scholarly journals A Branch-and-bound algorithm for concave minimization problem with upper bounded variables

2018 ◽  
Vol 7 (2.12) ◽  
pp. 333
Author(s):  
Se Ho Oh
Keyword(s):  
Branch And Bound ◽  
Branching Process ◽  
Optimal Solution ◽  
Concave Minimization ◽  
Branch And Bound Algorithm ◽  
Local Optimum ◽  
Minimization Problems ◽  
Minimal Points ◽  
Bounded Variables ◽  
Concave Minimization Problem

This paper presents a branch-and-bound algorithm for solving the concave minimization problems with upper bounded variables. The algorithm uses simplex to construct the branching and the bounding procedure. The linear convex envelope (the objective function of the subproblem) is uniquely determined on the candidate simplex which contains the subset of the local minimal points. The optimal solution of the subproblem is a local optimum of the original concave problem and used in reducing the list of active subproblems. The branching process splits the candidate simplex into two subsimplices by fixing the selected branching variable at value 0 or upper bound. Then the subsimplices are one less dimensional than the candidate. It means that the size of the subproblems gradually decreases. Further research needs to be focused on the efficient determination method of the simplex. The algorithm of this paper can be applied to solving the concave minimization problems under knapsack type constraints. 

scholarly journals EMI-aware central processing point deployment in wireless networks for e-healthcare services.

2021 ◽  
Author(s):  
Nick Majedi
Keyword(s):  
Branch And Bound ◽  
Medical Devices ◽  
Attenuation Factor ◽  
Optimal Solution ◽  
Healthcare Services ◽  
Branch And Bound Algorithm ◽  
Mixed Integer ◽  
Central Processing ◽  
Numerical Result ◽  
Wireless Users

In this thesis, we introduce an approach to jointly minimizing energy consumption of wireless transmitters and the harmful interference on sensitive medical devices, and optimizing the central controller placement for collecting data from transmitters. More specifically, a multi-objective non-convex mixed-integer non-linear programming (MINLP) problem is defined and formulated to optimize transmit power of wireless users and CPP deployment along with guaranteeing minimized EMI to comply with the immunity level of medical devices. To solve this problem, an important step is to convexify it. Then we propose the use of a standard branch-and-bound algorithm. Also the program is coded in MATLAB with the help of OPTItoolbox to find the optimal solution. To conduct a numerical result analysis, we considered different cases within a single floor of a hospital and a few scenarios for a two-story hospital building. The values of different variables are changed throughout the simulation and the results are compared. These variables include immunity level of sensitive medical devices, maximum transmission power of wireless users, floor attenuation factor, etc. Our results show the improvement in throughput and guaranteed immunity for medical devices, when the proposed formulation is deployed along with a branch-and-bound algorithm.

A Branch-and-Bound Algorithm for Two-Agent Scheduling with Learning Effect and Late Work Criterion

2018 ◽  
Vol 35 (05) ◽  
pp. 1850037 ◽  
Author(s):  
Shang-Chia Liu ◽  
Jiahui Duan ◽  
Win-Chin Lin ◽  
Wen-Hsiang Wu ◽  
Jan-Yee Kung ◽  
...  
Keyword(s):  
Branch And Bound ◽  
Learning Effect ◽  
Optimal Schedule ◽  
Optimal Solution ◽  
Single Machine Scheduling ◽  
Branch And Bound Algorithm ◽  
Scheduling Problem ◽  
Late Work ◽  
Processing Times ◽  
Agent Scheduling

This paper studies a two-agent single-machine scheduling problem with sum-of-processing-times-based learning consideration. The goal is to find an optimal schedule to minimize the total late work of the first agent subject to the restriction that the maximum lateness of the second agent has an upper bound. For this problem, a branch-and-bound algorithm along with several dominances and a lower bound is developed to find the optimal solution, and a tabu algorithm with several improvements is proposed to find the near-optimal solution. Computational experiments are provided to further measure the performance of the proposed algorithms.

scholarly journals Note on a Single-Machine Scheduling Problem with Sum of Processing Times Based Learning and Ready Times

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Shang-Chia Liu ◽  
Wei-Ling Hung ◽  
Chin-Chia Wu
Keyword(s):  
Branch And Bound ◽  
Heuristic Algorithm ◽  
Single Machine ◽  
Learning Effect ◽  
Optimal Solution ◽  
Single Machine Scheduling ◽  
Branch And Bound Algorithm ◽  
Release Time ◽  
Average Error ◽  
Processing Times

In the recent 20 years, scheduling with learning effect has received considerable attention. However, considering the learning effect along with release time is limited. In light of these observations, in this paper, we investigate a single-machine problem with sum of processing times based learning and ready times where the objective is to minimize the makespan. For solving this problem, we build a branch-and-bound algorithm and a heuristic algorithm for the optimal solution and near-optimal solution, respectively. The computational experiments indicate that the branch-and-bound algorithm can perform well the problem instances up to 24 jobs in terms of CPU time and node numbers, and the average error percentage of the proposed heuristic algorithm is less than 0.5%.

