A multi-neighborhood search algorithm for orthogonal packing of identical rectangular items within arbitrary convex regions

In this paper, we propose an efficient heuristic algorithm named the multi-neighborhood search (MNS) algorithm for the problem of packing orthogonally identical rectangles within random convex regions, which is a global optimization problem with many important applications. The problem involves the discrete and continuous optimizations and is shown to be NP-hard. To deal with the discrete and continuous aspects of problem, the proposed global optimization algorithm integrates two neighborhood search methods and the limited-memory BFGS method. Moreover, the algorithm employs a Metropolis acceptance criterion to accept a neighborhood solution as the current solution. The performance of proposed algorithm is assessed on a number of benchmark instances widely used in the literature. Computational results show that the proposed algorithm is quite efficient compared with the existing algorithms in the literature. Particularly, the proposed MNS algorithm is able to find the best known solution for all the tested instances and the computational time is short compared to those of existing algorithms.