Central Force Optimization Research Articles

Application of Central Force Optimization Method to Design Transient Protection Devices for Water Transmission Pipelines

One of the major challenges in designing under pressure water transmission pipeline is the system protection against water-hammer pressures due to a pump trip. The best strategy is to use air-chamber; which imposes considerable costs. To mitigate the air-chamber volume, the use of air-inletvalvesis also suggested. Determination of air-chamber volume as well as the type and proper locations of air-inlet valves, aiming at the cost reduction, introduces an optimization problem. To solve this problem, this study exploitsthe central force optimization (CFO) method. Herein, a case study pipeline is optimized using the proposed model based on the CFO and is compared with results of a genetic algorithm (GA) based model. Both methods yielded almost the same results and led to about 30% saving in the system protection cost. However, a comparison between the methods showed that the CFO dramaticallyoutperforms GA in both terms of computational efficiency and reliability of the results.

Synchronization clustering based on central force optimization and its extension for large-scale datasets

Although research on clustering methods has been active in recent years, not only must most current clustering methods pre-set the number of clusters or other user-specific parameters but they also perform on large-scale datasets inefficiently. In this paper, we study the clustering problem by exploring the metaphor of gravitational kinematics based on Central Force Optimization (CFO). However, different from the global synchronization of CFO, we propose a new algorithm G-Sync by simulating the partial synchronization phenomenon. Specifically, we view each data object as a probe and simulate the dynamic interaction behaviour of data objects in the gravitational field. As time evolves, similar data objects will naturally come into partial synchronization and form distinct clusters measured by the proposed degree of local synchronization, and the dynamic interaction behaviour of the data objects is continually simulated over time. By introducing the Davies–Bouldin (DB) index, G-Sync can determine clusters of arbitrary size, shape and density. Moreover, pre-setting the number of clusters to be found is not required. The algorithm is further extended for handling large-scale datasets with the scalable S-G-Sync algorithm, which is based on fast kernel density estimation (FastKDE). S-G-Sync initially condenses a large-scale dataset quickly into its reduced dataset, followed by adaptive clustering on the reduced dataset using G-Sync. Finally, the Clustering on Remaining Objects (CRO) algorithm is proposed to cluster the remaining objects in the large-scale dataset and to capture outlier and singleton clusters effectively. The effectiveness of the G-Sync and S-G-Sync algorithms is theoretically analysed and experimentally verified on synthetic and real-world datasets.

Synthesis of unequally‐spaced linear array using modified central force optimisation algorithm

In this study, a modified version of the central force optimisation (MCFO) algorithm is presented. This modified version is based on the idea of combining the ability of social thinking in particle swarm optimisation (PSO) with the search capability of the original CFO, along with the addition of time-varying acceleration coefficients, to effectively control the global search and enhance the CFO convergence capability. The convergence capability of the MCFO approach is compared with that of other recent evolutionary-based algorithms, using 12 benchmark functions grouped into unimodal and multimodal functions. Furthermore, the MCFO algorithm is considered for the synthesis of unequally-spaced linear arrays with minimum sidelobe levels and/or null placement in certain directions as well as a specified maximum null-to-null beamwidth. The comparison of the simulations of different algorithms shows that the MCFO technique is superior to other evolutionary algorithms such as the genetic algorithm, ant colony optimisation, PSO algorithm, and gravitational search algorithm, as well as other improved CFO algorithms.

Development of central force optimization for pipe-sizing of water distribution networks

Due to the economic crisis and water scarcity happening in recent years, many researchers have focused on the water distribution network optimization problem. On this specified subject, all recent research has applied stochastic meta-heuristic algorithms to solve these sets of problems. In this study, the application of a novel deterministic physically inspired heuristic algorithm for minimizing the cost of pipe-sizing in the water distribution system (WDS) is investigated. In fact, the algorithm used in this research is the modified central force optimization algorithm to solve the water distribution network problem called CFOnet. The approach is applied to optimize the design of the Kadu and Khorramshahr networks. For this purpose, CFOnet method is programmed in MATLAB and interfaced with the hydraulic simulation model, EPANET. The obtained solutions in this study are compared with those stochastic methods in the WDS optimization literature. This comparison shows that CFOnet is more efficient in obtaining lower cost than other optimization methods for solving the two mentioned WDSs, while it enjoys the merits of a deterministic optimization method.

