Memetic Algorithm for Solving the 0-1 Multidimensional Knapsack Problem

Multidimensional 0-1 Knapsack Problem (MKP) is a well-known integer programming problems. The objective of MKP is to find a subset of items with maximum value satisfying the capacity constraints. A Memetic algorithm on the basis of Design and Implementation Methodology for Metaheuristic Algorithms (DIMMA) is proposed to solve MKP. DIMMA is a new methodology to develop a metaheuristic algorithm. The Memetic algorithm is categorized as metaheuristics and is a particular class of evolutionary algorithms. The parameters of the proposed algorithm are tuned by Design of Experiments (DOE) approach. DOE refers to the process of planning the experiment so that appropriate data that can be analyzed by statistical methods will be collected, resulting in valid and objective conclusions. The proposed algorithm is tested on several MKP standard instances from OR-Library. The results show the efficiency and effectiveness of the proposed algorithm.

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A Memetic Lagrangian Heuristic for the 0-1 Multidimensional Knapsack Problem

Discrete Dynamics in Nature and Society ◽

10.1155/2013/474852 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 6

Author(s):

Yourim Yoon ◽

Yong-Hyuk Kim

Keyword(s):

Knapsack Problem ◽

Lagrange Multipliers ◽

Empirical Investigation ◽

Memetic Algorithm ◽

Capacity Constraints ◽

Multidimensional Knapsack Problem ◽

Benchmark Data ◽

Multidimensional Knapsack ◽

Lagrangian Heuristic ◽

Traditional Approaches

We present a new evolutionary algorithm to solve the 0-1 multidimensional knapsack problem. We tackle the problem using duality concept, differently from traditional approaches. Our method is based on Lagrangian relaxation. Lagrange multipliers transform the problem, keeping the optimality as well as decreasing the complexity. However, it is not easy to find Lagrange multipliers nearest to the capacity constraints of the problem. Through empirical investigation of Lagrangian space, we can see the potentiality of using a memetic algorithm. So we use a memetic algorithm to find the optimal Lagrange multipliers. We show the efficiency of the proposed method by the experiments on well-known benchmark data.

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

Mathematics ◽

10.3390/math9101126 ◽

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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