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Maximum Multiplicative Programming: Theory, Algorithms, and Applications.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Maximum Multiplicative Programming: Theory, Algorithms, and Applications./
作者:	Ghasemi Saghand, Payman.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	252 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
Contained By:	Dissertations Abstracts International83-02B.
標題:	Operations research. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28549601
ISBN:	9798534695649

Maximum Multiplicative Programming: Theory, Algorithms, and Applications.
Ghasemi Saghand, Payman.

Maximum Multiplicative Programming: Theory, Algorithms, and Applications. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 252 p.

Source: Dissertations Abstracts International, Volume: 83-02, Section: B.

Thesis (Ph.D.)--University of South Florida, 2021.

This item must not be sold to any third party vendors.

This dissertation presents three different contributions to an important class of optimization problems known as Multiplicative Programs (MPs). The first group of contributions contains the development and analysis of several multi-objective optimization-based based algorithms designed to find the optimal solution of Mixed Integer Linear MPs. As for the second group, the application of a special class of MPs in radiotherapy planning is presented. Finally, in the last group, a new technique for conducting the multiplication process in the objectives of MPs is presented. Using this technique, we introduce a family of novel solution methods that are capable of solving both maximum and minimum MPs.Regarding the first group of contributions, we show that MPs can be viewed as special cases of the problem of optimization over the efficient set in Multi-objective optimization. Based on this observation, we develop several solution approaches with their own unique properties. In the first solution approach, we embed an existing algorithm capable of solving continuous MPs with two multiplying terms in a branch-and-bound framework to solve mixed integer instances. In our second approach, we develop a criterion space search algorithm for solving any mixed integer MPs with any number of multiplying terms. In our last solution approach, we develop three different algorithms that, in addition to solving any mixed integer MPs with any number of multiplying terms, are capable of handling the multiplying terms with different powers. Specifically, the advantage of our last solution approach is that it handles the powers with the minimal impact on the computational complexity in practice.In the second group of contributions, we study the fluency map optimization problem in Intensity Modulated Radiation Therapy (IMRT) from a cooperative game theory point of view. We consider the cancerous and healthy organs in a patient's body as players of a game, where cancerous organs seek to eliminate the cancerous cells and healthy organs seek to receive no harm. We balance these trade-off by transforming the fluency map optimization problem into a bargaining game. Then, using the concept of Nash Social Welfare, we find a solution for our bargaining game by creating and optimizing an MP. The importance of our solution is that it simultaneously satisfies efficiency and fairness in the trade-offs. Finally, we demonstrate the advantages of our proposed approach by implementing it on two different cancer cases.In the third and last group of contributions, we present the novel idea of binary-encoding the multiplication operation analogously to how a computer conducts it internally. Based on this idea, we develop a new family of solution methods for MPs. One of our methods is to solve the multiplicative programs bit-by-bit, i.e., iteratively computing the optimal value of each bit of the objective function. In an extensive computational study, we explore a number of solution methods that solve MPs faster and more accurately.

ISBN: 9798534695649Subjects--Topical Terms:

547123
Operations research.
Subjects--Index Terms:

Geometric mean optimization

Maximum Multiplicative Programming: Theory, Algorithms, and Applications.
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245 1 0 $a Maximum Multiplicative Programming: Theory, Algorithms, and Applications.
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300 $a 252 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-02, Section: B.
500 $a Advisor: Charkhgard, Hadi.
502 $a Thesis (Ph.D.)--University of South Florida, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a This dissertation presents three different contributions to an important class of optimization problems known as Multiplicative Programs (MPs). The first group of contributions contains the development and analysis of several multi-objective optimization-based based algorithms designed to find the optimal solution of Mixed Integer Linear MPs. As for the second group, the application of a special class of MPs in radiotherapy planning is presented. Finally, in the last group, a new technique for conducting the multiplication process in the objectives of MPs is presented. Using this technique, we introduce a family of novel solution methods that are capable of solving both maximum and minimum MPs.Regarding the first group of contributions, we show that MPs can be viewed as special cases of the problem of optimization over the efficient set in Multi-objective optimization. Based on this observation, we develop several solution approaches with their own unique properties. In the first solution approach, we embed an existing algorithm capable of solving continuous MPs with two multiplying terms in a branch-and-bound framework to solve mixed integer instances. In our second approach, we develop a criterion space search algorithm for solving any mixed integer MPs with any number of multiplying terms. In our last solution approach, we develop three different algorithms that, in addition to solving any mixed integer MPs with any number of multiplying terms, are capable of handling the multiplying terms with different powers. Specifically, the advantage of our last solution approach is that it handles the powers with the minimal impact on the computational complexity in practice.In the second group of contributions, we study the fluency map optimization problem in Intensity Modulated Radiation Therapy (IMRT) from a cooperative game theory point of view. We consider the cancerous and healthy organs in a patient's body as players of a game, where cancerous organs seek to eliminate the cancerous cells and healthy organs seek to receive no harm. We balance these trade-off by transforming the fluency map optimization problem into a bargaining game. Then, using the concept of Nash Social Welfare, we find a solution for our bargaining game by creating and optimizing an MP. The importance of our solution is that it simultaneously satisfies efficiency and fairness in the trade-offs. Finally, we demonstrate the advantages of our proposed approach by implementing it on two different cancer cases.In the third and last group of contributions, we present the novel idea of binary-encoding the multiplication operation analogously to how a computer conducts it internally. Based on this idea, we develop a new family of solution methods for MPs. One of our methods is to solve the multiplicative programs bit-by-bit, i.e., iteratively computing the optimal value of each bit of the objective function. In an extensive computational study, we explore a number of solution methods that solve MPs faster and more accurately.
590 $a School code: 0206.
650 4 $a Operations research. $3 547123
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Industrial engineering. $3 526216
650 4 $a Applied mathematics. $3 2122814
650 4 $a Optimization. $3 891104
650 4 $a Biodiversity. $3 627066
650 4 $a Subject fields. $3 3681760
650 4 $a Efficiency. $3 753744
650 4 $a Liver. $3 3564653
650 4 $a Experiments. $3 525909
650 4 $a Planning. $3 552734
650 4 $a Decision making. $3 517204
650 4 $a Game theory. $3 532607
650 4 $a Variables. $3 3548259
650 4 $a Primary care. $3 3681757
650 4 $a Convex analysis. $3 3681761
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650 4 $a Algorithms. $3 536374
650 4 $a Radiation therapy. $3 3557731
653 $a Geometric mean optimization
653 $a Multi-objective optimization
653 $a Nash bargaining solution
653 $a Nash social welfare
653 $a Optimization over the efficient set
653 $a Multiplicative Programs
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690 $a 0642
690 $a 0454
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710 2 $a University of South Florida. $b Industrial and Management Systems Engineering. $3 2102438
773 0 $t Dissertations Abstracts International $g 83-02B.
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791 $a Ph.D.
792 $a 2021
793 $a English
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