• Korean Management Science Review
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• v.13 no.2
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• pp.73-94
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• 1996

Knapsack problems represent many business application such as cargo loading, project selection, and capital budgeting. In this research we developed a knapsack problem solver based on Martello-Toth algorithm using a relational database management system on the PC platform. The solver used the menu-driven user interface. The solver can be easily integrated with the database of decision support system because the solver can access the database to retrieve the data for the model and to store the result directly.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.4
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• pp.1-10
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• 1998

We consider the precedence-constrained knapsack problem. which is a knapsack problem with precedence constraints imposed on the set of variables. Especially, we focus on the case where the precedence constraints cir be represented as a bipartite graph, which occurs most frequently in applications. Based on the previous studios for the general case, we specialize the polyhedral results on the related polytope and derive stronger results on the facet-defining properties of the inequalities.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.611-628
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• 2021

In this paper, we propose a new branch-reduction-and-bound algorithm to solve the nonlinear knapsack problems by using general discrete monotonic optimization techniques. The specific properties of the problem are exploited to increase the efficiency of the algorithm. Computational experiments of the algorithm on problems with up to 30 variables and 5 different constraints are reported.

• Journal of the Korean Institute of Intelligent Systems
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• v.15 no.6
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• pp.730-735
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• 2005

Though Knapsack Problem appears to be simple, it is a NP-hard problem that is not solved in polynomial time as combinational optimization problems. To solve this problem, GA(Genetic Algorithms) was used in the past. However, there were difficulties in real experiments because the conventional method didn't reflect the precise characteristics of DNA. In this paper we proposed ACO (Algorithm for Code Optimization) that applies DNA coding method to DNA computing to solve problems of Knapsack Problem. ACO was applied to (0,1) Knapsack Problem; as a result, it reduced experimental errors as compared with conventional methods, and found accurate solutions more rapidly.

• Management Science and Financial Engineering
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• v.10 no.1
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• pp.97-106
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• 2004

In this paper, we propose an effective cut generation method based on the Chvatal-Gomory procedure for a variable-capacity (0,l)-Knapsack problem with two general integer variables. We first derive a class of valid inequalities for the problem using Chvatal-Gomory procedure, then analyze the associated separation problem. Based on the results, we show that there exists a pseudo-polynomial time algorithm to solve the separation problem. By analyzing the theoretical strength of the inequalities which can be generated by the proposed cut generation method, we show that generated inequalties define facets under mild conditions. We also extend the result to the case in which a nontrivial upper bound is imposed on a general integer variable.

• Journal of Korean Institute of Industrial Engineers
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• v.9 no.2
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• pp.3-8
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• 1983

The multiple choice knapsack problem is modified. To solve this modified multiple choice knapsack problem, Lagrangian relaxation is used, and to take advantage of the special structure of subproblems obtained by decomposing this relaxed Lagrangian problem, a modified ranking algorithm is used. The K best rank order solutions obtained from each subproblem as a result of applying modified ranking algorithm are used to formulate restricted problems of the original problem. The optimality for the original problem of solutions obtained from the restricted problems is judged from the upper bound and lower bounds calculated iteratively from the relaxed problem and restricted problems, respectively.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2000.08a
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• pp.341-344
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• 2000

The 0-1 knapsack processor performing dynamic programming is designed and implemented on a programmable logic device. Three types of a processor, each with different behavioral models, are presented, and the operation of a processor of each type is verified with an instance of the 0-1 knapsack problem.

• Journal of the military operations research society of Korea
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• v.10 no.1
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• pp.57-63
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• 1984

The 0-1 multi-period Knapsack problem (MPKP) has a horizon of m periods, each having a number of types of projects with values and weights. Subject to the requirement, the cummulative capacity of the problem in each period i cannot be exceeded by the total weight of the projects selected in period 1, 2, ..., i. It is a problem of selecting the projects in such a way that the total value in the knapsack through the horizon of m periods is maximized. A search algorithm is developed and tested in this paper. Search rules that avoid the search of redundant partial solutions are used in the algorithm. Using the property of MPKP, a surrogate constraint concerned with the most available requirement is used in the bounding technique.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.3
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• pp.258-263
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• 2011

We study on a generalization of the two dimensional linear programming knapsack problem with the extended GUB constraint, which was presented in paper Won(2001). We identify some new parametric properties of the generalized problem and derive a solution algorithm based on the identified parametric properties. The solution algorithm has a worst case time complexity of order O($n^2logn$), where n is the total number of variables. We illustrate a numerical example.

• International Journal of Computer Science & Network Security
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• v.24 no.2
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• pp.15-24
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• 2024

One of the most significant issues in combinatorial optimization is the classical NP-complete conundrum known as the 0/1 Knapsack Problem. This study delves deeply into the investigation of practical solutions, emphasizing two classic algorithmic paradigms, brute force, and dynamic programming, along with the metaheuristic and nature-inspired family algorithm known as the Genetic Algorithm (GA). The research begins with a thorough analysis of the dynamic programming technique, utilizing its ability to handle overlapping subproblems and an ideal substructure. We evaluate the benefits of dynamic programming in the context of the 0/1 Knapsack Problem by carefully dissecting its nuances in contrast to GA. Simultaneously, the study examines the brute force algorithm, a simple yet comprehensive method compared to Branch & Bound. This strategy entails investigating every potential combination, offering a starting point for comparison with more advanced techniques. The paper explores the computational complexity of the brute force approach, highlighting its limitations and usefulness in resolving the 0/1 Knapsack Problem in contrast to the set above of algorithms.