A Filter-and-Fan Metaheuristic for the 0-1 Multidimensional Knapsack Problem

2012 ◽  
Vol 3 (4) ◽  
pp. 43-63 ◽  
Author(s):  
Mahdi Khemakhem ◽  
Boukthir Haddar ◽  
Khalil Chebil ◽  
Saïd Hanafi
Keyword(s):  
Tabu Search ◽  
Knapsack Problem ◽  
Search Algorithm ◽  
Neighborhood Search ◽  
Benchmark Problems ◽  
Tree Search ◽  
Search Procedure ◽  
Multidimensional Knapsack Problem ◽  
Multidimensional Knapsack ◽  
Adaptive Neighborhood

This paper proposes a new hybrid tree search algorithm to the Multidimensional Knapsack Problem (MKP) that effectively combines tabu search with a dynamic and adaptive neighborhood search procedure. The authors’ heuristic, based on a filter-and-fan (F&F) procedure, uses a Linear Programming-based Heuristic to generate a starting solution to the F&F process. A tabu search procedure is used to try to enhance the best solution value provided by the F&F method that generates compound moves by a strategically truncated form of tree search. They report the first application of the F&F method to the MKP. Experimental results obtained on a wide set of benchmark problems clearly demonstrate the competitiveness of the proposed method compared to the state-of-the-art heuristic methods.

scholarly journals Neural, Genetic, And Neurogenetic Approaches For Solving The 0-1 Multidimensional Knapsack Problem

2012 ◽  
Vol 17 (1) ◽  
pp. 43 ◽  
Author(s):  
Jason Deane ◽  
Anurag Agarwal
Keyword(s):  
Genetic Algorithms ◽  
Knapsack Problem ◽  
Search Algorithm ◽  
Benchmark Problems ◽  
Initial Population ◽  
Local Search Algorithm ◽  
Genetic Approach ◽  
Multidimensional Knapsack Problem ◽  
Problem Space ◽  
Multidimensional Knapsack

The multi-dimensional knapsack problem (MDKP) is a well-studied problem in Decision Sciences. The problems NP-Hard nature prevents the successful application of exact procedures such as branch and bound, implicit enumeration and dynamic programming for larger problems. As a result, various approximate solution approaches, such as the relaxation approaches, heuristic and metaheuristic approaches have been developed and applied effectively to this problem. In this study, we propose a Neural approach, a Genetic Algorithms approach and a Neurogenetic approach, which is a hybrid of the Neural and the Genetic Algorithms approach. The Neural approach is essentially a problem-space based non-deterministic local-search algorithm. In the Genetic Algorithms approach we propose a new way of generating initial population. In the Neurogenetic approach, we show that the Neural and Genetic iterations, when interleaved appropriately, can complement each other and provide better solutions than either the Neural or the Genetic approach alone. Within the overall search, the Genetic approach provides diversification while the Neural provides intensification. We demonstrate the effectiveness of our proposed approaches through an empirical study performed on several sets of benchmark problems commonly used in the literature.

scholarly journals A Binary differential search algorithm for the 0–1 multidimensional knapsack problem

2016 ◽  
Vol 40 (23-24) ◽  
pp. 9788-9805 ◽  
Author(s):  
Jianjun Liu ◽  
Changzhi Wu ◽  
Jiang Cao ◽  
Xiangyu Wang ◽  
Kok Lay Teo
Keyword(s):  
Knapsack Problem ◽  
Search Algorithm ◽  
Multidimensional Knapsack Problem ◽  
Multidimensional Knapsack

scholarly journals Optimization Method to Address Psychosocial Risks through Adaptation of the Multidimensional Knapsack Problem

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1126
Author(s):  
Marta Lilia Eraña-Díaz ◽  
Marco Antonio Cruz-Chávez ◽  
Fredy Juárez-Pérez ◽  
Juana Enriquez-Urbano ◽  
Rafael Rivera-López ◽  
...  
Keyword(s):  
Risk Factors ◽  
Simulated Annealing ◽  
Knapsack Problem ◽  
Simulated Annealing Algorithm ◽  
Psychosocial Risk Factors ◽  
Psychosocial Risk ◽  
Multidimensional Knapsack Problem ◽  
Optimal Subset ◽  
Multidimensional Knapsack ◽  
A Company

This paper presents a methodological scheme to obtain the maximum benefit in occupational health by attending to psychosocial risk factors in a company. This scheme is based on selecting an optimal subset of psychosocial risk factors, considering the departments’ budget in a company as problem constraints. This methodology can be summarized in three steps: First, psychosocial risk factors in the company are identified and weighted, applying several instruments recommended by business regulations. Next, a mathematical model is built using the identified psychosocial risk factors information and the company budget for risk factors attention. This model represents the psychosocial risk optimization problem as a Multidimensional Knapsack Problem (MKP). Finally, since Multidimensional Knapsack Problem is NP-hard, one simulated annealing algorithm is applied to find a near-optimal subset of factors maximizing the psychosocial risk care level. This subset is according to the budgets assigned for each of the company’s departments. The proposed methodology is detailed using a case of study, and thirty instances of the Multidimensional Knapsack Problem are tested, and the results are interpreted under psychosocial risk problems to evaluate the simulated annealing algorithm’s performance (efficiency and efficacy) in solving these optimization problems. This evaluation shows that the proposed methodology can be used for the attention of psychosocial risk factors in real companies’ cases.

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