New heuristics for packing unequal circles into a circular container

Abstract

We propose two new heuristics to pack unequal circles into a two dimensional circular container. The first one, denoted by A1.0, is a basic heurisitc which selects the next circle to place according to the maximal hole degree rule. The second one, denoted by A1.5, uses a self lookahead strategy to improve A1.0. We evaluate A1.0 and A1.5 on a series of instances up to 100 circles from the literature and compare them with existing approaches. We also study the behaviour of our approach for packing equal circles comparing with a specified approach in the literature. Experimental results show that our approach has a good performance in terms of solution quality and computational time for packing unequal circles.

Efficient approaches for furnace loading of cylindrical parts

“…They formulated this problem as a nonlinear optimization problem and developed a heuristic simulated annealing algorithm for solving this problem. Huang et al [15] proposed two new heuristics to pack unequal circles into a two-dimensional circular container. The first one, denoted by A1.0, is a basic heuristic which selects the next circle to place according to the maximal hole degree rule.…”

Adaptive and restarting techniques-based algorithms for circular packing problems

“…Packing circles into the smallest containing circle has been addressed by Wang et al [28], Zhang and Deng [29] and Huang et al [14,16,17] who developed approximate algorithms inspired from human packing strategies and meta-heuristics such as tabu search and simulated annealing. Mladenovic et al [20] proposed an approximate algorithm that solves iteratively, till converging to a local optimum, two reformulations of the unit circular packing problem: one using the Cartesian coordinates and one using Polar coordinates.…”

PERM for solving circle packing problem

“…Recently, Huang et al [13,14] proposed a heuristic, the principle of maximum cave degree for corner-occupying actions (COAs), to select and pack the circles one by one, and they proposed a two level search strategy to improve the basic heuristic algorithm. In addition, Pruned-Enriched-Rosenbluth Method (PERM), also called population control algorithm, is a powerful strategy for pruning and enriching branches when searching the solution space and it has shown to be very efficient for solving protein folding problem [15,16].…”