An Adaptive Central Force Optimization (ACFO) and Feed Forward Back Propagation Neural Network (FFBNN) based iris recognition system

Iris Recognition that emerged two decades back has a number of algorithms developed and vast amount of work has been carried out since its inception. Iris recognition uses pattern-recognition techniques based on high-resolution images of the person. This paper proposes a novel iris recognition system using FFBNN-ACFO. Initially the given input images are preprocessed using adaptive median filter to remove noise. Then the features which are extracted from the preprocessed image are used to train the FFBNN. During training, FFBNN parameters are optimized by ACFO to get high recognition accuracy. In the testing phase sufficient number of iris images, are utilized to analyze the performance of the proposed iris recognition system. The results of the proposed method are compared with FFBNN-AAPSO, FFBNN-PSO, and FFBNN techniques. The comparison result shows that the proposed iris recognition system based on FFBNN-ACFO, gives higher recognition accuracy than the existing iris recognition systems.

Metaheuristic algorithms for dispersion optimization of photonic crystal fibers

In this paper, recent metaheuristic algorithms such as central force optimization (CFO) and particle swarm optimization (PSO) have been used for efficient calculation and optimization of the dispersion properties of photonic crystal fibers (PCFs), in an easy, efficient, and simple way. The suggested approach depends on the use of full vectorial finite difference method along with the optimization techniques for PCF dispersion optimization. The design of ultra-flattened zero dispersion PCF over a wide band of wavelengths from 1.25 to 1.6 µm is carried out in order to introduce the advantages of using these algorithms in conjunction with the numerical methods. Additionally, the CFO and PSO algorithms have a strong potential to be intriguing tools for the design and optimization of different photonic devices. Further, these algorithms prove to be powerful techniques for solving the inverse problems.

A comparative study among different parallel hybrid artificial intelligent approaches to solve the capacitated vehicle routing problem

The vehicle routing problem involves distribution management in the fields of transportation, distribution, and logistics, and it is one of the most important, and studied, combinatorial optimisation problems. The capacitated vehicle routing problem is an NP-hard problem, which was introduced by Dantzig and Ramser in 1959. The objective is to minimise the total distance and to maximise capacity for all of the vehicles. In this paper, the proposed parallel hybrid artificial intelligent approaches are based on cuckoo search that uses the positive features of two other optimisation techniques, central force optimisation and chemical reaction optimisation, for enhancing local search and improving the quality of the initial population, respectively. The motivation for this work is to improve the computational efficiency by getting even better results than the previous best known solutions, to study of the dynamics of various parameters of proposed approaches in searching optimum solutions, and to quicken the process of finding the optimal solution. The proposed approaches are tested on standard test instances from the literature. The test results demonstrate the effectiveness of the proposed approaches in solving the capacitated vehicle routing problem efficiently.

Trajectory optimization of multiple quad-rotor UAVs in collaborative assembling task

A hierarchic optimization strategy based on the offline path planning process and online trajectory planning process is presented to solve the trajectory optimization problem of multiple quad-rotor unmanned aerial vehicles in the collaborative assembling task. Firstly, the path planning process is solved by a novel parallel intelligent optimization algorithm, the central force optimization-genetic algorithm (CFO-GA), which combines the central force optimization (CFO) algorithm with the genetic algorithm (GA). Because of the immaturity of the CFO, the convergence analysis of the CFO is completed by the stability theory of the linear time-variant discrete-time systems. The results show that the parallel CFO-GA algorithm converges faster than the parallel CFO and the central force optimization-sequential quadratic programming (CFO-SQP) algorithm. Then, the trajectory planning problem is established based on the path planning results. In order to limit the range of the attitude angle and guarantee the flight stability, the optimized object is changed from the ordinary six-degree-of-freedom rigid-body dynamic model to the dynamic model with an inner-loop attitude controller. The results show that the trajectory planning process can be solved by the mature SQP algorithm easily. Finally, the discussion and analysis of the real-time performance of the hierarchic optimization strategy are presented around the group number of the waypoints and the equal interval time.

Optimised diffusion spots’ locations for simultaneous improvement in SNR and delay spread

In this paper, two recent global optimisation techniques: particle swarm optimisation and central force optimisation are considered for optimising the location of the diffusion spots, which are used as transmitters in an indoor optical wireless communications system. The diffusion spots are uniformly distributed along a circle on the ceiling of the communications environment. The location of the diffusion spots is optimised for maximising the signal-to-noise ratio and minimising the root-mean-square delay spread at the receivers in the presence of noise sources. A performance comparison between the central located position of the spots and the optimised positions for three different scenarios is considered to validate and show the strengths of the applied optimisation techniques in solving this sort of problems. The used techniques can provide the communication system with the ability to adapt to changes in the surrounding environment, which will benefit future switching towards real-time intelligent systems.

