Category Archives: Software

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Particle Swarm Optimization (PSO) 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.

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Solving the Magic Square Problem Using Modern Heuristic Methods

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]
    Title = {Meta-LS Solver for Magic Square Competition},
    Author = {Xiao-Feng Xie},
    Institution={International Optimisation Competition},
    Year = {2011}