A Variable Neighborhood Search with Integer Programming for the Zero-One Multiple-Choice Knapsack Problem with Setup

Adouani, Yassine; Jarboui, Bassem; Masmoudi, Mohamed

doi:10.1007/978-3-030-15843-9_13

Cited by 4 publications

(24 citation statements)

References 31 publications

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“…A few other variants obtain encouraging results with this limitation of 2 seconds. When increasing the running time of VNS to 5 seconds we observed that the most important gain was obtained when starting from solutions provided by GKP(0) and GKP (1). Considering the other heuristics the most disappointing results were undoubtedly those obtained when GKP( 2) is used to initialize the search.…”

Section: Applying Greedy Algorithms and Vns Without Reductionmentioning

confidence: 94%

“…In several cases it is combined with another metaheuristic such that in [30] where authors considered a differential evolution algorithm with VNS to solve the multidimensional knapsack problem (MKP). It can also be combined with integer programming approaches like in [24,1] where authors deal with the MKP and the multiple-choice knapsack problem with setup, respectively. VNS has also be applied "alone" to solve knapsack problems like in [29] where authors considered very recently the irregular knapsack problem.…”

Section: Constructive Heuristicsmentioning

confidence: 99%

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Heuristic and exact fixation-based approaches for the discounted 0-1 knapsack problem

Wilbaut¹,

Todosijević²,

Hanafi³

et al. 2021

Preprint

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In this paper we consider the discounted 0-1 knapsack problem (DKP), which is an extension of the classical knapsack problem where a set of items is decomposed into groups of three items. At most one item can be chosen from each group and the aim is to maximize the total profit of the selected items while respecting the knapsack capacity constraint. The DKP is a relatively recent problem in the literature. We propose several efficient heuristic ways to solve the DKP using fixation techniques. One of the objectives of this work is to show that heuristic approaches dealing with the DKP can be strongly improved by using both heuristic and exact fixation rules. We propose several greedy algorithms and a new variable neighborhood search (VNS) to solve the DKP, and we evaluate the behavior of these methods on two sets of available instances when they are applied with or without fixation. Experiments show that VNS with fixation globally dominates approaches from the literature. Finally, we consider a dynamic programming-based approach where the fixation is incorporated, leading to a very efficient heuristic providing near optimal solutions and an exact approach to solve all the existing instances in less than 2 seconds.

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Section: Applying Greedy Algorithms and Vns Without Reductionmentioning

confidence: 94%

Section: Constructive Heuristicsmentioning

confidence: 99%

Heuristic and exact fixation-based approaches for the discounted 0-1 knapsack problem

Wilbaut¹,

Todosijević²,

Hanafi³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Herein, VND-LB's behavior is studied in the four sets (representing a total of 120 medium and large-scale benchmark instances of the literature, divided into three groups). The VND-LBs' results are compared to those taken from Adouani et al (2019): a VNS using linear integer programming (noted VNS-IP), and the state-of-the-art Cplex solver (noted Cplex). It is well known that the Cplex is a specialized optimal solver (like the Gurobi solver) that can be used for optimally solving MIP (with linear and quadratic functions).…”

Section: Performance Of Vnd-lb Versus Other Methodsmentioning

confidence: 99%

“…Finally, the returned best bound is realizing the best value. We note that all best lower bounds, with corresponding upper bounds, were taken from Adouani et al (2019) and we also corrected these bounds when necessary (as discussed above: the wrong upper bound of each instance reported in Adouani et al ( 2019) is marked with " †"). Therefore, we analyze the results provided by VND-LB to those obtained by the aforementioned algorithms.…”

Section: Performance Of Vnd-lb Versus Other Methodsmentioning

confidence: 99%

“…Table 2 displays all approximation ratios related to the Cplex (column 3 under z Cplex ), and to Start (column 4 under z Start ). However, since some published bounds in Adouani et al (2019) are wrong (all instances are marked with the symbol " †" under UB C plex in Tables 1, 4, and 5), we executed the Cplex solver for 1 hour (for overall instances) and reported the maximum objective value corresponding to each tested instance. Now, we comment on the results related to both Tables 1 and 2: • Start is able to achieve an average ratio of 0.99445 (Table 2) while the Cplex solver realizes an average value of 0.99616 representing a gap closest to 0.17%.…”

Section: The Starting Solution and Its Qualitymentioning

confidence: 99%

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Combining local branching and descent method for solving the multiple‐choice knapsack problem with setups

Boukhari

Hifi

2023

Int Trans Operational Res

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In this paper, the multiple‐choice knapsack problem with setups is tackled with an iterative method, where both local branching and descent method cooperate. First, an iterative procedure is designed for solving a series of mixed integer programming problems combined with a special reduced subproblem; that is, a combined model built by injecting some valid cardinality constraints. Second, the local branching‐based learning strategy is embedded into an iterative search to mimic the variable neighborhood descent method, such that the local branching strategy drives the search process for enhancing the quality of the solutions. Third, the proposed method is experimentally analyzed on benchmark instances extracted from the literature, where its provided (lower) bounds are compared to those reached by methods published in the literature and the Cplex solver. Finally, its performance is evaluated by providing a statistical analysis.

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Iterative integer linear programming-based heuristic for solving the multiple-choice knapsack problem with setups

Adouani,

Masmoudi,

Jarray

et al. 2024

Expert Systems with Applications

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A Variable Neighborhood Search with Integer Programming for the Zero-One Multiple-Choice Knapsack Problem with Setup

Cited by 4 publications

References 31 publications

Heuristic and exact fixation-based approaches for the discounted 0-1 knapsack problem

Heuristic and exact fixation-based approaches for the discounted 0-1 knapsack problem

Combining local branching and descent method for solving the multiple‐choice knapsack problem with setups

Iterative integer linear programming-based heuristic for solving the multiple-choice knapsack problem with setups

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