Central Force Optimization Research Articles

Are Near Earth Objects the Key to Optimization Theory

This note suggests that near earth objects and Central Force Optimization have something in common, that NEO theory may hold the key to solving some vexing problems in deterministic optimization: local trapping and proof of convergence. CFO analogizes Newton's laws to locate the global maxima of a function. The NEO-CFO nexus is the striking similarity between CFO's Davg and an NEO's Delta-V curves. Both exhibit oscillatory plateau-like regions connected by jumps, suggesting that CFO's metaphorical gravity indeed behaves like real gravity, thereby connecting NEOs and CFO and being the basis for speculating that NEO theory may address difficult issues in optimization.

DESIGN BLUETOOTH AND NOTCHED-UWB E-SHAPE ANTENNA USING OPTIMIZATION TECHNIQUES

In this article, an optimized E-shaped patch antenna for Bluetooth (2.4{2.484GHz) and UWB (3.1{10.6GHz) applications with WLAN (5.15{5.825GHz) band-notched characteristics is proposed. The dimensions of the E-shaped antenna structure in addition to the position of the slotted C-shape in the ground plane are optimized using recent optimization techniques such as Modifled Particle Swarm Optimization (MPSO), Bacterial Swarm Optimization (BSO), and Central Force Optimization (CFO). The optimization algorithms were implemented using MATLAB-software and linked to the CST Microwave Studio to simulate the antenna. Next, the efiects of the Laptop structure on the antenna radiation characteristics are considered. Finally, the antenna structures are simulated by the flnite difierence time domain method (FDTD) to validate the results. The measured results exhibit good agreement with the simulation from CST and the Finite Difierence Time Domain (FDTD) program written with matlab.

CIRCULAR, HEXAGONAL AND OCTAGONAL ARRAY GEOMETRIES FOR SMART ANTENNA SYSTEMS USING HYBRID CFO-HC ALGORITHM

In this paper, circular, hexagonal and Octagonal array geometries for smart antenna applications are compared. Uniform circular (UCA), uniform hexagonal (UHA) and uniform Octagonal arrays (UOA) with 24 half-wave dipole elements are examined. An efficient global hybrid optimization method is proposed combining the Central Force Optimization (CFO) as a global optimizer and Hillclimbing (HC) algorithm as a local optimizer. After the final global iteration, a local optimization can be followed to further improve the solution obtained from the CFO. The CFO-HC algorithm is used to optimize the complex excitations, amplitudes and phases, of the adaptive arrays elements for beamforming, the CFO-HC algorithm was implemented using MATLAB-software and linked to the CST simulator to simulate the adaptive arrays.

Convergence analysis and performance of an extended central force optimization algorithm

Simple central force optimization (SCFO) algorithm is a novel physically-inspired optimization algorithm as simulating annealing (SA). To enhance the global search ability of SCFO and accelerate its convergence, a novel extended/enhanced central force optimization (ECFO) algorithm is proposed through both adding the historical information and defining an adaptive mass. SCFO and ECFO are all motivated by gravitational kinematics, in which the compound gravitation impels particles to the optima. The convergence of ECFO is proved based on a more complex characteristic equation than SCFO, i.e. the second order difference equation. The stability theory of discrete-time-linear system is used to analyze the motion equations of particles. Stability conditions limit their eigenvalues inside the unit cycle in complex plane and corresponding convergence conditions are deduced related with ECFO’s parameters. Finally, ECFO are tested against a suite of benchmark functions with deterministic and excellent results. Experiments results show that ECFO converges faster than SCFO with higher global searching ability.

Detection of Leakage Freshwater and Friction Factor Calibration in Drinking Networks Using Central Force Optimization

Inverse Transient Analysis (ITA) is a powerful approach for leak detection and calibration of friction factors in pressurized pipes. Through this method, a transient flow is initiated and pressures are measured somewhere in the system. Then, a nonlinear programming (NLP) problem with a least-squares criterion objective function is developed to minimize discrepancies between the measured and calculated pressures at measurement sites. Solving the raised NLP results in the problem’s unknowns being leakage specifications and pipe friction factors. For this purpose, various optimization techniques may be utilized. This issue is a major challenge for ITA-based methods. The present work aims at applying the new method of Central Force Optimization (CFO) to the problem of ITA. CFO is a deterministic metaheuristic inspired by gravitational kinematics in which small objects in space are dragged by bigger ones. Herein, the concept and main structure of CFO are represented as well as of CFO. A reference pipe-network is considered to be solved using the ITA equipped with CFO. The results are then discussed compared to the previous works. It is concluded that CFO is easy to implement, computationally efficient and has a remarkable performance in solving leak detection problem.

