Packing equal disks in a unit square : An immunological optimization approach

• Packing equal disks in a unit square is a classical geometrical problem which arises in many industrial and scientific fields. Finding optimal solutions has been proved to be NPhard, therefore, only local optimal solutions can be identified. We tackle this problem by means of the optimization Immune Algorithm (optIA), which has been proved to be among the best derivativefree optimization algorithms. In particular, OPTIA is used to pack up to 150 disks in a unit square. Experimental results show that the immune algorithm is able to locate the putative global optimum for all the instances. Moreover, a comparison with the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) shows that OPTIA is more robust.

Ämnesord

NATURVETENSKAP  -- Matematik -- Annan matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Other Mathematics (hsv//eng)

Nyckelord

Algorithms

Covariance matrix

Evolutionary algorithms

Immune system

Immunology

Optimal systems

Covariance matrix adaptation evolution strategies

Derivative-free optimization algorithms

Geometrical problems

Immune algorithms

Local optimal solution

Optimal solutions

Optimization approach

Scientific fields

Publikations- och innehållstyp

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