A Fast Heuristic Parallel Ant Colony Algorithm for Circles Packing Problem with the Equilibrium Constraints

Circles packing problem with equilibrium constraints is difficult to solve due to its NP-hard nature. A fast heuristic parallel ant colony algorithm is proposed for this problem. Both circular radius and mass are taken as the probability factors of the roulette selection and the circles are located by arranging round existing circles in peripheral with counter-clockwise movement. Its diverse population individuals (no more than 3 circles are overlapped in each one) are constructed through the proposed heuristic method. The ant colony optimization combined with parallel search mechanism is adopted to obtain an optimal solution or an approximate optimal solution with 1-3 overlapping circles. The steepest descent method based on physical model is used to adjust the approximate optimal solution into the optimal one without overlapping. The combination of heuristic strategy, ant colony search mechanism in parallel, and fast adjustment strategy can improve the computational precision and efficiency of the proposed algorithm. The experiment results show that the proposed algorithm is superior to the existing algorithms in performance.