Modified central force optimization (MCFO) algorithm for 3D UAV path planning

Path planning for the three-dimensional (3D) unmanned aerial vehicles (UAV) is a very important element of the whole UAV autonomous control system. In this paper, a modified central force optimization (MCFO) method is introduced to solve this complicated path-optimization problem for the rotary wing vertical take-off and landing (VTOL) aircraft. In the path planning process, the idea from the particle swarm optimization (PSO) algorithm and the mutation operator of the genetic algorithm (GA) are applied to improve the original CFO method. Furthermore, the convergence analysis of the whole MCFO method is established by the linear difference equation method. Then, in order to verify the effectiveness and practicality of this new path planning method, the path following process is put forward based on the six-degree-of-freedom quadrotor helicopter control system. At last, the comparison simulations among the six algorithms show that the trajectories produced by the whole MCFO method are more superior than the original CFO algorithm, the GA, the Firefly algorithm (FA), the PSO algorithm, the random search (RS) way and the other MCFO algorithm under the same conditions. What is more, the path following process results show that the path planning results are practical for the real dynamic model of the quadrotor helicopter.

Convergence analysis and application of the central force optimization algorithm

Convergence analysis and application of the central force optimization algorithm

Adaptive Central Force Optimization Algorithm Based on the Stability Analysis

In order to enhance the convergence capability of the central force optimization (CFO) algorithm, an adaptive central force optimization (ACFO) algorithm is presented by introducing an adaptive weight and defining an adaptive gravitational constant. The adaptive weight and gravitational constant are selected based on the stability theory of discrete time-varying dynamic systems. The convergence capability of ACFO algorithm is compared with the other improved CFO algorithm and evolutionary-based algorithm using 23 unimodal and multimodal benchmark functions. Experiments results show that ACFO substantially enhances the performance of CFO in terms of global optimality and solution accuracy.

A multi-start central force optimization for global optimization

Central force optimization (CFO) is an efficient and powerful population-based intelligence algorithm for optimization problems. CFO is deterministic in nature, unlike the most widely used metaheuristics. CFO, however, is not completely free from the problems of premature convergence. One way to overcome local optimality is to utilize the multi-start strategy. By combining the respective advantages of CFO and the multi-start strategy, a multi-start central force optimization (MCFO) algorithm is proposed in this paper. The performance of the MCFO approach is evaluated on a comprehensive set of benchmark functions. The experimental results demonstrate that MCFO not only saves the computational cost, but also performs better than some state-of-the-art CFO algorithms. MCFO is also compared with representative evolutionary algorithms. The results show that MCFO is highly competitive, achieving promising performance.

Neural network ensembles based on copula methods and Distributed Multiobjective Central Force Optimization algorithm

Copula is a function with multivariate distribution. It has uniformly distributed marginals. Central Force Optimization is a new algorithm which is based on kinematics. It has been illustrated that this algorithm is better than other heuristic methods, when these techniques are applied to the classification problems. This paper proposes a technique of neural network ensembles which use the distributed Central Force algorithm to optimize each individual component network, simultaneously. The distributed Central Force algorithm incorporates an additional regularization term and utilizes the multiobjective architectures to design component networks. Furthermore it proposes that a new method of combining the component networks is to use Copula function theory as an effective design tool which generates the combining weights. The experimental results show that the copula-based ensemble network achieves better performance than other ensemble methods and that Distributed Multiobjective Central Force Optimization is capable of achieving better solutions in the light of converging speed and local minima. In the experimental discussion, the paper gives several reasons why the proposed method outperforms others.

Convergence Proof for Central Force Optimization Algorithm and Application in Neural Networks

Central force optimization(CFO) is a new deterministic multi-dimensional search metaheuristic based on the metaphor of gravitational kinematics.CFO is a deterministic algorithm that explores a decision space by "flying" a group of probes whose trajectories are governed by Newton's laws.Based on in-deph studies on the probes movement governed by the equations of gravitational motion,this paper utilizes Celestial Mechanics theory to deduce moving formulas,establishes the relationship between CFO algorithm and Celestial Mechanics,and analyzes CFO convergence through mathematics analysis of Celestial Mechanics.It concludes that no matter how initial probe distribute,all probes converge deterministically in CFO space with optimal solution.To test CFO's effectiveness,a hybrid CFO-BP algorithm is proposed for joint optimization of three-layer feed forward artificial neural network(ANN) structure and parameters(weights and bias).The experimental results show that the proposed hybrid CFO-BP algorithm is better than other algorithms in convergent speed and convergent accuracy.

