Particle Swarm Optimization (PSO) Software

  • September 21, 2015
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Particle Swarm Optimization (PSO) Software

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Category : Software

Particle swarm optimization (PSO) is a population-based stochastic optimization technique inspired by swarm intelligence. The underlying motivation for the development of PSO algorithm was social behavior of animals such as bird flocking, fish schooling, and swarm theory. The fundamental to the development of PSO is a hypothesis that social sharing of information among peers offers an evolutionary advantage. One of reasons that PSO is attractive is that there are very few parameters to be adjusted.

The following PSO software are provided in the Code Library:

  • DPSO (Dissipative Particle Swarm Optimization) [Project Portal & Code | Doc]: It is a PSO variant that was developed according to the self-organization of dissipative structure. The negative entropy is introduced to construct an opening dissipative system that is far-from-equilibrium so as to driving the irreversible evolution process towards a better fitness.
  • DEPSO (or called DEPS) [Project Portal & Code | Doc]: It is an algorithm that hybridizes the advantages of both PSO and Differential Evolution (DE) for solving (constrained) numerical optimization problem (NOP).

PSO has been incorporated into the cooperative group optimization (CGO) system for realizing various competitive hybrid algorithms.

  • September 21, 2015
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Polymath8: Bounded Gaps between Primes

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Category : Projects

The Polymath8 project, led by the Fields Medalist Dr. Terence Tao and in collaboration with a team of top mathematicians, was launched to optimize the records of the bounded gaps between primes based on the breakthrough work of “Bounded gaps between primes” by Dr. Yitang Zhang. He proved that there are infinitely many pairs of primes with a finite gap, and thus resolved a weak form of the twin prime conjecture.

Introduction

In number theory, an admissible k-tuple is a set of k distinct integers that do not include the complete modulo set of residue classes (i.e. the values 0 through p – 1) of any prime p ≤ k.

Zhang showed that in some k0 values, for every admissible k0-tuple, there are infinitely many positive integers n to shift the k0-tuple such that each shifted k0-tuple contains at least two primes, and thus the width H of the admissible k0-tuple establishes the upper bound for the gap between primes.

Zhang initally showed any k0 ≥ 3,500,000 (which leads to H ≤ 70,000,000) is adequate for the bounding purpose. A polymath8 project was then started to find smaller k0 values and smaller H(k0) values for them.

Code & Data
  • Here is the code K0Finder (Java, bash, and maple are required), and a k0 Table, for optimal k0 of MPZ(i)(ϖ, δ) in different settings of cϖ, cδ, i.
  • Here is the code KTupleFinder (Java) for minimizing the width value H of an admissible k-tuple for a given k.
Publications

Polymath8a authors: Wouter Castryck, Etienne Fouvry, Gergely Harcos, Emmanuel Kowalski, Philippe Michel, Paul Nelson, Eytan Paldi, Janos Pintz, Andrew V. Sutherland, Terence Tao, Xiao-Feng Xie

Polymath8b authors: Ignace Bogaert, Aubrey de Grey, Gergely Harcos, Emmanuel Kowalski, Philippe Michel, James Maynard, Paul Nelson, Pace Nielsen, Eytan Paldi, Andrew V. Sutherland, Terence Tao, Xiao-Feng Xie

Other Information

rnoti-jj-15-cov1– Media coverage: Notices of the AMS; Der Spiegel

– Polymath8 project for finding bounded intervals with primes.

– New bounds on gaps between primes by Andrew V. Sutherland.

– A new database has been set for collecting narrow admissible k-Tuples.

– The theoretical progress can be found in the blog of Terence Tao.

  • December 26, 2014
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Differential Evolution (DE)

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Category : Research

Differential Evolution (DE) is an optimizatin method developed by Price and Storn in 1995. DE is original proposed as an evolution strategy (ES). It may also be considered as an swarm intelligence (SI) based method.

DE has been implemented into the Cooperative Group Optimization System (CGOS). DEPSO is a effective algorithm to combine the advantages of both DE and PSO.

