Consistent neighborhood search for one-dimensional bin packing and two-dimensional vector packing

Abstract

We propose a consistent neighborhood search approach for solving the one-dimensional bin packing problem (BPP). The goal of this local search is to derive a feasible solution with a given number of bins, m, starting from m=UB−1, where UB is an upper bound obtained by using a variant of the classical First Fit heuristic. To this end, the local search was performed on a partial solution with m−2 bins, i.e. a solution containing a subset of items packed into m−2 bins without capacity violations and a set of non-assigned items, with the objective of minimizing the total weight of non-assigned items and, ultimately, packing all the non-assigned items into two bins. A partial solution was constructed by deleting bins from the last complete solution. Local moves include rearranging the items assigned to a single bin along with non-assigned items, i.e. removing and adding items to the bin. A tabu search was performed with moves featuring a limited number of items to be added/dropped, plus a hill climbing/descent procedure with general (unlimited) add/drop moves, in order to minimize a given objective function. The very same procedure was used for all instances under consideration, with the same initial solution, same parameters, same order of neighborhood exploration, etc. Promising results were obtained for a wide range of benchmark instances; solutions equal to or better than the best known solutions found by heuristic methods were obtained for all the instances considered, successfully outperforming published results for the particular class of instances hard28, which appears to cause the greatest degree of difficulty for BPP algorithms. The method was also tested on the vector packing problem (VPP) and evaluated for classical two-dimensional VPP (2-DVPP) benchmarks, in all instances yielding optimal or best-known solutions.