Central force optimization on a GPU: a case study in high performance metaheuristics

Central Force Optimization (CFO) is a new and deterministic population based metaheuristic algorithm that has been demonstrated to be competitive with other metaheuristic algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Group Search Optimization (GSO). While CFO often shows superiority in terms of functional evaluations and solution quality, the algorithm is complex and typically requires increased computational time. In order to decrease the computational time required for convergence when using CFO, this study presents the first parallel implementation of CFO on a Graphics Processing Unit (GPU) using the NVIDIA Compute Unified Device Architecture (CUDA). Two versions of the CFO algorithm, Parameter-Free CFO (PF-CFO) and Pseudo-Random CFO (PR-CFO), are implemented using CUDA on a NVIDIA Quadro 1000M and examined using four test problems ranging from 10 to 50 dimensions. Discussion is made concerning the implementation of the CFO algorithms in terms of problem decomposition, memory access, scalability, and divergent code. Results demonstrate substantial speedups ranging from roughly 1 to 28 depending on problem size and complexity.

Improving Bandwidth of Yagi-Uda Arrays

A novel approach for improving antenna bandwidth is described using a 6-element Yagi-Uda array as an example. The new approach applies Central Force Optimization, a deterministic metaheuristic, and Variable Z0 technology, a novel, proprietary design and optimization methodology, to produce an array with 33.09% fractional impedance bandwidth. This array’s performance is compared to its CFO-optimized Fixed Z0counterpart, and to the performance of a 6-ele- ment Dominating Cone Line Search-optimized array. Both CFO-optimized antennas exhibit better performance than the DCLS array, especially with respect to impedance bandwidth. Although the Yagi-Uda antenna was chosen to illustrate this new approach to antenna design and optimization, the methodology is entirely general and can be applied to any antenna against any set of performance objectives.

Central Force Optimization: Nelder-Mead Hybrid Algorithm for Rectangular Microstrip Antenna Design

In this article, an efficient global hybrid optimization method is proposed combining central force optimization as a global optimizer and the Nelder-Mead algorithm as a local optimizer. After the final global iteration, a local optimization can be followed to further improve the solution obtained from central force optimization. The convergence capability of the hybrid central force optimization–Nelder-Mead approach is compared with other recent evolutionary-based algorithms using 13 benchmark functions grouped into unimodal and multimodal functions. In addition, the proposed algorithm is used to calculate accurately the resonant frequency and feed-point position of rectangular microstrip patch antenna elements with various dimensions and various substrate thicknesses. It is found that, in addition to decreasing the required evaluation number and the required processing time, excellent results are obtained.

Training neural networks using Central Force Optimization and Particle Swarm Optimization: Insights and comparisons

Central Force Optimization (CFO) is a novel and upcoming metaheuristic technique that is based upon physical kinematics. It has previously been demonstrated that CFO is effective when compared with other metaheuristic techniques when applied to multiple benchmark problems and some real world applications. This work applies the CFO algorithm to training neural networks for data classification. As a proof of concept, the CFO algorithm is first applied to train a basic neural network that represents the logical XOR function. This work is then extended to train two different neural networks in order to properly classify members of the Iris data set. These results are compared and contrasted to results gathered using Particle Swarm Optimization (PSO) in the same applications. Similarities and differences between CFO and PSO are also explored in the areas of algorithm design, computational complexity, and natural basis. The paper concludes that CFO is a novel and promising meta-heuristic that is competitive with if not superior to the PSO algorithm, and there is much room to further improve it.

Central Force Optimization with variable initial probes and adaptive decision space

An implementation of Central Force Optimization (CFO) utilizing variable initial probes and decision space adaptation is presented. The algorithm is tested against a suite of benchmark functions and CFO’s results compared to those of other algorithms. CFO performs well against the benchmarks, and also in scalability tests in 300-dimensions.

NEW TECHNIQUES FOR INCREASING ANTENNA BANDWIDTH WITH IMPEDANCE LOADING

New methods are presented for increasing the bandwidth of wire antennas using impedance loading. This paper extends the seminal Wu-King theory of the internal impedance proflle that produces travelling-wave only current modes on a center-fed dipole antenna. It also presents a numerical optimization methodology based on Central Force Optimization, a new deterministic multidimensional search and optimization metaheuristic useful for problems in applied electromagnetics. A CFO-optimized loaded monopole antenna is described in detail and compared to the same structure loaded with a fractional Wu-King proflle. The CFO monopole generally performs better than other designs using either the full or fractional Wu-King proflles or the extended Wu-King proflles. The methods described in this paper should be useful in any wire antenna design that utilizes impedance loading to increase bandwidth.

