Please cite this article as: C.D. Cifuentes and M.C. Riff, G-CREM: A GRASP approach to solve the container relocation problem for multibays, Applied Soft Computing Journal (2020) 106721, https://doi.org/10.1016/j.asoc.2020.106721. Applied Soft Computing Journal xxx (xxxx) xxx Contents lists available at ScienceDirect Applied Soft Computing Journal journal homepage: www.elsevier.com/locate/asoc G-CREM: A GRASP approach to solve the container relocation problem for multibays Camila Díaz Cifuentes 1 , María Cristina Riff ∗,1 Department of Computer Science, Federico Santa María Technical University Valparaíso, Chile article info Article history: Received 13 April 2018 Received in revised form 6 June 2020 Accepted 10 September 2020 Available online xxxx Keywords: Container relocation problem Multibays Greedy Randomized Adaptive Search Procedure abstract The Container Relocation Problem for multiple bays consists of finding the minimum number of moves to load a set of stacked containers on a ship according to a given loading sequence, and in minimizing the crane’s working time for an entire yard of multiple bays. This is a crucial problem for every commercial port in the world given the maximum time requirements and the costs associated with the containers’ retrieval. In this paper, we propose a Greedy Randomized Adaptive Search Procedure to solve this problem. We use a myopic function specially designed to produce feasible candidate solutions with a structure that allows a local search procedure to optimize relocations. In order to validate our approach, we use a large set of well-known Container Relocation Problems for multiples bays, as well as a statistical analysis of our results. Our experiments show new bounds for various instances. © 2020 Elsevier B.V. All rights reserved. 1. Introduction In a port, containers are temporarily stacked in a container yard before leaving the port. Nowadays, ports try to continuously improve the quality of service in order to have more customers. The most important criteria to measure the quality of service (QOS) is the waiting time of a ship which must load a set of containers. When a ship arrives at a port, containers must be loaded into the ship in a given sequence. Most of the time a container is at the bottom of the stack and all containers above it must be moved. This kind of movement, called relocation, is unproductive and requires too much time. There are many approaches in the literature to tackle the container relocation problem. Many of these approaches concern the optimization of the number of container movements into one storage bay. Recently we have proposed a Greedy Random- ized Adaptive Search Procedure (GRASP) which is a metaheuris- tic approach to solve the container relocation problem for one bay [1]. Using this algorithm we have reported new bounds for the well-known instances of the one bay problem. A new version of this problem has been proposed by Lee & Lee in [2]: The container relocation problem for multiple bays. It is a harder problem where containers can be moved between bays and, given the defined ship sequence, could also be retrieved ∗ Corresponding author. E-mail addresses: camila.diaz@alumnos.usm.cl (C.D. Cifuentes), mcriff@inf.utfsm.cl (M.C. Riff). 1 We have worked together in all steps of the paper. from any bay of the yard. Moreover, new times are included, such as the gantry time to move a container from a bay to another, as well as the trolley time associated with the moves within a bay. In the literature, the gantry and the trolley are called a crane. In this paper, we focus on the multiple bays problem. In a multiple bays container relocation problem there is a storage area (the yard) formed by B bays and each bay is composed of rows of container stacks. The retrieval process requires taking a set of containers from the yard in a given sequence. A sequence is the ordered list of the containers identifications (numbers). The sequence of the containers required for a ship is only known when the ship is docked, thus no preprocessing is possible. The goal of the container relocation problem for multiple bays is to minimize both the number of container relocations and the total working time (gantry and trolley) in order to retrieve con- tainers in the required sequence. In Section 2 we present an overview of the state of art for the single and multiple bays problem and a discussion about its relationship to our approach. A detailed description of the problem as well as a mathematical model is presented in Section 3. From the techniques proposed to solve this problem we find the Lee & Lee [2] and Bian & Jin [3] approaches. The approach of Lee & Lee has three steps ending with a mixed integer programming model. Their results show that the approach is able to solve instances with more than 700 containers. However, the high computational time of their heuristic makes it difficult to use in a real world situation. Bian & Jin also proposed a multi-phase approach using dynamic programming. They improved some results obtained by Lee & Lee in terms of the movements and crane time for the same randomly https://doi.org/10.1016/j.asoc.2020.106721 1568-4946/© 2020 Elsevier B.V. All rights reserved.