Extremal Optimization with Local Search for the Circular Packing Problem

optimization (EO) is a heuristic nature-inspired algorithm and has been applied to solve some discrete combinatorial optimization problems. In this paper, a continuous version of EO, called EO with local search (EOLS), is presented to solve the problem of packing unequal circles into a larger circular container. First, an equivalent physical model of the problem is adopted to handle the constraints. In order to optimize the continuous energy function of the model, EOLS performs an additional local search procedure after every update step of the original EO. The approach combines the power of conventional gradient method to find local minima and that of EO method in global optimization. The computational results on some problem instances taken from the previous literatures show that the proposed approach produces high-quality solutions within reasonable runtime. It should be noted that for all but two instances we found new lower bounds missed in previous papers.