An action-space-based global optimization algorithm for packing circles into a square container

Packing unequal circles into a square container based on the narrow action spaces

“…For each instance, the search process will terminate if PAS-PCI yields a feasible solution no worse than the current best results or if it reaches the time limit. We compared PAS-PCI with both our previous Action Space based Global Optimization (ASGO) algorithm [5] and the best results downloaded from the Packomania website, which were obtained by different authors [27]. The new records obtained in these experiments are published on www.packomania.com by Eckard Specht [27].…”

“…For random swap of C i , C i + 1 of a set and C j , C j+1 of another set, we mean swap C i and C j and swap C i+1 and C j+1 . 5 For each set of (S 1 , S 2 , S 3 , S 4 ), select a circle item C i with the greatest pain degree P i and swap C i with C i+1 . Thus, obtain four new patterns.…”

“…Fig. 9 illustrates the comparison of the parameters for PAS-PCI and ASGO [5] in the framework. In previous work, He et al [5] generated 16 initial patterns and choose 2 patterns at the end of each LBFGS iteration.…”

“…9 illustrates the comparison of the parameters for PAS-PCI and ASGO [5] in the framework. In previous work, He et al [5] generated 16 initial patterns and choose 2 patterns at the end of each LBFGS iteration. To increase the diversity, we double the initial number of random patterns to G = 32, and select m = 3 patterns with the lowest elastic potential energy at the end of each LBFGS iteration.…”

“…Finally, a post-processing procedure is applied to reduce the container size further when a feasible packing pattern is reached. We perform computational experiments on two sets of benchmark instances and demonstrate the effectiveness of the proposed method by comparing it with ASGO [5], the current best algorithm published in the literature, and the best-known results downloaded from the Packomania website [27].…”