A knowledge-based heuristic particle swarm optimization approach with the adjustment strategy for the weighted circle packing problem

The weighted circle packing problem is a kind of important combination optimization problem and has the NP-hard property. Inspired by the No Free Lunch Theorem, a knowledge-based heuristic particle swarm optimization approach with the adjustment strategy (KHPSOA) is developed for this problem. The knowledge (e.g., the relation between its weight matrix and better solution) is obtained from this problem itself and existing layout scheme diagrams and applied to form more effective ordering and positioning rules of the proposed heuristic method. A better layout scheme of larger circles is obtained through the heuristic method. The optimal solution of this problem is obtained by inserting a few residual smaller circles into the gaps of the better layout scheme and further optimizing it through the proposed particle swarm optimization with the adjustment strategy. The numerical experiments show that KHPSOA is superior to the existing algorithms in the performances.