scholarly journals An Effective Branch and Bound Algorithm for Minimax Linear Fractional Programming

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hong-Wei Jiao ◽  
Feng-Hui Wang ◽  
Yong-Qiang Chen
Keyword(s):  
Branch And Bound ◽  
Fractional Programming ◽  
Optimal Solution ◽  
Branch And Bound Algorithm ◽  
Linear Relaxation ◽  
Feasible Region ◽  
Test Problems ◽  
Linear Fractional Programming ◽  
Successive Refinement ◽  
Global Optimal

An effective branch and bound algorithm is proposed for globally solving minimax linear fractional programming problem (MLFP). In this algorithm, the lower bounds are computed during the branch and bound search by solving a sequence of linear relaxation programming problems (LRP) of the problem (MLFP), which can be derived by using a new linear relaxation bounding technique, and which can be effectively solved by the simplex method. The proposed branch and bound algorithm is convergent to the global optimal solution of the problem (MLFP) through the successive refinement of the feasible region and solutions of a series of the LRP. Numerical results for several test problems are reported to show the feasibility and effectiveness of the proposed algorithm.

scholarly journals Energy-Efficient User Association Strategy for Hyperdense Heterogeneous Networking in the Fifth Generation Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Lei Li ◽  
Hao Jin ◽  
Zhipeng Yan ◽  
Changqing Yang ◽  
Yong Wu
Keyword(s):  
Cellular Networks ◽  
Original Problem ◽  
Optimal Solution ◽  
Concave Minimization ◽  
High Rate ◽  
User Association ◽  
Improve Energy Efficiency ◽  
Fifth Generation ◽  
First Case ◽  
Concave Minimization Problem

Redesigning user association strategies to improve energy efficiency (EE) has been viewed as one of the promising shifting paradigms for the fifth generation (5G) cellular networks. In this paper, we investigate how to optimize users’ association to enhance EE for hyper dense heterogeneous networking in the 5G cellular networks, where the low-power node (LPN) much outnumbers the high-power node (HPN). To characterize that densely deployed LPNs would undertake a majority of high-rate services, while HPNs mainly support coverage; the EE metric is defined as average weighted EE of access nodes with the unit of bit per joule. Then, the EE optimization objective function is formulated and proved to be nonconvex. Two mathematical transformation techniques are presented to solve the nonconvex problem. In the first case, the original problem is reformulated as an equivalent problem involving the maximization of a biconcave function. In the second case, it is equivalent to a concave minimization problem. We focus on the solution of the biconcave framework, and, by exploiting the biconcave structure, a novel iterative algorithm based on dual theory is proposed, where a partially optimal solution can be achieved. Simulation results have verified the effectiveness of the proposed algorithm.

scholarly journals Linear programs with an additional separable concave constraint

2004 ◽  
Vol 8 (3) ◽  
pp. 155-174 ◽  
Author(s):  
Takahito Kuno ◽  
Jianming Shi
Keyword(s):  
Local Search ◽  
Branch And Bound ◽  
Special Class ◽  
Concave Function ◽  
Concave Minimization ◽  
Simplex Algorithm ◽  
Direct Application ◽  
Special Structure ◽  
Branch And Bound Algorithm ◽  
Linear Programs

In this paper, we develop two algorithms for globally optimizing a special class of linear programs with an additional concave constraint. We assume that the concave constraint is defined by a separable concave function. Exploiting this special structure, we apply Falk-Soland's branch-and-bound algorithm for concave minimization in both direct and indirect manners. In the direct application, we solve the problem alternating local search and branch-and-bound. In the indirect application, we carry out the bounding operation using a parametric right-hand-side simplex algorithm.

scholarly journals Performance Analysis of DSR in MANET using Optimized Branch and Bound Algorithm

2019 ◽  
Vol 8 (4) ◽  
pp. 4249-4255
Keyword(s):  
Branch And Bound ◽  
Network Lifetime ◽  
Performance Metrics ◽  
Optimal Solution ◽  
Branch And Bound Algorithm ◽  
Delivery Ratio ◽  
Well Performance ◽  
Network Nodes ◽  
Mobile Adhoc Network ◽  
Dynamic Source

Mobile Adhoc NETwork (MANET) is a compilation of autonomous and arbitrarily located movable nodes forms an shemaless network. Nodes in MANET are dynamically changing in nature. MANET has different kinds of routing protocols. In this work MANET’s reactive Dynamic Source Routing (DSR) protocol is developed with the Branch and Bound (BB) algorithm to obtain a possible feasible elucidation with greater optimality. Branch and Bound Algorithm is mainly applicable for obtaining the optimal solution. In this paper, DSR protocol is evaluated with the proposed approaches namely, DSR with BB in MANET and DSR with Modified Branch and Bound (DSRMBB) is analyzed. Simulation metrics namely End to End delay, Packet Delivery Ratio (PDR), Routing Overhead, Throughput, Network Lifetime and Nodes energy were compared to evaluate their performances. From the observation, proposed work DSRMBB performs well. Performance metrics like Network lifetime, Nodes Energy and throughput has increased in considerable amount when comparedto the traditional DSR protocol.

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