• Journal of Korean Institute of Industrial Engineers
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• v.27 no.1
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• pp.25-29
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• 2001

We present a two dimensional linear programming knapsack problem with the extended GUB constraint. The presented problem is an extension of the cardinality constrained linear programming knapsack problem. We identify some new properties of the problem and derive a solution algorithm based on the parametric analysis for the knapsack right-hand-side. The solution algorithm has a worst case time complexity of order O($n^2logn$). A numerical example is given.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.19 no.40
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• pp.137-142
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• 1996

An algorithm for solving the cardinality constrained linear programming knapsack problem is presented. The algorithm has a convenient structure for a branch-and-bound approach to the integer version, especially to the 0-1 collapsing knapsack problem. A numerical example is given.

• Convergence Security Journal
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• v.14 no.7
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• pp.59-64
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• 2014

We investigate $p(n){\cdot}2^{O(\sqrt{n})}$ algorithm for 0/1 knapsack problem where x is the total bit length of a list of sizes of n objects. The algorithm is adaptable of method that achieves a similar complexity for the partition and Subset Sum problem. The method can be applied to other optimization or decision problem based on a list of numerics sizes or weights. 0/1 knapsack problem can be used to solve NP-Complete Problems with pseudo-polynomial time algorithm. We try to apply this technique to bio-informatics problem which has pseudo-polynomial time complexity.

• Journal of Information Processing Systems
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• v.18 no.5
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• pp.665-676
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• 2022

In modern logistics, the effective use of the vehicle volume and loading capacity will reduce the logistic cost. Many heuristic algorithms can solve this knapsack problem, but lots of these algorithms have a drawback, that is, they often fall into locally optimal solutions. A fusion optimization method based on simulated annealing algorithm (SA) and binary particle swarm optimization algorithm (BPSO) is proposed in the paper. We establish a logistics knapsack model of the fusion optimization algorithm. Then, a new model of express logistics simulation system is used for comparing three algorithms. The experiment verifies the effectiveness of the algorithm proposed in this paper. The experimental results show that the use of BPSO-SA algorithm can improve the utilization rate and the load rate of logistics distribution vehicles. So, the number of vehicles used for distribution and the average driving distance will be reduced. The purposes of the logistics knapsack problem optimization are achieved.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.16 no.9
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• pp.883-892
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• 1991

In this thesis explanation of new knapsack algorithm for public key system difficulty test and parallel architecture for implementation are suggested. Past Merkle-Hellman’s knapsack is weak in Shamir or Brickell`s attack by the effects of mapping into other easy sequenoes. But linearly shift knapsack system compensates them.

• 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.

• Management Science and Financial Engineering
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• v.14 no.1
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• pp.91-96
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• 2008

Robust knapsack problem appears when dealing with data uncertainty on the knapsack constraint. This note presents a generalization of the cover inequality for the problem with its lifting procedure. Specifically, we show that the lifting can be done in a polynomial time as in the usual knapsack problem. The results can serve as a building block in devising an efficient branch-and-cut algorithm for the general robust (0, 1) IP problem.

• Journal of Korean Institute of Industrial Engineers
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• v.23 no.4
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• pp.661-667
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• 1997

We consider a generalized problem of the continuous multiple choice knapsack problem and study on the LP relaxation of the candidate problems which are generated in the branch and bound algorithm for solving the generalized problem. The LP relaxed candidate problem is called the generalized continuous multiple choice linear knapsack problem and characterized by some variables which are partitioned into continuous multiple choice constraints and the others which only belong to simple upper bound constraints. An efficient algorithm of order O($n^2logn$) is developed by exploiting some structural properties and applying binary search to ordered solution sets, where n is the total number of variables. A numerical example is presented.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.773-774
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• 2005

The knapsack problem (KP) is one of the traditional optimization problems. Specially, multiconstrained knapsack problem (MKP) is well-known NP-hard problem. Many heuristic algorithms and evolutionary algorithms have tackled this problem and shown good performance. This paper presents a novel genetic algorithm for the multiconstrained knapsack problem. The proposed algorithm is called 'Adaptive Link Adjustment'. It is based on integer random key representation and uses additional ${\alpha}$ and ${\beta}$-process as well as selection, crossover and mutation. The experiment results show that it can be archive good performance.

• Journal of the Korean Operations Research and Management Science Society
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• v.31 no.1
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• pp.55-71
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• 2006

We perform a computational study on 0-1 knapsack problems generated under explicit correlation induction. A total of 2000 100-variable test problems are solved. We use two solution methods: (1) a well known heuristic and (2) a representative branch and bound type algorithm. Two different performance measures are considered: (1) the number of nodes needed to find an optimal solution and (2) the relative error of the heuristic solution. We also examine the effect of different joint probability mass functions (pmfs) for the coefficient values on the performance of the solution procedure.