• Journal of the Korea Society of Computer and Information
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• v.20 no.9
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• pp.21-29
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• 2015

The set partitioning problem is a well-known NP-hard combinatorial optimization problem, and it is formulated as an integer programming model. This paper proposes an Integer Programming-based Local Search for solving the set partitioning problem. The key point is to solve the set partitioning problem as the set covering problem. First, an initial solution is generated by a simple heuristic for the set covering problem, and then the solution is set as the current solution. Next, the following process is repeated. The original set covering problem is reduced based on the current solution, and the reduced problem is solved by Integer Programming which includes a specific element in the objective function to derive the solution for the set partitioning problem. Experimental results on a set of OR-Library instances show that the proposed algorithm outperforms pure integer programming as well as the existing heuristic algorithms both in solution quality and time.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.1
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• pp.29-35
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• 2016

In this paper, we consider a convex optimization problem with a convex integrable objective function and a geometric constraint set. We characterize the solution set of the problem when we know its one solution.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.65-70
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• 2021

We characterize the solution set for a second-order cone linear fractional optimization problem (P). We present sequential Lagrange multiplier characterizations of the solution set for the problem (P) in terms of sequential Lagrange multipliers of a known solution of (P).

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.2
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• pp.129-138
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• 2003

The traveling salesman problem (TSP) is an NP-hard problem. As the number of nodes increases, it takes a lot of time to find an optimal solution. Instead of considering all arcs, if we select and consider only some arcs more likely to be included in an optimal solution, we can find efficiently an optimal solution. Arc candidate set is a group of some good arcs. For the Lack of study in the asymmetric TSP. it needs to research arc candidate set for the asymmetric TSP systematically. In this paper, we suggest a regression function determining arc candidate set for the asymmetric TSP. We established the function based on 2100 experiments, and we proved the goodness of fit for the model through various 787problems. The result showed that the optimal solutions obtained from our arc candidate set are equal to the ones of original problems. We expect that this function would be very useful to reduce the complexity of TSP.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.375-381
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• 2008

Boundedness for the set of all the $\epsilon$-approximate solutions for convex optimization problems are considered. We give necessary and sufficient conditions for the sets of all the $\epsilon$-approximate solutions of a convex optimization problem involving finitely many convex functions and a convex semidefinite problem involving a linear matrix inequality to be bounded. Furthermore, we give examples illustrating our results for the boundedness.

• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.288-294
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• 2008

Motivated by the fact that upper solution bounds for the continuous Lyapunov equation are valid under some very restrictive conditions, an attempt is made to extend the set of Hurwitz matrices for which such bounds are applicable. It is shown that the matrix set for which solution bounds are available is only a subset of another stable matrices set. This helps to loosen the validity restriction. The new bounds are illustrated by examples.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.1
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• pp.147-158
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• 1995

In this paper a face optimization algorithm is developed for solving the problem (P) of optimizing a linear function over the set of efficient solution of a bicriterion linear program. We show that problem (P) can arise in a variety of practical situations. Since the efficient set is in general a nonoconvex set, problem (P) can be classified as a global optimization problem. The algorithm for solving problem (P) is guaranteed to find an exact optimal or almost exact optimal solution for the problem in a finite number of iterations. The algorithm can be easily implemented using only linear programming method.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.181-191
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• 2006

In this paper, multiobjective generalized fractional programming problems with set functions are considered, in which objective functions are maximum of finite fractional set functions. At first, optimality conditions are established. Then, saddle existence theorem is proved.

• Management Science and Financial Engineering
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• v.18 no.2
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• pp.13-17
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• 2012

Set covering has widely been accepted as a staple tool for feature selection in data mining. We present a generalized version of this classical combinatorial optimization model to make it better suited for the purpose and propose a surrogate relaxation-based procedure for its meta-heuristic solution. Mathematically and also numerically with experiments on 25 set covering instances, we demonstrate the utility of the proposed model and the proposed solution method.

• Journal of Distribution Science
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• v.15 no.2
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• pp.15-20
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• 2017

Purpose - This paper aims to suggest a delivery constrained internet shopping optimization problem (DISOP) which must be solved for online recommendation system to provide a customized service considering cost and delivery conditions at the same time. Research design, data, and methodology - To solve a (DISOP), we propose a multi-objective formulation and a solution approach. By using a commercial optimization software (LINDO), a (DISOP) can be solved iteratively and a pareto optimal set can be calculated for real-sized problem. Results - We propose a new research problem which is different with internet shopping optimization problem since our problem considers not only the purchasing cost but also delivery conditions at the same time. Furthermore, we suggest a multi-objective mathematical formulation for our research problem and provide a solution approach to get a pareto optimal set by using numerical example. Conclusions - This paper proposes a multi-objective optimization problem to solve internet shopping optimization problem with delivery constraint and a solution approach to get a pareto optimal set. The results of research will contribute to develop a customized comparison and recommendation system to help more easy and smart online shopping service.