  • Xiao-Feng Xie, Jiming Liu, and Zun-Jing Wang. A cooperative group optimization system. Soft Computing, 18(3): 469-495, 2014. [PDF] [DOI] [Bibtex]
    @Article{xie2014cooperative,
Title = {A cooperative group optimization system},
Author = {Xie, Xiao-Feng and Liu, Jiming and Wang, Zun-Jing},
Journal = {Soft Computing},
Year = {2014},
Number = {3},
Pages = {469--495},
Volume = {18},
PDF={http://www.wiomax.com/team/xie/paper/SOCO14.pdf},
DOI={10.1007/s00500-013-1069-8},
Publisher = {Springer}
}
  • Xiao-Feng Xie and Jiming Liu. A compact multiagent system based on autonomy oriented computing. In IEEE/WIC/ACM International Conference on Intelligent Agent Technology (IAT), pages 38-44, Compiegne, France, 2005. IEEE. [PDF] [DOI] [Bibtex]
    @InProceedings{Xie:2005p1406,
Title = {A compact multiagent system based on autonomy oriented computing},
Author = {Xiao-Feng Xie and Jiming Liu},
Booktitle = {IEEE/WIC/ACM International Conference on Intelligent Agent Technology (IAT)},
Address = {Compiegne, France},
Year = {2005},
PDF={http://www.wiomax.com/team/xie/paper/IAT05.pdf},
DOI={10.1109/IAT.2005.6},
Pages = {38--44},
Publisher = {IEEE}
}
  • Xiao-Feng Xie and Wen-Jun Zhang. SWAF: Swarm algorithm framework for numerical optimization. In Genetic and Evolutionary Computation Conference (GECCO), pages 238-250, Seattle, WA, USA, 2004. Springer. [PDF] [DOI] [Bibtex]
    @InProceedings{Xie:2004p238,
Title = {{SWAF}: Swarm algorithm framework for numerical optimization},
Author = {Xiao-Feng Xie and Wen-Jun Zhang},
Booktitle = {Genetic and Evolutionary Computation Conference (GECCO)},
Year = {2004},
PDF={http://www.wiomax.com/team/xie/paper/GECCO04_SWAF.pdf},
DOI={10.1007/978-3-540-24854-5_21},
Address = {Seattle, WA, USA},
Pages = {238--250},
Publisher = {Springer}
}
  • Xiao-Feng Xie, Wen-Jun Zhang, and De-Chun Bi. Handling equality constraints by adaptive relaxing rule for swarm algorithms. In Congress on Evolutionary Computation (CEC), pages 2012-2016, Portland, OR, USA, 2004. [PDF] [DOI] [Bibtex]
    @InProceedings{Xie:2004p2012,
Title = {Handling equality constraints by adaptive relaxing rule for swarm algorithms},
Author = {Xiao-Feng Xie and Wen-Jun Zhang and De-Chun Bi},
Year = {2004},
Pages = {2012--2016},
Booktitle = {Congress on Evolutionary Computation (CEC)},
PDF={http://www.wiomax.com/team/xie/paper/CEC04_ECH.pdf},
DOI={10.1109/CEC.2004.1331143},
Address = {Portland, OR, USA}
}
  • Wen-Jun Zhang and Xiao-Feng Xie. DEPSO: Hybrid particle swarm with differential evolution operator. In IEEE International Conference on Systems, Man, and Cybernetics, pages 3816-3821, Washington, DC, USA, 2003. IEEE. [PDF] [Code] [DOI] [Bibtex]
    @InProceedings{Zhang:2003p3816,
Title = {{DEPSO}: Hybrid particle swarm with differential evolution operator},
Author = {Wen-Jun Zhang and Xiao-Feng Xie},
Booktitle = {IEEE International Conference on Systems, Man, and Cybernetics},
Year = {2003},
PDF={http://www.wiomax.com/team/xie/paper/SMCC03.pdf},
DOI={10.1109/ICSMC.2003.1244483},
Code={http://www.wiomax.com/depso},
Address = {Washington, DC, USA},
Pages = {3816--3821},
Publisher = {IEEE}
}
  • December 23, 2014
  • 0

Expert System for Model Quality Assurance

Tags :

Category : Projects

EDA_All1 Model Quality Assurance (MQA) is automated and customizable circuit model library validation software for advanced technologies. Unlike the traditional manual scripting methods, MQA enables you to check your circuit model, compare models and generate QA reports in a complete and efficient way. MQA has become the industry standard for circuit model acceptance and signoff and is widely adopted by leading integrated device manufacturers (IDMs), foundries and design houses.

“Unlike the traditional manual scripting methods, MQA enables you to check your circuit model, compare models and generate reports in a complete and efficient way. With more than ten years of history, MQA has become the industry standard for circuit model acceptance and signoff and is widely adopted by leading integrated device manufacturers, foundries and design houses.”

Dr. Xie was the main developer of first commercial version of the expert system for Model Quality Assurance (MQA). This system was developed for Accelicon (now acquired by Keysight Technologies, Inc NYSE:KEYS).

  • December 20, 2011
  • 0

Solving the Magic Square Problem Using Modern Heuristic Methods

Tags :

Category : News , Software

Ms_sf_2This problem is to solve the Magic Square Problem (constrained and unconstrained versions), a combinatorial optimization problem, using modern heuristic methods.

Magic squares have been a source of fascination since ancient times, over 4,000 years. A magic square is a square matrix of size n, containing each of the numbers 1 to n2 exactly once, in which each column, each row, and both diagonals add up to the same magic number.

It is possible to impose many different constraints on a standard magic square problem. Here the constrained version stipulates that the solution matrix must have a pre-defined contiguous sub-matrix.

Here is the binary code, and here is the readme file. As the 2nd runner-up, this program solved the constrained version of 400 x 400 magic square within a minute in the 2011 International Optimisation Competition.

  • X. Xie, “Meta-LS Solver for Magic Square Competition,” International Optimisation Competition, 2011. [PDF] [Code] [Bibtex]
    @TechReport{xie2011tr00,
Title = {Meta-LS Solver for Magic Square Competition},
Author = {Xiao-Feng Xie},
Code={http://www.wiomax.com/team/xie/project/magic/MagicSquare.jar},
PDF={http://www.wiomax.com/team/xie/project/magic/IOC_readme.pdf},
Institution={International Optimisation Competition},
Year = {2011}
}
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