Coevolving heuristics for the Distributor´s Pallet Packing Problem

Efficient heuristics are required for on-line optimization problems where search-based methods are unfeasible due to frequent dynamics in the environment. This is especially apparent when operating on combinatorial NP-complete problems involving a large number of items. However, designing new heuristics for these problems may be a difficult and time-consuming task even for domain experts. Therefore, automating this design process may benefit the industry when facing new and difficult optimization problems. The Distributor´s Pallet Packing Problem (DPPP) is the problem of loading a pallet of non-homogenous items coming off a production line and is an instance of a range of resource-constrained, NP-complete, scheduling problems that are highly relevant for practical tasks in the industry. Common heuristics for the DPPP typically decompose the problem into two sub-problems; one of pre-scheduling all items on the production line and one of packing the items on the pallet. In this paper we concentrate on a two dimensional version of the DPPP and the more realistic scenario of having knowledge about only a limited set of the items on the production line. This paper aims at demonstrating that such an unknown heuristic may be evolved by Gene Expression Programming and Cooperative Coevolution. By taking advantage of the natural problem decomposition, two species evolve heuristics for pre-scheduling and packing respectively. We also argue that the evolved heuristics form part of a developmental stage in the construction of the finished phenotype, that is, the loaded pallet.