functions. Furthermore, the EESWHO was applied to the modified IEEE‐30 bus test system to demonstrate its supremacy and efficacy in achieving the optimal solution. The simulation results show that the proposed EESWHO algorithm is highly effective and robust in achieving the optimal solution to the OPF problem with stochastic RES. This approach provides a practical solution to the challenges posed by the integration of RES into power networks, allowing for maximum energy efficiency while minimizing system complexity.

Study on Multi-UAV Cooperative Path Planning for Complex Patrol Tasks in Large Cities

Unmanned Aerial Vehicles (UAVs) are increasingly utilized for urban patrol and defense owing to their low cost, high mobility, and rapid deployment. This paper proposes a multi-UAV mission planning model that takes into account mission execution rates, flight energy consumption costs, and impact costs. A kinematics and dynamics model of a quadcopter UAV is established, and the UAV’s flight state is analyzed. Due to the difficulties in addressing 3D UAV kinematic constraints and poor uniformity using traditional optimization algorithms, a lightning search algorithm (LSA) based on multi-layer nesting and random walk strategies (MNRW-LSA) is proposed. The convergence performance of the MNRW-LSA algorithm is demonstrated by comparing it with several other algorithms, such as the Golden Jackal Optimization (GJO), Hunter–Prey Optimization (HPO), Pelican Optimization Algorithm (POA), Reptile Search Algorithm (RSA), and the Golden Eagle Optimization (GEO) using optimization test functions, Friedman and Nemenyi tests. Additionally, a greedy strategy is added to the Rapidly-Exploring Random Tree (RRT) algorithm to initialize the trajectories for simulation experiments using a 3D city model. The results indicate that the proposed algorithm can enhance global convergence and robustness, shorten convergence time, improve UAV execution coverage, and reduce energy consumption. Compared with other algorithms, such as Particle Swarm Optimization (PSO), Simulated Annealing (SA), and LSA, the proposed method has greater advantages in addressing multi-UAV trajectory planning problems.

Improved QoS with Fog computing based on Adaptive Load Balancing Algorithm

As the number of sensing devices rises, traffic on the cloud servers is boosting day by day. When a device connected to the IoTwants access to data, cloud computing encourages the pairing of fog & cloud nodes to provide that information. One of the key needs in a fog-based cloud system, is efficient job scheduling to decrease the data delay and improve the QoS (Quality of Service). The researchers have used a variety of strategies to maintain the QoS criteria. However, because of the increased service delay caused by the busty traffic, job scheduling is impacted which leads to the unbalanced load on the fog environment. The proposed work uses a novel model which curates the features and working style of Genetic algorithm and the optimization algorithm with the load balancing scheduling on the fog nodes. The performance of the proposed hybrid model is contrasted with the other well-known algorithms in contrast to the fundamental benchmark optimization test functions. The proposed work displays better results in sustaining the task scheduling process when compared to the existing algorithms, which include Round Robin (RR) method, Hybrid RR, Hybrid Threshold based and Hybrid Predictive Based models, which ensures the efficacy of the proposed load balancing model to improve the quality of service in fog environment.

THE NEW RANK ONE CLASS FOR UNCONSTRAINED PROBLEMS SOLVING

One of the most well-known methods for unconstrained problems is the quasi-Newton approach, iterative solutions. The great precision and quick convergence of the quasi-Newton methods are well recognized. In this work, the new algorithm for the symmetric rank one SR1 method is driven. The strong Wolfe line search criteria define the step length selection. We also proved the new quasi-Newton equation and positive definite matrix theorem. Preliminary computer testing on the set of fourteen unrestricted optimization test functions leads to the conclusion that this new method is more effective and durable than the implementation of classical SR1 method in terms of iterations count and functions.

Evolving Marine Predators Algorithm by dynamic foraging strategy for real-world engineering optimization problems

The Marine Predators Algorithm (MPA) is a novel hunting-based optimizer. The MPA’s central concept is based on the well-known Lévy Flight (LF) and Brownian Motion (BM) strategies as well as a simple transition model between these two strategies. The canonical MPA proposes three static steps to tune the transition behavior between the LF and BM strategies. Although MPA provides exemplary performance in many test functions, the discrete transition between the two mentioned phases causes it to get stuck in local optima when faced with real-world optimization problems. In order to address this shortcoming, this paper proposes a soft dynamic transition between LF and BM to model this encounter naturally, considering the continuous nature of the transition between LF and BM in marine predators’ real life. In order to evaluate the performance of the developed Dynamic Foraging Strategy MPA (DFSMPA), twenty-nine optimization test functions, thirty complex CEC-BC-2017 functions, ten benchmarks of CEC06-2019 test suit, and ten real applicable engineering problems, including power system design, synthesis and process design, industrial chemical producer, power-electronic design, mechanical design, and animal feed ratio, are employed. The DFSMPA is evaluated against four groups of standard optimization approaches, including (1) Arithmetic Optimization Algorithm (AOA), Slime Mould Algorithm (SMA), Equilibrium Optimizer (EO), Niching Chimp Optimization Algorithm (ChOA), Henry Gas Solubility Optimization (HGSO) as recent optimization algorithms, (2) Lévy Flight GWO (LGWO) and Evolutionary Algorithms with Adaptive Lévy Mutations (EALM) as the two best dynamic Lévy-based optimization algorithms, (3) SHADE, CMA-ES, and LSHADESPACMA as the three state-of-the-art optimization algorithms, and jDE100, DISHchain1e+12, CIPDE, and EBOwithCMAR as best performing algorithms in IEEE CEC06-2019 competition. Three non-parametric statistical tests, including the Wilcoxon rank-sum, Bonferroni–Dunn and Holm, and Friedman average rank tests, are utilized to perform a comprehensive assessment. The results show that the DFSMPA achieved the first rank among 46 out of 70 benchmark functions and engineering problems and exhibited similar results compared with SHADE and CMA-ES in other benchmarks. The statistical analysis demonstrated that DFSMPA is a significantly superior optimizer than the three first categories’ benchmark algorithms, while its result is statistically similar to jDE100, DISHchain1e+12.

