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

• Journal of the Korean Operations Research and Management Science Society
• /
• v.22 no.3
• /
• pp.11-22
• /
• 1997

The aim of this paper is to develop the B & B type algorithms for globally minimizing concave function under 0-1 knapsack constraint. The linear convex envelope underestimating the concave object function is introduced for the bounding operations which locate the vertices of the solution set. And the simplex containing the solution set is sequentially partitioned into the subsimplices over which the convex envelopes are calculated in the candidate problems. The adoption of cutting plane method enhances the efficiency of the algorithm. These mean valid inequalities with respect to the integer solution which eliminate the nonintegral points before the bounding operation. The implementations are effectively concretized in connection with the branching stategys.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.28 no.4
• /
• pp.191-198
• /
• 2003

The generalized knapsack problem or gknap is the combinatorial optimization problem of optimizing a nonnegative linear function over the integral hull of the intersection of a polynomially separable 0-1 polytope and a knapsack constraint. The knapsack, the restricted shortest path, and the constrained spanning tree problem are a partial list of gknap. More interesting1y, all the problem that are known to have a fully polynomial approximation scheme, or FPTAS are gknap. We establish some necessary and sufficient conditions for a gknap to admit an FPTAS. To do so, we recapture the standard scaling and approximate binary search techniques in the framework of gknap. This also enables us to find a weaker sufficient condition than the strong NP-hardness that a gknap does not have an FPTAS. Finally, we apply the conditions to explore the fully polynomial approximability of the constrained spanning problem whose fully polynomial approximability is still open.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.15 no.2
• /
• pp.33-44
• /
• 1990

An efficient algorithm is developed for the linear programming relaxation of generalized multiple choice knaspack problem. The generalized multiple choice knaspack problem is an extension of the multiple choice knaspack problem whose relaxed LP problem has been studied extensively. In the worst case, the computational coimplexity of the proposed algorithm is of order 0(n. $n_{max}$)$^{2}$), where n is the total number of variables and $n_{max}$ denotes the cardinality of the largest multiple choice set. The algorithm can be easily embedded in a branch-and-bound procedure for the generalized multiple choice knapsack problem. A numerical example is presented and computational aspects are discussed.sed.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.40 no.12
• /
• pp.2372-2380
• /
• 2015

In this paper, we propose frequency allocation and path selection scheme in underlay cognitive radio (CR) networks using network coding. In the proposed scheme, we choose the path with consideration of network coding and interference temperature in underlay CR networks and propose an optimization problem to maximize the system throughput of secondary users (SUs). Then, we represent the proposed optimization problem as the multi-dimensional multiple-choice knapsack problem and give the theoretical upper bound for the system throughput of SUs by using linear programming. Finally, we compute the system throughput of SUs by using brute-force search (BFS) and link quality first (LQF) scheme in underlay CR networks. Simulation results show that the system throughput of SUs with BFS is higher than that with LQF in underlay CR networks with and without application of network coding, respectively.

• Journal of the Korea Convergence Society
• /
• v.7 no.5
• /
• pp.213-219
• /
• 2016

This paper presents a branch-and-bound algorithm for solving the concave minimization problem with upper bounded variables whose single constraint is linear. The algorithm uses simplex as partition element. Because the convex envelope which most tightly underestimates the concave function on the simplex is uniquely determined by solving the related linear equations. Every branching process generates two subsimplices one lower dimensional than the candidate simplex by adding 0 and upper bound constraints. Subsequently the feasible points are partitioned into two sets. During the bounding process, the linear programming problems defined over subsimplices are minimized to calculate the lower bound and to update the incumbent. Consequently the simplices which do certainly not contain the global minimum are excluded from consideration. The major advantage of the algorithm is that the subproblems are defined on the one less dimensinal space. It means that the amount of work required for the subproblem decreases whenever the branching occurs. Our approach can be applied to solving the concave minimization problems under knapsack type constraints.

• Journal of Korean Institute of Industrial Engineers
• /
• v.19 no.2
• /
• pp.3-13
• /
• 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 the Korea Institute of Information and Communication Engineering
• /
• v.17 no.11
• /
• pp.2661-2667
• /
• 2013

Recently, at Home and abroad, Internet of Things era things(Thing) is participating as a subject of communication in human communication paradigm of existing (lot/M2M) is in full swing. Automobile, refrigerator, bicycle, until shoes, and communication functions generation of information is installed and has created a fusion of new service IT infrastructure. Its use and application are broadening to various areas and the number of devices used for it is increasing to increase the number of information transmitted for each object. When the traffic reaches its limit while each set of data is transmitted from the devices divided into each group through the mobile network, M2M communications service might not be processed smoothly. This study used the Knapsack Problem algorithm to create a virtual simulator for a smooth M2M service when the mobile network used for the M2M communications reaches its limit. The virtual simulator applies smooth processing of services from the M2M communications that should be processed first to other subsequent services when data comes to each group of devices. As the M2M technology develops to make many objects more compact in size, it would help with smoother processing of M2M services for the mobile network with fast-increasing traffic.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.40 no.1
• /
• pp.61-69
• /
• 2015

Through Virtual Machine technology(VM), VMs can be packed into much fewer number of physical servers than that of VMs. Since even an idle physical server wastes more than 60% of max power consumption, it has been considered as one of energy saving technologies to minimize the number of physical servers by using the knapsack problem solution based on the computing resources. However, this paper shows that this tightly packed consolidation may not achieve the efficient energy saving. Instead, a service pattern-based VM consolidation algorithm is proposed. The proposed algorithm takes the service time of each VM into account, and consolidates VMs to physical servers in the way to minimize energy consumption. The comprehensive simulation results show that the proposed algorithm gains more than 30% power saving.

• Journal of the Korea Society for Simulation
• /
• v.26 no.3
• /
• pp.105-113
• /
• 2017

This study considers an optimal investment planning for improving survivability from an air threat in the layered air defense system. To establish an optimization model, we first represent the layered air defense system as a network model, and then, present two optimization models minimizing the failure probability of counteracting an air threat subject to budget limitation, in which one deals with whether to invest and the other enables continuous investment on the subset of nodes. Nonlinear objective functions are linearized using log function, and we suggest dynamic programming algorithm and linear programing for solving the proposed models. After designing a layered air defense system based on a virtual scenario, we solve the two optimization problems and analyze the corresponding optimal solutions. This provides necessity and an approach for an effective investment planning of the layered air defense system.