• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.283-293
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• 2010

In this paper, inverse constrained minimum spanning tree problem under Hamming distance. Such an inverse problem is to modify the weights with bound constrains so that a given feasible solution becomes an optimal solution, and the deviation of the weights, measured by the weighted Hamming distance, is minimum. We present a strongly polynomial time algorithm to solve the inverse constrained minimum spanning tree problem under Hamming distance.

• 한국컴퓨터정보학회논문지
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• 제18권12호
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• pp.75-82
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• 2013

본 논문은 NP-완전으로 다항시간 알고리즘이 존재하지 않는 대규모 외판원 문제의 최적 해를 $O(n^2)$의 다항시간으로 구하는 알고리즘을 제안하였다. 대규모 외판원 문제에서 가장 큰 문제는 처리될 데이터가 $n{\times}n$으로 n이 커질수록 기하급수적으로 증가한다. 본 논문에서는 먼저, 데이터의 양을 약 n/2의 크기로 축소시킨다. 다음으로 임의의 정점에서 시작하여 양방향으로 경로를 탐색하는 방법을 적용하였다. 제안된 알고리즘을 26개의 유럽 도시들을 방문하는 TSP-1과 46개 미국 도시들을 방문하는 TSP-2에 적용한 결과 모두 최적 해를 $O(n^2)$ 수행 복잡도로 빠르게 구하는데 성공하였다. 따라서 제안된 알고리즘은 TSP의 일반화된 알고리즘으로 적용할 수 있을 것이다.

• 한국인터넷방송통신학회논문지
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• 제20권2호
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• pp.209-214
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• 2020

동등분할 문제(EPP)는 학생이 특정 분야에 대한 경험 유무인 [0/1]이진수 형태를 갖는 경우와 [1,2,3,4,5]와 같은 정수형의 기량 수준을 갖고 있는 문제로 분류된다. 이진수형 EPP에 대해서는 다항시간으로 최적 해를 구하는 알고리즘이 알려져 있다. 반면에, 정수형 기량 수준을 갖는 EPP에 대해서는 다항시간으로 해를 구하는 알고리즘이 존재하지 않아 아직까지는 메타휴리스틱의 일종인 타부탐색법만이 알려져 있는 난제이다. 본 논문은 NP-난제인 정수형 기량 수준을 갖는 EPP에 대해 다항시간으로 해를 찾아가는 규칙을 가진 휴리스틱 탐욕방법을 제안한다. 제안된 알고리즘은 각 분야의 기량 수준별 빈도수 내림차순으로 그룹 수를 충족하는 하한치(LB)를 구하고, LB 이상인 기량수준을 가진 학생들을 각 그룹 상자에 우선하여 채우고, LB 이하 기량수준을 가진 학생들을 추가로 각 상자에 배분하는 방법을 제안하였다. 제안된 알고리즘을 실험 데이터에 적용한 결과 기존의 타부탐색법으로 구한 결과를 개선하는 효과도 얻었다.

• 전기학회논문지
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• 제59권2호
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• pp.407-410
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• 2010

This paper presents an advanced load allocation algorithm in Direct Load Control(DLC) system. It is important to aggregate a various demand side resource which is surely controllable at the peak power time for a successful DLC system. Previous load allocation algorithm appropriate for DLC system is based on interchanged information, but, this algorithm can not derive optimal solutions. In this paper, we develop the optimal algorithm and the new load allocation algorithm in polynomial time. The simulation results show that the proposed heuristic algorithm for DLC system is very effective.

• 대한산업공학회지
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• 제19권4호
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• pp.3-11
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• 1993

We propose a new dual simplex method using a primal interior point. The dropping variable is chosen by utilizing the primal feasible interior point. For a given dual feasible basis, its corresponding primal infeasible basic vector and the interior point are used for obtaining a decreasing primal feasible point The computation time of moving on interior point in our method takes much less than that od Karmarker-type interior methods. Since any polynomial time interior methods can be applied to our method we conjectured that a slight modification of our method can give a polynomial time complexity.