An efficient spectral minimization of the Dai-Yuan method with application to image reconstruction

<abstract><p>In this paper, a spectral Dai and Yuan conjugate gradient (CG) method is proposed based on the generalized conjugacy condition for large-scale unconstrained optimization, in which the spectral parameter is motivated by some interesting theoretical features of quadratic convergence associated with the Newton method. Accordingly, utilizing the strong Wolfe line search to yield the step-length, the search direction of the proposed spectral method is sufficiently descending and converges globally. By applying some standard Euclidean optimization test functions, numerical results reports show the advantage of the method over some modified Dai and Yuan CG schemes in literature. In addition, the method also shows some reliable results, when applied to solve an image reconstruction model.</p></abstract>

UAV trajectory planning based on an improved sparrow optimization algorithm with multi-strategy integration

Real-time monitoring of urban high-altitude data is an important goal in the construction and development of smart cities today. However, with the development of modern cities, the monitoring space becomes complicated and narrow because of the different building heights and no-fly zones, which makes UAV trajectory planning more difficult. In this paper, a multi-strategy sparrow search algorithm (MSSA) is proposed to solve the UAV trajectory planning problem in a three-dimensional environment. The algorithm aims to minimize the flight distance and maximize the use efficiency of the UAV. First, the improved algorithm employed a reverse-learning strategy based on the law of refraction to improve the search range and enhance the optimization performance. Second, we introduced a random step size generated by Levy flight into the position update strategy of the participant. The algorithm accuracy and speed of convergence were improved by the randomness feature. Finally, the algorithm incorporated the Cauchy mutation to improve the scout position, which enhanced its ability to jump out of the local optimum of the algorithm. Sixteen benchmark test functions, Wilcoxon rank sum test, and 30 CEC2014 test function optimization results demonstrated that MSSA had better optimization accuracy, convergence speed, and robustness than the comparison algorithms. In addition, the proposed algorithm was applied to the UAV trajectory planning problem in different complex 3D environments. The results confirmed that the MSSA outperformed the other algorithms in complex 3D trajectory planning problems.

Hybrid heuristic algorithm for cost-efficient QoS aware task scheduling in fog–cloud environment

Fog cloud computing promotes the combination of fog and cloud nodes to satisfy the requests of data accessing from IoT (Internet of Things) devices. To reduce the data delay and enhancing the QoS (Quality of Service), effective task scheduling is one of the major requirements in fog cloud environment. Numerous approaches have been deployed by the researchers for maintaining the QoS requirements. However, the emergence of bursty traffic affects the process of task scheduling due to high service latency. Effective QoS is promoted by minimizing the costs of computation, communication and deadline violation cost. To achieve the main objective of cost minimization, the proposed work is implemented by adopting a novel model called HFSGA (Hybrid Flamingo Search with a Genetic Algorithm) for better task scheduling. Seven basic benchmark optimization test functions are used to compare the performance of HFSGA with other well-known algorithms. Also, Friedman Rank Test is performed to demonstrate the significance of the results. The implemented model presents better outcomes with respect to PDST (Percentage of deadline satisfied task), makespan and cost. When compared to the existing algorithms that include Ant colony optimization (ACO), Particle swarm optimization (PSO), Genetic Algorithm (GA), Min-CCV, Min-V and Round Robin (RR) approach, the proposed work shows better output in satisfying the task scheduling process.

Binary Interaction Methods for High Dimensional Global Optimization and Machine Learning

In this work we introduce a new class of gradient-free global optimization methods based on a binary interaction dynamics governed by a Boltzmann type equation. In each interaction the particles act taking into account both the best microscopic binary position and the best macroscopic collective position. For the resulting kinetic optimization methods, convergence to the global minimizer is guaranteed for a large class of functions under appropriate parameter constraints that do not depend on the dimension of the problem. In the mean-field limit we show that the resulting Fokker-Planck partial differential equations generalize the current class of consensus based optimization (CBO) methods. Algorithmic implementations inspired by the well-known direct simulation Monte Carlo methods in kinetic theory are derived and discussed. Several examples on prototype test functions for global optimization are reported including an application to machine learning.