Marco Caserta

Applying the corridor method to a blocks relocation problem

In this paper, we present a corridor method inspired algorithm for a blocks relocation problem in block stacking systems. Typical applications of such problem are found in the stacking of container terminals in a yard, of pallets and boxes in a warehouse, etc. The proposed algorithm applies a recently proposed metaheuristic. In a method-based neighborhood we define a two-dimensional “corridor” around the incumbent blocks configuration by imposing exogenous constraints on the solution space of the problem and apply a dynamic programming algorithm capturing the state of the system after each block movement for exploring the neighborhoods. Computational results on medium- and large-size problem instances allow to draw conclusions about the effectiveness of the proposed scheme.

A mathematical formulation and complexity considerations for the blocks relocation problem

The blocks relocation problem (BRP) may be defined as follows: given a set of homogeneous blocks stored in a two-dimensional stock, which relocations are necessary to retrieve the blocks from the stock in a predefined order while minimizing the number of those relocations? In this paper, we first prove NP-hardness of the BRP as well as a special case, closing open research questions. Moreover, we propose different solution approaches. First, a mathematical model is presented that provides optimal solutions to the general BRP in cases where instances are small. To overcome such limitation, some realistic assumption taken from the literature is introduced, leading to the definition of a binary linear programming model. In terms of computational time, this approach is reasonably fast to be used to solve medium-sized instances. In addition, we propose a simple heuristic based upon a set of relocation rules. This heuristic is used to generate “good” quality solutions for larger instances in very short computational time, and, consequently, is proposed for tackling problem instances where solutions are required (almost) immediately. Solution quality of the heuristic is measured against optimal solutions obtained using a state-of-the-art commercial solver and both of them are compared with reference results from literature.

A Corridor Method-Based Algorithm for the Pre-marshalling Problem

To ease the situation and to ensure a high performance of ship, train and truck operations at container terminals, containers sometimes are pre-stowed near to the loading place and in such an order that it fits the loading sequence. This is done after the stowage plan is finished and before ship loading starts. Such a problem may be referred to as pre-marshalling. Motivated by most recent publications on this problem we describe a metaheuristic approach which is able to solve this type of problem. The approach utilizes the paradigm of the corridor method.

A cross entropy-Lagrangean hybrid algorithm for the multi-item capacitated lot-sizing problem with setup times

The aim of this article is to introduce a hybrid algorithm for the multi-item multi-period capacitated lot-sizing problem with setups. In this problem, demands over a finite planning horizon must be met, where several items compete for space with limited resources in each period, and a portion of these resources is used by setups. The proposed scheme considers a Lagrangean relaxation of the problem and applies a cross entropy-based metaheuristic to the uncapacitated version of the original problem. A thorough experimental plan has been designed and implemented to test the effectiveness and the robustness of the algorithm: first, drawing inspiration from the response surface methodology, we calibrate the algorithm by identifying the optimal parameters value for any given instance size. Next, we carry out experiments on large scale instances, collecting information about solution quality and computational time, and comparing these results with those offered by a global optimizer.

Container Rehandling at Maritime Container Terminals

In this paper, we review recent contributions dealing with the rehandling of containers at maritime container terminals. The problems studied in the paper refer to a post-stacking situation, i.e. problems arising after the stacking area has already been arranged. In order to increase efficiency of loading/unloading operations, once updated information about the state of the containers as well as of the vessels becomes available, it is possible to reshuffle the container yard, or a portion of it, in such a way that future loading operations are carried out with maximal efficiency. The increase in efficiency of loading/unloading operations has a bearing on the berthing time of the vessels, which, in turn, is a widely accepted indicator of port efficiency. Three types of post-stacking problems have been identified, namely (i) the remarshalling problem, (ii) the premarshalling problem, and (iii) the relocation problem. With respect to each of these problems, a thorough explanation of the problem itself, its relevance and its connections with other container handling issues are offered. In addition, algorithmic approaches to tackle such problems are summarized.

Corridor Selection and Fine Tuning for the Corridor Method

In this paper we present a novel hybrid algorithm, in which ideas from the genetic algorithm and the GRASP metaheuristic are cooperatively used and intertwined to dynamically adjust a key parameter of the corridor method, i.e., the corridor width, during the search process. In addition, a fine-tuning technique for the corridor method is then presented. The response surface methodology is employed in order to determine a good set of parameter values given a specific problem input size. The effectiveness of both the algorithm and the validation of the fine tuning technique are illustrated on a specific problem selected from the domain of container terminal logistics, known as the blocks relocation problem, where one wants to retrieve a set of blocks from a bay in a specified order, while minimizing the overall number of movements and relocations. Computational results on 160 benchmark instances attest the quality of the algorithm and validate the fine tuning process.

Metaheuristics: Intelligent Problem Solving

Metaheuristics support managers in decision making with robust tools providing high quality solutions to important problems in business, engineering, economics and science in reasonable time horizons. While find- ing exact solutions in these applications still poses a real challenge despite the impact of recent advances in computer technology and the great inter- actions between computer science, management science/operations research and mathematics, (meta-) heuristics still seem to be the methods of choice in many (not to say most) applications. In this chapter we give some insight into the state of the art of metaheuristics. It focuses on the significant progress regarding the methods themselves as well as the advances regarding their interplay and hybridization with exact methods.

A cross entropy-based metaheuristic algorithm for large-scale capacitated facility location problems

In this paper, we present a metaheuristic-based algorithm for the capacitated facility location problem. The proposed scheme is made up by three phases: (i) solution construction phase, in which a cross entropy-based scheme is used to ‘intelligently’ guess which facilities should be opened; (ii) local search phase, aimed at exploring the neighbourhood of ‘elite’ solutions of the previous phase; and (iii) learning phase, aimed at fine-tuning the stochastic parameters of the algorithm. The algorithm has been thoroughly tested on large-scale random generated instances as well as on benchmark problems and computational results show the effectiveness and robustness of the algorithm.

An exact algorithm for the reliability redundancy allocation problem

The redundancy allocation problem is the problem of finding an optimal allocation of redundant components subject to a set of resource constraints. The problem studied in this paper refers to a series-parallel system configuration and allows for component mixing. We propose a new modeling/solution approach, in which the problem is transformed into a multiple choice knapsack problem and solved to optimality via a branch and cut algorithm. The algorithm is tested on well-known sets of benchmark instances. All instances have been solved to optimality in milliseconds or very few seconds on a normal workstation.

Tuning metaheuristics: A data mining based approach for particle swarm optimization

The paper is concerned with practices for tuning the parameters of metaheuristics. Settings such as, e.g., the cooling factor in simulated annealing, may greatly affect a metaheuristics efficiency as well as effectiveness in solving a given decision problem. However, procedures for organizing parameter calibration are scarce and commonly limited to particular metaheuristics. We argue that the parameter selection task can appropriately be addressed by means of a data mining based approach. In particular, a hybrid system is devised, which employs regression models to learn suitable parameter values from past moves of a metaheuristic in an online fashion. In order to identify a suitable regression method and, more generally, to demonstrate the feasibility of the proposed approach, a case study of particle swarm optimization is conducted. Empirical results suggest that characteristics of the decision problem as well as search history data indeed embody information that allows suitable parameter values to be determined, and that this type of information can successfully be extracted by means of nonlinear regression models.