Heuristic-based energy landscape paving for the circular packing problem with performance constraints of equilibrium

The optimal layout problem of circle group in a circular container with performance constraints of equilibrium belongs to a class of NP-hard problem. The key obstacle of solving this problem is the lack of an effective global optimization method. We convert the circular packing problem with performance constraints of equilibrium into the unconstrained optimization problem by using quasi-physical strategy and penalty function method. By putting forward a new updating mechanism of the histogram function in energy landscape paving (ELP) method and incorporating heuristic conformation update strategies into the ELP method, we obtain an improved ELP (IELP) method. Subsequently, by combining the IELP method and the local search (LS) procedure, we put forward a hybrid algorithm, denoted by IELP-LS, for the circular packing problem with performance constraints of equilibrium. We test three sets of benchmarks consisting of 21 representative instances from the current literature. The proposed algorithm breaks the records of all 10 instances in the first set, and achieves the same or even better results than other methods in literature for 10 out of 11 instances in the second and third sets. The computational results show that the proposed algorithm is an effective method for solving the circular packing problem with performance constraints of equilibrium.