• Journal of Korean Institute of Industrial Engineers
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• v.37 no.2
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• pp.124-131
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• 2011

In this research report, we propose a heuristic algorithm with some primal recovery strategies for capacitated facility location problems (CFLP), which is a well-known combinatorial optimization problem with applications in distribution, transportation and production planning. Many algorithms employ the branch-and-bound technique in order to solve the CFLP. There are also some different approaches which can recover primal solutions while exploiting the primal and dual structure simultaneously. One of them is a MVCD (Mean Value Cross Decomposition) ensuring convergence without solving a master problem. The MVCD was designed to handle LP-problems, but it was applied in mixed integer problems. However the MVCD has been applied to only uncapacitated facility location problems (UFLP), because it was very difficult to obtain "Integrality" property of Lagrangian dual subproblems sustaining the feasibility to primal problems. We present some heuristic strategies to recover primal feasible integer solutions, handling the accumulated primal solutions of the dual subproblem, which are used as input to the primal subproblem in the mean value cross decomposition technique, without requiring solutions to a master problem. Computational results for a set of various problem instances are reported.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.8
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• pp.67-75
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• 2013

The advantages of the orthogonal frequency division multiplexing (OFDM) are high spectral efficiency, resiliency to RF interference, and lower multi-path distortion. To further utilize vast channel capacity of the multiuser OFDM, one has to find the efficient adaptive subchannel and bit allocation among users. In this paper, we compare the performance of the linear programming dual of the 0-1 integer programming formulation with the existing convex optimization approach for the optimal subchannel and bit allocation problem of the multiuser OFDM. Utilizing tight lower bound provided by the LP dual formulation, we develop a primal heurisitc algorithm based on the LP dual solution. The performance of the primal heuristic is compared with MAO, ESA heuristic solutions, and integer programming solution on MATLAB simulation on a system employing M-ary quadrature amplitude modulation (MQAM) assuming a frequency-selective channel consisting of three independent Rayleigh multi-paths.

• Journal of Korean Institute of Industrial Engineers
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• v.29 no.3
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• pp.206-212
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• 2003

In this paper, we propose a mathematical optimization model with a suitable algorithm to determine delivery and backlogging quantities by minimizing the total cost including the penalty costs for delay. The system has fixed transshipment costs and demands are fulfilled by some delivery units that represent the volume of delivery amount to be shipped in a single time period. Since, backlogging is allowed, demands could be delivered later at the expense of some penalty costs. The model provides the optimal decisions on when and how much to he delivered while minimizing the total costs. To solve the problem, we propose an algorithm that uses the Lagrangian dual in conjunction with some primal heuristic techniques that exploit the special structure of the problem. Finally, we present some computational test results along with comments on the further study.

• The Journal of Information Technology
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• v.3 no.2
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• pp.73-85
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• 2000

The efficient algorithms are suggested in this study for solving the multicommodity network flow problems applied to Communications Systems. These problems are typical NP-complete optimization problems that require integer solution and in which the computational complexity increases numerically in appropriate with the problem size. Although the suggested algorithms are not absolutely optimal, they are developed for computationally efficient and produce near-optimal and primal integral solutions. We supplement the traditional Lagrangian method with a price-directive decomposition. It proceeded as follows. First, A primal heuristic from which good initial feasible solutions can be obtained is developed. Second, the dual is initialized using marginal values from the primal heuristic. Generally, the Lagrangian optimization is conducted from a naive dual solution which is set as ${\lambda}=0$. The dual optimization converged very slowly because these values have sort of gaps from the optimum. Better dual solutions improve the primal solution, and better primal bounds improve the step size used by the dual optimization. Third, a limitation that the Lagrangian decomposition approach has Is dealt with. Because this method is dual based, the solution need not converge to the optimal solution in the multicommodity network problem. So as to adjust relaxed solution to a feasible one, we made efficient re-allocation heuristic. In addition, the computational performances of various versions of the developed algorithms are compared and evaluated. First, commercial LP software, LINGO 4.0 extended version for LINDO system is utilized for the purpose of implementation that is robust and efficient. Tested problem sets are generated randomly Numerical results on randomly generated examples demonstrate that our algorithm is near-optimal (< 2% from the optimum) and has a quite computational efficiency.

