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 NP-hard, 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 derivative-free 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.