A New Lower Bound for the Block Relocation Problem

The bounded beam search algorithm for the block relocation problem

“…In this Section, we present a new lower bound, called Unordered Blocks Assignment Lower Bound (UBALB), for the restricted BRP. A preliminary version of this contribution can be found in Bacci et al [3].…”

“…The instances of group 2 (Wu and Ting [31]) are grouped according to the number of stacks w ∈ [3,12] and height h ∈ [3,12]. Therefore, we have 100 problem classes, each with 40 instances.…”

“…All of them have up to 10 bays, w ∈[3,16], h ∈ {6, 8}, and n ∈ [70, 720]. Here we allow reshuffles of blocks between different bays: therefore, an instance with 10 bays and 16 stacks is equivalent to an instance with 1 bay and 160 stacks.…”

“…group 4 includes a set of 880 instances introduced in Caserta et al[7]. Such instances are randomly generated with w ∈ {3, 4, 5, 6, 10, 100}, h ∈ {5, 6, ..., 12, 102} and n = w × (h − 2).The 8000 instances of group 5 (Unluyurt and Aydin[29]) are generated with w ∈[3,7], h ∈[4,7] and different densities of the blocks. They can be balanced (b), if the stacks have the same number of stored blocks, or unbalanced (u).In group 6, we consider the 12500 instances described in Zhu et al[39].…”

“…They can be balanced (b), if the stacks have the same number of stored blocks, or unbalanced (u).In group 6, we consider the 12500 instances described in Zhu et al[39]. Such instances are grouped into 125 classes of size 100, according to the values of w ∈ [6, 10], h ∈[3,7], and n ∈ [(w − 1) × h, w × h − 1].…”