New Randomized Response Procedure for Finding Optimal Solution Using Branch and Bound Method

AbstractIn this paper we study the question of parallelization of a variant of Branch-and-Bound method for solving of the subset sum problem which is a special case of the Boolean knapsack problem. The following natural approach to the solution of this question is considered. At the first stage one of the processors (control processor) performs some number of algorithm steps of solving a given problem with generating some number of subproblems of the problem. In the second stage the generated subproblems are sent to other processors for solving (one subproblem per processor). Processors solve completely the received subproblems and return their solutions to the control processor which chooses the optimal solution of the initial problem from these solutions. For this approach we define formally a model of parallel computing (frontal parallelization scheme) and the notion of complexity of the frontal scheme. We study the asymptotic behavior of the complexity of the frontal scheme for two special cases of the subset sum problem.

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Linear Integer Optimization Model for Two-Stage Guillotine Cutting Stock Problem Using Branch and Bound Method in the Garment Industry

International Journal of Global Operations Research ◽

10.47194/ijgor.v1i1.17 ◽

2020 ◽

Vol 1 (1) ◽

pp. 40-52

Author(s):

Eman Lesmana ◽

Julita Nahar ◽

Annisa D. P

Keyword(s):

Branch And Bound ◽

Optimal Solution ◽

Garment Industry ◽

Cutting Stock Problem ◽

Cutting Stock ◽

Branch And Bound Method ◽

Integer Optimization ◽

Two Stage ◽

Stock Cutting ◽

Guillotine Cutting

This paper discusses the Two-Stage Guillotine Cutting Stock Problem (2GCSP) in the garment industry, namely how to determine the two-stage guillotine pattern that is used to cut fabric stocks into several certain size t-shirt materials that are produced based on the demand for each size of the shirt. 2GCSP is modeled in the form of Linear Integer Optimization and finding solutions using the Branch and Bound method. In this paper also presented a Graphical User Interface with Maple software as an interactive tool to find the best fabric stock cutting patterns. The results show that the optimal solution can be determined by solving numerically using the Branch and Bound method and Maple optimization packages. The solution is shown with an illustration of the pattern and the amount of fabric cut based on the pattern.

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MODEL VEHICLE ROUTING PROBLEM DALAM MENGOPTIMUMKAN RUTE PENGANGKUTAN SAMPAH DI KOTA BOGOR

Jurnal Matematika Statistika dan Komputasi ◽

10.20956/jmsk.v16i2.7023 ◽

2019 ◽

Vol 16 (2) ◽

pp. 241

Author(s):

Maya Widyastiti ◽

Isti Kamila

Keyword(s):

Vehicle Routing ◽

Branch And Bound ◽

Vehicle Routing Problem ◽

Minimum Distance ◽

Optimal Solution ◽

Landfill Site ◽

Branch And Bound Method ◽

Routing Problem ◽

Problem Model ◽

Environmental Agency

Garbage is a common problem that often occurs in many cities, including in Bogor. Every day, the volume of garbage in Bogor reaches 600 tons and only 475 tons can be transported to the Galuga Landfill Site. However, the vehicle which is owned by the Environmental Agency of Bogor is limited and has certain capacity.In this study, we formulated garbage transportation in the form of a Vehicle Routing Problem model with Branch and Bound method and completed using LINGO 11.0. The optimal solution obtained is a garbage transport route with a minimum distance, and obtained a distance is 1583.24 km, with West Bogor is 172.6 km, Central Bogor is 344.99 km, East Bogor is 298.79 km, North Bogor is 267.4 km, South Bogor is 252.41 km and Tanah Sareal is 247.05 km. Of the six sub-districts, there was a decrease in the distance of garbage transportation from Temporary Disposal sites to the Galuga Landfill. Keywords: Garbage transportation, Optimization, Vehicle Routing Problem.

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Optimized Load Distributed of Power Plant Units Based on Branch and Bound Method

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.239-240.1565 ◽

2012 ◽

Vol 239-240 ◽

pp. 1565-1569

Author(s):

Li Xiao Zhang ◽

Wen Tan ◽

Xiao Bin Huang

Keyword(s):

Branch And Bound ◽

Load Distribution ◽

Power Plants ◽

Thermal Power ◽

Computational Simulation ◽

Optimal Solution ◽

Branch And Bound Method ◽

Unit Load ◽

Coal Consumption ◽

Optimal Load

Power consumption is increasing significantly with the rapid economic development. In order to improve the competitiveness of thermal power plants, the problem of units' optimal load dispatch becomes a hot topic of the research about reducing coal consumption. The branch and bound method is presented to solve the problem based on a load dispatch model with velocity constraint in this paper. Branch can create the conditions for the optimal solution of unit load distribution, bound can improve the search efficiency of the optimal solution [1]. Through the computational Simulation, it proves the method described in the paper has the higher convergence speed and can be better applied to the problem of units' optimal load dispatch.

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