• Journal of the Korean Operations Research and Management Science Society
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• v.25 no.1
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• pp.27-36
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• 2000

We perform a computational complexity analysis of a heuristic algotithm proposed in the literature for the combinatorial optimization problems extended with a single side-constraint. This algorithm, although such a view was not given in the original work, is a disguised version of an optimal Lagrangian dual solution technique. It also has been observed to be a very efficient heuristic producing near-optimal solutions for the primal problems in some experiments. Especially, the number of iterations grows sublinearly in terms of the network node size so that the heuristic seems to be particularly suitable for the applicatons such as routing with semi-real time requirements. The goal of this paper is to establish a polynomal worst-case complexity of the algorithm. In particular, the obtained complexity bound suports the sublinear growth of the required iterations.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.530-533
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• 1996

This paper deals with finding an initial solution and modifying search direction by the centrering force in the predictor-corrector method which is a variant of the primal-dual barrier method. These methods were tested with NETLIB problems. Initial solutions which are located close to the center of the feasible set lower the number of iterations, as they enlarge the step length. Three heuristic methods to find such initial solution are suggested. The new methods reduce the average number of iterations by 52% to at most, compared with the old method assigning 1 to initial valurs. Solutions can move closer to the central path fast by enlarging the centering force in early steps. It enlarge the step length, so reduces the number of iterations. The more effective this method is the closer the initial solution is to the boundary of the feasible set.

• Korean Management Science Review
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• v.11 no.3
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• pp.13-26
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• 1994

In this paper we studied an integration scheme of some simplex algorithms and some efficient techniques to get the stable solution in linear programming code. And we developed a linear programming package (LPAK) by introducing this scheme and techniques. In LPAK three different algorithms were integrated, which were two primal simplex algorithms using Two phase method and big-M method respectively, and the dual simplex algorithm. LPAK introduces several heuristic techniques in each step of simplex method in order to enhance the stability and efficiency. They were new heuristic methods in structuring initial basis, choosing entering variable, choosing dropping variable and performing reinversion. The experimental results on the NETLIB problems showed that LPAK provided the stable solutions.

• Journal of the Korean Operations Research and Management Science Society
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• v.13 no.2
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• pp.9-17
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• 1988

This vehicle scheduling problem with multiple depots and multiple vehicle types (VMM) is to determine the optimal vehicle routes to minimize the total travel costs. The object of this paper is to develope an exact algorithm for the VMM. In this paper the VMM is transformed into a mathematical model of the vehicle problem with multiple depots. Then an efficient branch and bound algorithm is developed to obtain an exact solution for this model. In order to enhance the efficiency, this algorithm emphasizes the follows; First, a heuristic algorithm is developed to get a good initial upper bound. Second, an primal-dual approach is used to solve subproblems which are called the quasi-assignment problem, formed by branching strategy is presented to reduce the number of the candidate subproblems.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.1
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• pp.16-26
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• 1989

The terminal layout problem is fundamental in may centralized computer networks, which is generated formulated as the capaciated minimum spanning tree problem (CMSTP). We present an implementation of the dual-based procedure to solve the CMSTP. Dual ascent procedure generates a good feasible solutions to the dual of the linear programming relaxation of CMSTP. A feasible primal solution to CMSTP can then be constructed based on this dual solution. This procedure can be used either as a stand-alone heuristic or, else, it can be incorporated into a branch and bound algorithm. A numerical result is given with quite favorable results.

• Journal of Communications and Networks
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• v.13 no.6
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• pp.633-638
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• 2011

In this paper, we consider resource allocation with proportional fairness in the downlink orthogonal frequency division multiple access relay networks, in which relay nodes operate in decode-and-forward mode. A joint optimization problem is formulated for relay selection, subcarrier assignment and power allocation. Since the formulated primal problem is nondeterministic polynomial time-complete, we make continuous relaxation and solve the dual problem by Lagrangian dual decomposition method. A near-optimal solution is obtained using Karush-Kuhn-Tucker conditions. Simulation results show that the proposed algorithm provides superior system throughput and much better fairness among users comparing with a heuristic algorithm.