An Improved Central Force Optimization Algorithm for Multimodal Optimization

This paper proposes the hybrid CSM-CFO algorithm based on the simplex method (SM), clustering technique, and central force optimization (CFO) for unconstrained optimization. CSM-CFO is still a deterministic swarm intelligent algorithm, such that the complex statistical analysis of the numerical results can be omitted, and the convergence intends to produce faster and more accurate by clustering technique and good points set. When tested against benchmark functions, in low and high dimensions, the CSM-CFO algorithm has competitive performance in terms of accuracy and convergence speed compared to other evolutionary algorithms: particle swarm optimization, evolutionary program, and simulated annealing. The comparison results demonstrate that the proposed algorithm is effective and efficient.

Variable Z0applied to the optimal design of multi-stub matching network and a meander monopole

VariableZ0, a new concept in antenna design and optimization, is applied to two optimization problems: a multi-stub matching network (MSMN) using biogeography-based optimization (BBO), and an ultra wideband meander monopole antenna (MMA) using central force optimization (CFO). BBO is a newly-proposed stochastic global search and optimization evolutionary algorithm (EA) used to determine MSMN stub lengths and locations for optimum (minimum) reflection coefficient. CFO is a deterministic EA used to optimize the MMA's impedance bandwidth (IBW) while maintaining good average gain without considering the radiation pattern in detail. Two cases are investigated for both problems: (a) fixed characteristic impedanceZ0, and (b) variable characteristic impedance. In the first case,Z0is a fixed user-specified parameter (the traditional methodology), whereas in the second, it is a true variable quantity whose value is determined by the optimization methodology, which is a new technology. VariableZ0is a fundamentally different design approach in optimization problems. BBO's fixedZ0results for MSMN are compared to published data computed using Nelder–Mead optimization with BBO exhibiting better performance. BBO's results are improved even more using VariableZ0technology. A similar performance improvement is seen for VariableZ0applied to the CFO-optimized MMA.

UWB ANTENNA DESIGN USING GRAVITATIONAL SEARCH ALGORITHM

In this paper, a heuristic search method called Gravitational Search Algorithm (GSA) is proposed to design Ultra-wideband antennas (UWB) with irregular shape radiators. To measure the algorithm efficiency in practical antennas design, the results are compared with those obtained using the Central Force Optimization (CFO) technique. The optimization algorithms in MATLAB code are linked to Finite Element Method (FEM) solution technique (Ansoft HFSS-software) to simulate the antenna. The optimized compact antennas are fed by a microstrip line and built on an FR-4 substrate with 30 x 30 mm2 surface area and 1.5 mm thickness. The radiation characteristics of the designed antennas are completely analyzed, and the VSWR is then compared with the measurements to check the validity of the numerical results. Keywords: UWB Antenna, Central Force Optimization (CFO), Gravitational Search Algorithm (GSA).

CFO Parallel Implementation on GPU for Adaptive Beam-forming Applications

The scientific community is still interested in heuristic techniques and optimization algorithms that could be applied in complex problems such as the antenna adaptive beam forming problem. This paper presents an empirical study of solving the problem of antenna adaptive beam forming using Central Force Optimization (CFO) algorithm. The algorithm implemented using Compute Unified Device Architecture (CUDA) then applied on a graphics processing unit (GPU). CFO is well known alternatives for global optimization based on a nature-inspired Heuristic. Extensive experimentations were applied to compare their performance through a number of case studies. CFO has a higher computational complexity but it gives good results. The experimentations showed that the resulting beam-pattern optimized by the CFO required a large processing time which is not acceptable for an on line applications. Hence, the demand for a parallel solution that accelerates these computations is considered. Therefore, a parallel version of CFO is proposed and implemented using (CUDA) then applied on a (GPU). The comparison is presented to show how the parallel version of the CFO outperforms the sequential one, thus an online procedure is available for time-critical applications of the adaptive beamforming.

Pseudorandomness in Central Force Optimization

Central Force Optimization is a deterministic metaheuristic for an evolutionary algorithm that searches a decision space by flying probes whose trajectories are computed using a gravitational metaphor. CFO benefits substantially from the inclusion of a pseudorandom component (a numerical sequence that is precisely known by specification or calculation but otherwise arbitrary). The essential requirement is that the sequence is uncorrelated with the decision space topology, so that its effect is to pseudorandomly distribute probes throughout the landscape. While this process may appear to be similar to the randomness in an inherently stochastic algorithm, it is in fact fundamentally different because CFO remains deterministic at every step. Three pseudorandom methods are discussed (initial probe distribution, repositioning factor, and decision space adaptation). A sample problem is presented in detail and summary data included for a 23-function benchmark suite. CFO’s performance is quite good compared to other highly developed, state-of-the-art algorithms. Ver. 2 (typographical errors in Step (c) of Fig. 1 and discussion of Fig. 8 corrected; clarification of definition of best R r ; error in Table 2 test function f12 corrected; f12 source code in Appendix 3, page 60 corrected). 3 February 2010 Saint Augustine, Florida