• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.6
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• pp.755-760
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• 2010

In general, Lagrangian method for discrete optimization is a kind of technique to easily manage constraints. It is traditionally used for finding upper bounds in the branch-and-bound method. In this paper, we propose a new Lagrangian search method for the 0-1 knapsack problem with multiple constraints. A novel feature of the proposed method different from existing Lagrangian approaches is that it can find high-quality lower bounds, i.e., feasible solutions, efficiently based on a new property of Lagrangian vector. We show the performance improvement of the proposed Lagrangian method over existing ones through experiments on well-known large scale benchmark data.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.96-101
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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 (0,1)-Knapsack problem, which is the same problem as the ordinary binary knapsack problem except that a binary capacity variable is newly introduced. 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 pseudopolynomial time algorithm to solve the separation problem. Preliminary computational results are presented which show the effectiveness of the proposed cut generation method.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.2
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• pp.3-13
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• 1993

In this study, we develop a B & B type algorithm for the concave minimization problem with 0-1 knapsack constraint. Our algorithm reformulates the original problem into the singly linearly constrained concave minimization problem by relaxing 0-1 integer constraint in order to get a lower bound. But this relaxed problem is the concave minimization problem known as NP-hard. Thus the linear function that underestimates the concave objective function over the given domain set is introduced. The introduction of this function bears the following important meanings. Firstly, we can efficiently calculate the lower bound of the optimal object value using the conventional convex optimization methods. Secondly, the above linear function like the concave objective function generates the vertices of the relaxed solution set of the subproblem, which is used to update the upper bound. The fact that the linear underestimating function is uniquely determined over a given simplex enables us to fix underestimating function by considering the simplex containing the relaxed solution set. The initial containing simplex that is the intersection of the linear constraint and the nonnegative orthant is sequentially partitioned into the subsimplices which are related to subproblems.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.4
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• pp.142-148
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• 2012

Release planning for incremental software development is to select and assign features in sequence of releases along a specified planning horizon. It includes the technical precedence inherent in the features, the conflicting priorities as determined by the representative stakeholders, and the balance between required and available resources. The complexity of this consideration is getting more complicated when planning releases in software product lines. The problem is formulated as a precedence-constrained multiple 0-1 knapsack problem. In this research a genetic algorithm is developed for solving the release planning problems in software product lines as well as tests for the proposed solution methodology are conducted using data generated randomly.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.36 no.3
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• pp.17-24
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• 2013

Release planning in a software product line (SPL) is to select and assign the features of the multiple software products in the SPL in sequence of releases along a specified planning horizon satisfying the numerous constraints regarding technical precedence, conflicting priorities for features, and available resources. A greedy genetic algorithm is designed to solve the problems of release planning in SPL which is formulated as a precedence-constrained multiple 0-1 knapsack problem. To be guaranteed to obtain feasible solutions after the crossover and mutation operation, a greedy-like heuristic is developed as a repair operator and reflected into the genetic algorithm. The performance of the proposed solution methodology in this research is tested using a fractional factorial experimental design as well as compared with the performance of a genetic algorithm developed for the software release planning. The comparison shows that the solution approach proposed in this research yields better result than the genetic algorithm.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.9
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• pp.13-22
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• 1997

In this paper, we supposed allocating the number of redundancies as the model of 0-1 knapsack problem and formulated the problem to maximize the systems reliability for a mission length. The formulated problem reduced the problem size using the modified branch and bound algorithm by Lagrangian relaxation. The subgradient method can optimize the set of solution. To verify the proposed method, we presented the improved resutls of the systems composed of two and ten component groups as the commparison of those in other papers.

• The Transactions of the Korea Information Processing Society
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• v.4 no.6
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• pp.1550-1556
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• 1997

In this paper, we apply the evolutionary algorithm to the combinatorial optimization problem. Evolutionary algorithm useful for the optimization of the large space problem. This paper propose a method for the reuse of wastes of light water in atomic reactor system. These wastes contain several reusable elements, and they should be carefully selected and blended to satisfy requirements as an input material to the heavy water atomic reactor system. This problem belongs to an NP-hard like the 0/1 knapsack problem. Two evolutionary strategies are used as approximation algorithms in the highly constrained combinatorial optimization problem. One is the traditional strategy, using random operator with evaluation function, and the other is heuristic based search that uses the vector operator reducing between goal and current status. We also show the method which perform the feasible test and solution evaluation by using the vectored knowledge in problem domain. Finally, We compare the simulation results of using random operator and vector operator for such combinatorial optimization problems.

• Journal of Intelligence and Information Systems
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• v.3 no.2
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• pp.1-9
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• 1997

These papers propose an evolutionary algorithm for re-using output of waste fuel of light water reactor system in nuclear power plants. Evolutionary algorithm is useful for optimization of the large space problem. The wastes contain several re-useable elements, and they should be carefully selected and blended to satisfy requirements as input material to the heavy water nuclear reactor system. This problem belongs to a NP-hard like the 0/1 Knapsack problem. Two evolutionary strategies are used as a, pp.oximation algorithms in the highly constrained combinatorial optimization problem. One is the traditional strategy, using random operator with evaluation function, and the other is heuristic based search that uses the vector operator reducing between goal and current status. We also show the method, which performs the feasible teat and solution evaluation by using the vectorized data in problem. Finally, We compare the simulation results of using random operator and vector operator for such combinatorial optimization problems.

• Journal of the Institute of Convergence Signal Processing
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• v.4 no.3
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• pp.61-67
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• 2003

We propose a systolic array for dynamic programming which is a technique for solving combinatorial optimization problems. We derive a systolic array for single source shortest path Problem, SA SSSP, and then show that the systolic array serves as dynamic Programming systolic array which is applicable to any dynamic programming problem by developing a systolic array for 0 1 knapsack problem, SA 01KS, with SA SSSP for a basis. In this paper, each of SA SSSP and SA 01KS is modeled and simulated in RT level using VHDL, then synthesized to a schematic and finally implemented to a layout using the cell library based on 0.35${\mu}{\textrm}{m}$ 1 poly 4 metal CMOS technology.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.243-246
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• 2004

배낭 문제는 단순한 것 같지만 조합형 특성을 가진 NP-hard 문제이다 이 문제를 해결하기 위해 기존에는 GA(Genetic algorithms)를 이용하였으나 지역해에 빠질 수 있어 잘못된 해를 찾거나 찾지 못하는 문제점을 갖고 있다. 본 논문에서는 이러한 문제점들을 해결하기 위해 막대한 병렬성과 저장능력을 가진 DNA 컴퓨팅 기법에 DNA에 기반한 변형된 GA인 DNA 코딩 방법을 적용한 ACO(Algorithm for Code Optmization)를 제안한다. ACO는 배낭 문제 중 (0,1)-배낭 문제에 적용하였고, 그 결과 기존의 GA를 이용한 것 보다 초기 문제 표현에서 우수한 적합도를 생성했으며, 빠른 시간내에 우수한 해를 찾을 수 있었다.