In this paper, we propose a generalisation of the bin packing problem, obtained by adding precedences between items that can assume heterogeneous non-negative integer values. Such generalisation also models the well-known Simple Assembly Line Balancing Problem of type I. To solve the problem, we propose a simple and effective iterated local search algorithm that integrates in an innovative way of constructive procedures and neighbourhood structures to guide the search to local optimal solutions. Moreover, we apply some preprocessing procedures and adapt classical lower bounds from the literature. Extensive computational experiments on benchmark instances suggest that the developed algorithm is able to generate good quality solutions in a reasonable computational time.
A batching-move iterated local search algorithm for the bin packing problem with generalized precedence constraints / Kramer, Raphael; Dell'Amico, Mauro; Iori, Manuel. - In: INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH. - ISSN 0020-7543. - 55:21(2017), pp. 6288-6304. [10.1080/00207543.2017.1341065]