An iterative variable-based fixation heuristic for the 0-1 multidimensional knapsack problem

Wilbaut, Christophe; Salhi, Saı̈d; Hanafi, Saïd

doi:10.1016/j.ejor.2008.11.036

Cited by 25 publications

(6 citation statements)

References 28 publications

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“…Although, the bounded KP (Pisinger, 2000), the d-dimensional or multidimensional KP (Chen and Hao, 2014;Balev et al, 2008;Wilbaut et al, 2009), the multiple KP (MKP) (Garcia-Martinez et al, 2014;Yamada and Takeoka, 2009;Kataoka and Yamada, 2014), the MKP with assignment restrictions (Dawande et al, 2000) and different stochastic versions of the KP (Chen and Ross, 2014;Perboli et al, 2014;Dean et al, 2008) have been analysed in the area of combinatorial optimization, to the best of our knowledge, our previous studies (Diaz andHandl, 2014, 2015) are the only papers that have tried to tackle a problem similar to d-MBKARS.…”

Section: New Variants Of the Knapsack Problemmentioning

confidence: 99%

Integrating meta-heuristics, simulation and exact techniques for production planning of a failure-prone manufacturing system

Diaz

Handl

2018

European Journal of Operational Research

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This paper considers a real-world production planning problem in which production line failures cause uncertainty regarding the practical implementation of a given production plan. We provide a general formulation of this problem as an extended stochastic knapsack problem, in which uncertainty arises from non-trivial perturbations to the decision variables that cannot be represented in closed form. We then proceed by describing a combination of exact optimization, simulation and a meta-heuristic that can be employed in such a setting. Specifically, a discrete-event simulation (DES) of the production system is developed to estimate solution quality and to model perturbations to the decision variables. A genetic algorithm (GA) can then be used to search for optimal production plans, using a simulation-based optimization approach. To provide effective seeding to the GA, we propose initialization operators that exploit mathematical programming in combination with the DES model. The approach is benchmarked against integer linear programming and chance-constrained programming. We find that our approach significantly outperform contestant techniques under various levels of uncertainty.

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Section: New Variants Of the Knapsack Problemmentioning

confidence: 99%

Integrating meta-heuristics, simulation and exact techniques for production planning of a failure-prone manufacturing system

Diaz

Handl

2018

European Journal of Operational Research

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“…Moreover, the multi-dimensional zero-one knapsack problem itself is one of the well-studied optimization problems, which has been studied by several researchers [2,6,8,17,26,30,31]. In the context of preprocessing, Fréville and Plateau [9] provided a sequential reduction scheme based on their previous research given in [10,11] for the multi-dimensional zero-one knapsack problem.…”

Section: Introductionmentioning

confidence: 99%

Identifying redundancy in multi-dimensional knapsack constraints based on surrogate constraints

Choi

2014

International Journal of Computer Mathematics

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Redundancy identification techniques play an important role in improving the solvability of a linear program. In this paper, we address the redundancy in multi-dimensional knapsack constraints by proposing a new redundancy identification method. The proposed method is based on the constraint intercepts of Paulraj, Chellappan, and Natesan [A heuristic approach for identification of redundant constraints in linear programming models, Int. J. Comput. Math. 83 (2006), pp. 675-683] and surrogate constraints. In it, feasibility problems are constructed in order to determine the redundancy of the constraints, and are solved by a heuristic algorithm, which is developed to check the redundancy fast. The results of computational experiments show that the proposed method may be used in a preprocessing stage in order to reduce the number of knapsack constraints.

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“…Informally, the backbone of a SAT instance is the set of literals 1 which are true in every satisfying truth assignment (Monasson et al (1998); Kilby et al (2005)). Zhang (2004) presents an effective backbone-based heuristic for SAT and an example of a similar strategy is reported for the multidimensional knapsack problem in Wilbaut et al (2009). Such a strategy was also proposed in connection with exploiting strongly determined and consistent variables in Glover (1977), and has come to be one of the basic strategies associated with tabu search.…”

Section: Backbone-guided Tabu Search For Ubqpmentioning

confidence: 99%

Backbone guided tabu search for solving the UBQP problem

Wang

Glover

et al. 2011

J Heuristics

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We propose a backbone-guided tabu search (BGTS) algorithm for the Unconstrained Binary Quadratic Programming (UBQP) problem that alternates between two phases: (1) a basic tabu search procedure to optimize the objective function as far as possible; (2) a strategy using the TS notion of strongly determined variables to alternately fix and free backbone components of the solutions which are estimated likely to share values in common with an optimal solution. Experimental results show that the proposed method is capable of finding the best-known solutions for 21 large random instances with 3000 to 7000 variables and boosts the performance of the basic TS in terms of both solution quality and computational efficiency.

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An iterative variable-based fixation heuristic for the 0-1 multidimensional knapsack problem

Cited by 25 publications

References 28 publications

Integrating meta-heuristics, simulation and exact techniques for production planning of a failure-prone manufacturing system

Integrating meta-heuristics, simulation and exact techniques for production planning of a failure-prone manufacturing system

Identifying redundancy in multi-dimensional knapsack constraints based on surrogate constraints

Backbone guided tabu search for solving the UBQP problem

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