451 research outputs found
Pi Fractions for Generating Uniformly Distributed Sampling Points in Global Search and Optimization Algorithms
Pi Fractions are used to create deterministic uniformly distributed
pseudorandom decision space sample points for a global search and optimization
algorithm. These fractions appear to be uniformly distributed on [0,1] and can
be used in any stochastic algorithm rendering it effectively deterministic
without compromising its ability to explore the decision space. Pi Fractions
are generated using the BBP Pi digit extraction algorithm. The Pi Fraction
approach is tested using genetic algorithm Pi-GASR with very good results. A Pi
Fraction data file is available upon request.Comment: Discussion of bidimensional correlation has been adde
On the Utility of Directional Information for Repositioning Errant Probes in Central Force Optimization
Central Force Optimization is a global search and optimization algorithm that
searches a decision space by flying "probes" whose trajectories are
deterministically computed using two equations of motion. Because it is
possible for a probe to fly outside the domain of feasible solutions, a simple
errant probe retrieval method has been used previously that does not include
the directional information contained in a probe's acceleration vector. This
note investigates the effect of adding directionality to the "repositioning
factor" approach. As a general proposition, it appears that doing so does not
improve convergence speed or accuracy. In fact, adding directionality to the
original errant probe retrieval scheme appears to be highly inadvisable.
Nevertheless, there may be alternative probe retrieval schemes that do benefit
from directional information, and the results reported here may assist in or
encourage their development.Comment: Ver. 2, 6 June 2010 (Fig. 1 improved for clarity; minor typos
corrected
Central Force Optimization Applied to the PBM Suite of Antenna Benchmarks
Central Force Optimization (CFO) is a new nature-inspired deterministic
multi-dimensional search and optimization metaheuristic based on the metaphor
of gravitational kinematics. CFO is applied to the PBM antenna benchmark suite
and the results compared to published performance data for other optimization
algorithms. CFO acquits itself quite well. CFO's gradient-like nature is
discussed, and it is speculated that a "generalized hyperspace derivative"
might be defined for optimization problems as a new mathematical construct
based on the Unit Step function. What appears to be a sufficient but not
necessary condition for local trapping, oscillation in the probe average
distance curve, is discussed in the context of the theory of gravitational
"resonant returns" that gives rise to strikingly similar oscillatory curves. It
is suggested that the theory may be applicable to CFO as an aid to
understanding trapping and to developing effective mitigation techniques,
possibly based on a concept of "energy" in CFO space. It also is suggested that
CFO may be re-formulated as a "total energy" model by analogizing conservation
of energy for orbiting masses in physical space
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
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.
Includes corrections 02-03-2010.Comment: Includes Source Code and Corrections 02-03-201
Dipole-Loaded Monopole Optimized Using VSO, v.3
A dipole-loaded monopole antenna is optimized for uniform hemispherical
coverage using VSO, a new global search design and optimization algorithm. The
antenna's performance is compared to genetic algorithm and hill-climber
optimized loaded monopoles, and VSO is tested against two suites of benchmark
functions and several other algorithms.Comment: arXiv admin note: substantial text overlap with arXiv:1107.1437,
arXiv:1103.5629, arXiv:1108.0901, arXiv:1003.1039. Version 2, 02 Jul 2013:
minor typos corrected; hill climber material added; source code listing
updated. Version 3, 06 Jul 2013: replaces VSO diagram/pseudocode to clarify
algorithm's elitist nature; other minor change
A novel methodology for antenna design and optimization: Variable Zo
This paper describes "Variable Zo," a novel and proprietary approach to
antenna design and optimization. The new methodology is illustrated by applying
it to the design of a resistively-loaded bowtie antenna and to two broadband
Yagi-Uda arrays. Variable Zo is applicable to any antenna design or
optimization methodology. Using it will result in generally better antenna
designs across any user-specified set of performance objectives.Comment: Ver. 2 (14 July 2011). Adds Yagi-Uda array design example. Updates
source cod
Dynamic Threshold Optimization - A New Approach?
Dynamic Threshold Optimization (DTO) adaptively "compresses" the decision
space (DS) in a global search and optimization problem by bounding the
objective function from below. This approach is different from "shrinking" DS
by reducing bounds on the decision variables. DTO is applied to Schwefel's
Problem 2.26 in 2 and 30 dimensions with good results. DTO is universally
applicable, and the author believes it may be a novel approach to global search
and optimization.Comment: Rev. 05 June 2012: Typos & reference [1] corrected. Material adde
Comparative Results: Group Search Optimizer and Central Force Optimization
This note compares the performance of two multidimensional search and
optimization algorithms: Group Search Optimizer and Central Force Optimization.
GSO is a new state-of-the-art algorithm that has gained some notoriety,
consequently providing an excellent yardstick for measuring the performance of
other algorithms. CFO is a novel deterministic metaheuristic that has performed
well against GSO in previous tests. The CFO implementation reported here
includes architectural improvements in errant probe retrieval and decision
space adaptation that result in even better performance. Detailed results are
provided for the twenty-three function benchmark suite used to evaluate GSO.
CFO performs better than or essentially as well as GSO on twenty functions and
nearly as well on one of the remaining three. Includes update 24 February 2010.Comment: Includes detailed numerical results and source code in appendices.
Update 02-24-10: Replaces Fig. A2(b) for improved visualization; corrects
minor typos (note that trajectory plots were removed to meet file size
restrictions - see Ver. 1 for complete set
Issues in Antenna Optimization - A Monopole Case Study
A typical antenna optimization design problem is presented, and various
issues involved in the design process are discussed. Defining a suitable
objective function is a central question, as is the type of optimization
algorithm that should be used, stochastic versus deterministic. These questions
are addressed by way of an example. A single-resistor loaded broadband HF
monopole design is considered in detail, and the resulting antenna compared to
published results for similar continuously loaded and discrete resistor loaded
designs.Comment: Ver. 2. Corrects formatting in Table 1, updates references, and adds
source code in Appendi
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