The constrained compartmentalized knapsack problem: mathematical models and solution methods

Leão, Aline Aparecida de Souza; Santos, Maristela Oliveira dos; Hoto, Robinson; Arenales, Marcos Nereu

doi:10.1016/j.ejor.2011.02.016

Cited by 13 publications

(11 citation statements)

References 26 publications

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“…Malthouse et al (2012) applied the CKP in the marketing area to select media vehicles for marketing campaigns then, to determine the depth of purchase from each vehicle. Leão et al (2011) and Marques & Arenales (2007) proposed different mathematical formulations to handle the constrained CKP.…”

Section: Introductionmentioning

confidence: 99%

On solving the double loading problem using a modified particle swarm optimization

Tlili¹,

Krichen²

2015

Theoretical Computer Science

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Please cite this article in press as: T. Tlili, S. Krichen, On solving the double loading problem using a modified particle swarm optimization, Theoret. Comput. Sci. (2015), http://dx. AbstractWe consider in this paper a double loading problem (DLP), an NP-hard optimization problem of extreme economic relevance in industrial areas. The problem consists in loading items into bins, then stowing bins in a set of compartments. The main objective is to minimize the number of used bins. We state the mathematical model as well as a modified binary particle swarm optimization with FFD initialization that outperforms state-of-the-art approaches carried out on a large testbed instances.

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Section: Introductionmentioning

confidence: 99%

On solving the double loading problem using a modified particle swarm optimization

Tlili¹,

Krichen²

2015

Theoretical Computer Science

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“…In Leão et al. (), a linear treatment for the CKPR is presented next to a heuristic to solve it, called hybrid heuristic , which merges the “ z ” best compartments and the “ W ” capacities. The paper also presents a method for solving the constrained CKPR master problem using column generation, called the dynamic column generation method .…”

Section: Introductionmentioning

confidence: 99%

A strong integer linear optimization model to the compartmentalized knapsack problem

Quiroga‐Orozco

Carvalho

Hoto

2019

Int Trans Operational Res

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The compartmentalized knapsack problem (CKP) is a relatively new type of problem with a wide application in industrial processes, arising, for instance, in the case of cutting steel coils in two phases in the metallurgical industry. In the literature, there are two mathematical formulations for the CKP: a classical formulation, which is a nonlinear integer programming (IP) model, and a recent (linear) IP formulation, obtained by discretizing the compartments that can be built for each class of items; the latter is an important contribution, because it makes the problem amenable to solution by mixed‐integer linear programming tools. Combinatorial enumeration algorithms and several pseudo‐polynomial decomposition heuristics were also developed for the CKP. This paper presents a new model for the exact solution of the CKP, denoted as the strong integer linear model, derived from the (linear) IP formulation by strengthening data, reducing symmetry, and lifting, and also a new pseudo‐polynomial heuristic, the heuristic of the pk strong capacities. Computational experiments are presented with a large set of instances that show the advantage of the new approaches. The strong model solves the CKP exactly more than seven times faster, and the new heuristic is more efficient, presenting a good balance in the terms of effectiveness.

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“…In Leão et al. (), the upper bound given by the Marques and Arenales relaxation to verify the optimality of the solution by some heuristics is adopted. Another upper bound discussed by Leão et al.…”

Section: Introductionmentioning

confidence: 99%

“…A hybrid heuristic is also presented by Leão et al. (), exploring the ideas of the “Z” best compartment and “W” capacity heuristics.…”

Section: Introductionmentioning

confidence: 99%

“…In Leão et al (2011), the upper bound given by the Marques and Arenales relaxation to verify the optimality of the solution by some heuristics is adopted. Another upper bound discussed by Leão et al (2011) uses the column generation method to solve the knapsack compartmentalization problem, where, at each simplex interaction, some subproblems (one for each class) are calculated.…”

Section: Introductionmentioning

confidence: 99%

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An integer linear optimization model to the compartmentalized knapsack problem

Inarejos

Hoto

Maculan

2017

Int Trans Operational Res

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The compartmentalized knapsack problem arose from two‐phased cutting stock problems, especially with steel roll cutting. In its original formulation, it refers to an integer nonlinear optimization model, which, up to now, has been solved through decomposition heuristics. The objective of this article is to show that the constrained compartmentalized knapsack problem has a linear optimization model. Therefore, we have considered the original nonlinear model and propose a linear model for the problem, demonstrating their equivalence. We also propose a new decomposition heuristic and perform numerical tests to verify the limits of the proposed model and the quality of the heuristic solutions.

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The constrained compartmentalized knapsack problem: mathematical models and solution methods

Cited by 13 publications

References 26 publications

On solving the double loading problem using a modified particle swarm optimization

On solving the double loading problem using a modified particle swarm optimization

A strong integer linear optimization model to the compartmentalized knapsack problem

An integer linear optimization model to the compartmentalized knapsack problem

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