A Study on the Block Relocation Problem: Lower Bound Derivations and Strong Formulations

A Coronavirus Optimization Algorithm for Solving the Container Retrieval Problem

“…For example, the Dynamic CRP considers that new containers may go into the bay, while the container retrieval process occurs [37]. The CRP with Batch Moves states that handling equipment (e.g., a crane or straddle carrier) can move more than one container at a time, which is often seen in the steel industry [33]. The CRP with a Stowage Plan is another interesting variant, where a stowage plan in a vessel is given in advance, and it is taken into consideration when retrieving containers [41].…”

“…The CRP is a combinatorial optimization problem belonging to the NPhard class [7]. In literature, the CRP is also referred to as the Container Relocation Problem [14] or the Block (Relocation, Retrieval) Problem [11,33]. Minimizing the number of relocation operations is predominantly the CRP's main optimization goal and the primary objective function used to optimize yard operations [30].…”

“…This performance measure is highly regarded because having a lower number of relocations, empirically, implies a lower operational cost to retrieve all containers from the bay. With regard to this, optimal approaches can be found in [4,12,17,24,33,36,39,40], and near-optimal approaches in [3,14,16,25,26,42,43] to tackle larger instances. Optimal approaches guarantee optimal solutions, but because of the NP-hardness of the CRP, the size of the problem instances that such approaches can solve is very reduced when compared to near-optimal approaches, where near-optimal solutions are pursued.…”

“…Later, the individual with the best fitness is assigned to ind best , comparing the current best individual (ind best ) with the presently infected individual (in f ected) (line 30). At the end of each iteration, the infected population (i_ pop) is substituted by all individuals of the newly infected population (nii_ pop) (line 32), and the epidemic time (i.e., the number of iterations) is incremented (33). At this point, i_ pop is also sorted by fitness in ascending order just as in nii_ pop.…”

Automated Design of Heuristics for the Container Relocation Problem

“…CRP variants differ in restrictions on moves, retrieval priorities of blocks (whether they are distinct or not), whether all blocks need to be retrieved, how many blocks can be moved at a time, and whether the stacks are ordered in a single or multiple bays. A formal problem classification can be found in [3].…”