• 한국경영과학회지
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• 제16권2호
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• pp.14-35
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• 1991

The purpose of this study is to develop an efficient exact algorithm for the problem of scheduling n in dependent jobs on m unequal parallel processors to minimize makespan. Efficient solutions are already known for the preemptive case. But for the non-preemptive case, this problem belongs to a set of strong NP-complete problems. Hence, it is unlikely that the polynomial time algorithm can be found. This is the reason why most investigations have bben directed toward the fast approximate algorithms and the worst-case analysis of algorithms. Recently, great advances have been made in mathematical theories regarding Lagrangean relaxation and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining these mathematical tools with branch-and-bound procedures, these have been some successes in constructing pseudo-polynomial time algorithms for solving previously unsolved NP-complete problems. This study applied similar methodologies to the unequal parallel processor problem to find the efficient exact algorithm.

• 한국경영과학회지
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• 제16권2호
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• pp.13-35
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• 1991

The purpose of this study is to develop an efficient exact algorithm for the problem of scheduling n in dependent jobs on m unequal parallel processors to minimize makespan. Efficient solutions are already known for the preemptive case. But for the non-preemptive case, this problem belongs to a set of strong NP-complete problems. Hence, it is unlikely that the polynomial time algorithm can be found. This is the reason why most investigations have bben directed toward the fast approximate algorithms and the worst-case analysis of algorithms. Recently, great advances have been made in mathematical theories regarding Lagrangean relaxation and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining and the subgradient optimization procedure which updates the Lagrangean multipliers. By combining these mathematical tools with branch-and-bound procedures, these have been some successes in constructing pseudo-polynomial time algorithms for solving previously unsolved NP-complete problems. This study applied similar methodologies to the unequal parallel processor problem to find the efficient exact algorithm.

• 산업경영시스템학회지
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• 제44권2호
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• pp.58-65
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• 2021

Meta-heuristic algorithms have been developed to efficiently solve difficult problems and obtain a global optimal solution. A common feature mimics phenomenon occurring in nature and reliably improves the solution through repetition. And at the same time, the probability is used to deviate from the regional optimal solution and approach the global optimal solution. This study compares the algorithm created based on the above common points with existed SA and HS to show advantages in time and accuracy of results. Existing algorithms have problems of low accuracy, high memory, long runtime, and ignorance. In a two-variable polynomial, the existing algorithms show that the memory increases and the accuracy decrease. In order to improve the accuracy, the new algorithm increases the number of initial inputs and increases the efficiency of the search by introducing a direction using vectors. And, in order to solve the optimization problem, the results of the last experiment were learned to show the learning effect in the next experiment. The new algorithm found a solution in a short time under the experimental conditions of long iteration counts using a two-variable polynomial and showed high accuracy. And, it shows that the learning effect is effective in repeated experiments.

• 한국컴퓨터정보학회논문지
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• 제20권2호
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• pp.63-70
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• 2015

최대 지배집합의 수인 도메틱 수 문제 (DNP)는 정확한 해를 다항시간으로 구하는 알고리즘이 존재하지 않아 NP-완전 문제로 알려져 있다. 본 논문은 DNP의 해를 다항시간으로 구하는 알고리즘을 제안하였다. 그래프의 최대 차수 ${\Delta}(G)$ 정점 $v_i$를 $D_i,i=1,2,{\cdots},k$의 지배집합의 원소로 선택하는 방법을 적용하고, $V_{i+1}=V_i{\backslash}D_i$의 축소된 그래프에 대해 $D_{i+1}$을 구하였다. 또한 $V{\backslash}D_i=N_G(D_i)$로 $D_i$가 지배집합으로 되는지 여부를 검증하였다. 제안된 알고리즘을 15개의 다양한 그래프에 적용한 결과 정확한 해를 다항시간 복잡도 O(kn)으로 구하는데 성공하였다. 결국, 제안된 알고리즘은 도메틱 수 문제가 P-문제임을 보였다.

• 경영과학
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• 제24권2호
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• pp.33-42
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• 2007

In this paper we consider an alternate m machine scheduling problem in which each job having at most two eligible machines should be assigned with the objective of makespan minimization. For this problem. we propose a $O(m2^m)$ time rounding algorithm with performance ratio at most 1.5. For a little general problem where each job can be processed in at most three machines, we prove that a polynomial time algorithm does not exist with performance ratio less than 1.5.