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Solving mixed-integer linear programming problems in GAMS
Škoda, Štěpán ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
In the present work we study the problems of integer linear optimi- zation, at first from the theoretical point of view (Part I) and subsequently on the basis of empirical data (Part II). First section explains with what this field deals with and where is applied. Other sections contain annotated mathematical formulation of problems, definitions and theorems needed to understand the general methods for solving integer linear programs. In the last section of Part I, we introduce the two best known groups of algorithms that are used by commercial software. The second part provides more details on an Internet library that contains some practical problems, that has been needed to be solved in the past. Furthermore, there are sections dealing with solvers and the advanced options of GAMS. The last section presents data obtained in the course of solving problems using several codes (solvers) of software. 1
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Solving mixed-integer linear programming problems in GAMS
Škoda, Štěpán ; Branda, Martin (advisor) ; Kopa, Miloš (referee)
In the present work we study the problems of integer linear optimi- zation, at first from the theoretical point of view (Part I) and subsequently on the basis of empirical data (Part II). First section explains with what this field deals with and where is applied. Other sections contain annotated mathematical formulation of problems, definitions and theorems needed to understand the general methods for solving integer linear programs. In the last section of Part I, we introduce the two best known groups of algorithms that are used by commercial software. The second part provides more details on an Internet library that contains some practical problems, that has been needed to be solved in the past. Furthermore, there are sections dealing with solvers and the advanced options of GAMS. The last section presents data obtained in the course of solving problems using several codes (solvers) of software. 1
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The quadratic assignment problem and its solution
Nováčková, Monika ; Jablonský, Josef (advisor) ; Fábry, Jan (referee)
The QAP (quadratic assignment problem) is one of the most involved combinatorial optimization problems. This formidable decision problem is included in the complexity class called NP-complete. The QAP has been first time introduced by Koopmans and Beckman in year 1957. Since then the various methods for solving this problem have been investigated. The studied methods include both: exact algorithms and heuristic methods. Some of them will be shortly described in this paper. One of them, the branch and bound algorithm based on Gilmore Lawler bounds will be analyzed in detail. View applications of this problem will be also discussed. Described applications include the problem of localization of the departments or clinics in a hospital in order to minimize the total traveling distance among clinics by patients. Another described example of application of this problem is the task how to place the components on a computer motherboard optimally.
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