Test problems are generally used to effectively evaluate the algorithms for packing problem. Based on the engineering background of the layout optimization for a retrievable satellite module, this paper describes the test problems for circles packing problem with known optimization solution first. There are N(≦217) circular objects, different in size, packed in a circular container batch recursively, fulfilling the requirements of both inner and outer tangency. This test problem involves the packing optimization with or without behavioral constraints (such as equilibrium constraints). But the above test problems are not the problem with all the optimal solutions known. On the basis of above work, we construct 7 groups of test problems with all the optimal solutions containing N=4,9,17,25,41,49 circles. The test problems can be extended to 3-D packing optimization for spherical or cylindrical objects with dynamic equilibrium constraints, more similar to the case of layout optimization model for a satellite module.
View Test problems of circles in circle packing with behavior constraint and known the optimal solutions