MICROSTRIP PATCH ANTENNA OPTIMIZATION USING MODIFIED CENTRAL FORCE OPTIMIZATION

Central force optimization (CFO) is a new simple deterministic multi-dimensional search evolutionary algorithm (EA) inspired by gravitational kinematics. This paper evaluates CFO's performance and provides further examples on its efiectiveness. A new scheme, the acceleration clipping, is introduced, which enhances CFO's global search ability while maintaining its simplicity. The improved CFO algorithm is applied to the optimal design of two difierent wideband microstrip patch antennas. Speciflcally, a microstrip line fed E-shaped patch antenna and a coaxial line fed double-E-shaped patch antenna are designed and optimized using the CFO method. CFO's performance on these antennas is compared to that of the difierential evolution (DE) optimization. Both the CFO and DE methods are interfaced with the full-wave IE3D software. It is found that the CFO results are very close to those obtained using the DE technique.

Antenna benchmark performance and array synthesis using central force optimisation

Central force optimisation (CFO) is a new deterministic multi-dimensional search evolutionary algorithm (EA) inspired by gravitational kinematics. CFO is a simple technique that is still in its infancy. This study evaluates CFO's performance and provides further examples of its effectiveness by applying it to a set of 'real-world' antenna benchmarks and to pattern synthesis for linear and circular array antennas. A new selection scheme is introduced that enhances CFO's global search ability while maintaining its simplicity. The improved CFO algorithm is applied to the design of a circular array with very good results. CFO's performance on the antenna benchmarks and the synthesis problems is compared to that of other EAs.

IMPROVED CFO ALGORITHM FOR ANTENNA OPTIMIZATION

An improved Central Force Optimization (CFO) algorithm for antenna optimization is presented. CFO locates the global extrema an objective function to be maximized, in this case antenna directivity, by flying “probes” through the decision space (DS). The new implementation includes variable initial probe distribution and decision space adaptation. CFO’s performance is assessed against a recognized antenna benchmark problem specifically designed to evaluate optimization evolutionary algorithms for antenna applications. In addition, summary results also are presented for a standard twentythree function suite of analytic benchmarks. The improved CFO implementation exhibits excellent performance.

DESIGN OF MULTILAYER MICROWAVE BROADBAND ABSORBERS USING CENTRAL FORCE OPTIMIZATION

Central Force Optimization (CFO) is a new multi- dimensional search metaheuristic based on the metaphor of gravita- tional kinematics. In this paper, for the flrst time, a modifled CFO algorithm is applied to the optimal design of multilayer microwave absorbers (for normal incidence) in a speciflc frequency range. Sev- eral numerical examples are presented, in which the CFO results are compared with those found by other evolutionary algorithms. It is shown that the CFO results are comparable to those found by the self-adaptive difierential evolution (SADE) algorithm and better than those found by particle swarm optimization (PSO) and gravitational search algorithm (GSA).

Central force optimization: A new deterministic gradient-like optimization metaheuristic

This paper introduces central force optimization as a new, nature-inspired metaheuristic for multidimensional search and optimization based on the metaphor of gravitational kinematics. CFO is a “gradient-like” deterministic algorithm that explores a decision space by “flying” a group of “probes” whose trajectories are governed by equations analogous to the equations of gravitational motion in the physical universe. This paper suggests the possibility of creating a new “hyperspace directional derivative” using the Unit Step function to create positive-definite “masses” in “CFO space.” A simple CFO implementation is tested against several recognized benchmark functions with excellent results, suggesting that CFO merits further investigation.

Central force optimisation: a new gradient-like metaheuristic for multidimensional search and optimisation

This paper introduces central force optimisation, a novel, nature-inspired, deterministic search metaheuristic for constrained multidimensional optimisation in highly multimodal, smooth, or discontinuous decision spaces. CFO is based on the metaphor of gravitational kinematics. The algorithm searches a decision space by 'flying' its 'probes' through the space by analogy to masses moving through physical space under the influence of gravity. Equations are developed for the probes' positions and accelerations using the gravitational metaphor. Small objects in our universe can become trapped in close orbits around highly gravitating masses. In 'CFO space' probes are attracted to 'masses' created by a user-defined function of the value of an objective function to be maximised. CFO may be thought of in terms of a vector 'force field' or, loosely, as a 'generalised gradient' methodology because the force of gravity can be computed as the gradient of a scalar potential. The CFO algorithm is simple and easily implemented in a compact computer program. Its effectiveness is demonstrated by running CFO against several widely used benchmark functions. The algorithm exhibits very good performance, suggesting that it merits further study.