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Analysis of the performance growth of the optimization solvers
Škvarková, Alexandra ; Jablonský, Josef (advisor) ; Fábry, Jan (referee)
It would not be possible to solve real optimization problems, which usually contain a huge number of variables and constraints, without high-performance optimization systems. Today's software market offers a vast number of different systems available to provide solutions to linear and non-linear optimization tasks, including integer conditions. One such optimization system is called Gurobi. It is available in several versions. This thesis is focused on the performance comparison of three solver versions (i.e. 7.0.2, 6.0.5 and 5.0.2) using tasks that are in the MPS format, they are obtained from the MIPLIB 2010 electronic library, namely from the Benchmark section. The results are compared according to the time period needed to solve the task for each investigated version.
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Vertex coloring algorithms in scheduling problems under uncertainty
Hájek, Štěpán ; Branda, Martin (advisor) ; Lavička, Karel (referee)
This thesis concerns solutions to problems that arise in optimizing fixed interval scheduling under situations of uncertainty such as when there are random delays in job process times. These problems can be solved by using a vertex coloring with random edges and problems can be formulated using integer linear, quadratic and stochastic programming. In this thesis is propo- sed a new integer linear formulation. Under certain conditions there is proved its equivalence with stochastic formulation, where is maximized the schedule reliability. Moreover, we modified the proposed formulation to obtain bet- ter corresponding to real life situations. In a numerical study we compared computational time of individual formulations. It turns out that the propo- sed formulation is able to solve scheduling problems considerably faster than other formulations. 1
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Particular Problems Related to the Vehicle Routing Problem
Kuklis, Imrich ; Pergel, Martin (advisor) ; Majerech, Vladan (referee)
Title: Particular Problems Related to the Vehicle Routing problem Author: Imrich Kuklis Department: Department of Software and Computer Science Education Supervisor: RNDr. Martin Pergel, Ph.D., Department of Software and Computer Science Education Abstract: In this thesis we present and implement some scheduling algorithms. In the first part we discuss the vehicle routing problem and its variants. In the second part we describe the algorihms we used in the thesis. In the third part we compare the algorithm by their results on several tests. In the last chapter we describe the documentation of the programs which we implemented and discuss the possible future extension of the thesis. Powered by TCPDF (www.tcpdf.org)
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Vehicle Routing Problem
Kafka, Ondřej ; Branda, Martin (advisor) ; Hanzák, Tomáš (referee)
The thesis deals with optimization problems which arise at distribution planning. These problems can often be easily formulated as integer programming problems, but rarely can be solved using mixed integer programming techniques. Therefore, it is necessary to study the efficiency of heuristic algorithms. The main focus of the thesis is on the vehicle routing problem with time windows. A tabu search algorithm for this problem was developed and implemented. It uses integer programming to solve the set partitioning problem in order to find optimal distribution of all customers into feasible routes found during the search. The results of the classical integer programming approach, basic insertion heuristic and presented tabu search algorithm are compared in a numerical study.
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Management of production populations of forest tree species utilizing methods of mathematical programing
Hořejší, Matouš ; Lstibůrek, Milan (advisor) ; Stejskal, Jan (referee)
Breeding of forest tree species is a great opportunity for the entire forestry sector to succeed in the present modern World. Genetically improved forest trees have much better growing quality and they can sustain higher stress and unfavorable climatic conditions.
Efficient algorithms are necessary for optimizing and establishing seed orchards. These should optimally select clones as parents in future seed orchards. In the present thesis, we developed model, based on mathematical programming methods, which creates mix of clones with the maximum breeding value and constraints on genetic diversity.
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The spatial final cut optimisation
Kašpar, Jan ; Marušák, Róbert (advisor) ; Lstibůrek, Milan (referee)
For more than 150 years, timber indicators have been used for forest harvest scheduling in the region of current Czech Republic. With social changes and increased importance of forest yields and functions, there has been significant changes in forest management during this time. The changes in ownership structure after 1989 are most problematic from a sustainability standpoint. Also, the timber indicators cannot consider forest age structure, which is not ideal because even small changes related to abiotic and biotic disturbances may inhibit forest planning efforts. These changes to forest ownership and structure combined with current timber indicators make it difficult to ensure sustainable harvest levels over long time horizons. Methods of operations research, such as mathematical programming and heuristic methods, provide alternatives to historical harvest scheduling methods because they can account for forest age structure and spatial relationships over long scheduling horizons.
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Integer Optimization for Transportation Problems
Cabalka, Matouš ; Žák, Libor (referee) ; Popela, Pavel (advisor)
The thesis deals with optimization models in transportation problems with emphasis on traveling salesman problem. Brief introduction to the history is followed by theoretical part describing linear programming, integer programming and formulation of traveling salesman problem. Description of data preprocessing is included. Finally computational results are discussed and evaluated.
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Transformations of optimization models with aplications
Rychtář, Adam ; Bednář, Josef (referee) ; Popela, Pavel (advisor)
The thesis deals with recent problems of waste management in the Czech Republic. In connection with the existing software implementation, the author focuses on the gradual development of advanced mathematical programming models, which generalize existing approaches. The author applies acquired knowledge in the areas of network flows, linear, integer, and stochastic programming. The important role is played by modifications and transformations of the discussed models. They are further used to obtain the experimental results for real-world input data by implementation in GAMS.
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Models and methods for routing problems
Nevrlý, Vlastimír ; Žák, Libor (referee) ; Popela, Pavel (advisor)
This master's thesis deals with mathematical model building for routing problems and ways to solve them. There are discussed and implemented deterministic and heuristic approaches that are suitable to be utilized. A big effort is put into building of the mathematical model describing a real world problem from the field of waste management. Appropriate algorithms are developed and modified to solve a particular problem effectively. An original graphical environment is created to illustrate acquired results and perform testing computations.
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Planning cash delivery to exchange offices using Vehicle Routing Problem with Time Series
Mouchová, Denisa ; Skočdopolová, Veronika (advisor) ; Fábry, Jan (referee)
The purpose of this bachelor thesis is to apply vehicle routing problem with time series to a real case study. At first vehicle routing problem is classified into Operations Research and Travelling Salesman Problem. Then a simple vehicle routing problem and a multiple vehicle routing problem are described as well as their modifications with time series. Some heuristic algorithms and steps of nearest neighbour algorithm are described. The next part is focused on the application. It starts with introducing the company that is specialized in an exchange business and description of the situation that presents its assignments. There are three assignments in total. The first and second assignments are related to the optimization of cash delivery to company's branches. The second one also allows the company send a parcel with cash instead of its own delivery. The third assignment is to calculate whether a conversion cars into propellant gas is budget-wise or not. These assignments are solved and the results are commented.
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