ΜΕΘΟΔΟΙ ΔΙΑΚΡΙΤΗΣ ΒΕΛΤΙΣΤΟΠΟΙΗΣΗΣ ΚΑΤΑΣΚΕΥΩΝ ΜΕ ΒΑΣΗ ΤΗ ΘΕΩΡΙΑ ΠΑΙΓΝΙΩΝ

ΣΙΜΟΣ, ΝΙΚΟΛΑΟΣ; SIMOS, NIKOLAOS

dc.contributor.author	ΣΙΜΟΣ, ΝΙΚΟΛΑΟΣ	el
dc.contributor.author	SIMOS, NIKOLAOS	en
dc.date.accessioned	2020-10-13T07:39:19Z
dc.date.available	2020-10-13T07:39:19Z
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/51407
dc.identifier.uri	http://dx.doi.org/10.26240/heal.ntua.19105
dc.rights	Αναφορά Δημιουργού-Μη Εμπορική Χρήση-Όχι Παράγωγα Έργα 3.0 Ελλάδα	*
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/3.0/gr/	*
dc.subject	Structural Optimization	en
dc.subject	Game Theory	en
dc.subject	heuristic algorithms	en
dc.subject	Nash equilibrium	en
dc.subject	simulated annealing	en
dc.subject	Βέλτιστος Σχεδιασμός Κατασκευών	el
dc.subject	Θεωρία Παιγνίων	el
dc.subject	ευρετικοί αλγόριθμοι	el
dc.subject	Ισορροπία Nash	el
dc.subject	προσομοιωμένη ανόπτηση	el
dc.title	ΜΕΘΟΔΟΙ ΔΙΑΚΡΙΤΗΣ ΒΕΛΤΙΣΤΟΠΟΙΗΣΗΣ ΚΑΤΑΣΚΕΥΩΝ ΜΕ ΒΑΣΗ ΤΗ ΘΕΩΡΙΑ ΠΑΙΓΝΙΩΝ	el
dc.title	DISCRETE STRUCTURAL OPTIMIZATION METHODS USING GAME THEORY	en
heal.type	masterThesis
heal.classification	Βελτιστοποίηση Κατασκευών	el
heal.classification	Structural optimization	en
heal.classificationURI	http://id.loc.gov/authorities/subjects/sh88004614
heal.language	el
heal.access	free
heal.recordProvider	ntua	el
heal.publicationDate	2016-10-25
heal.abstract	The present MSc Thesis is a continuation of the attempt to use Game Theory in structural optimization which began by Gerasimos Panayiotakopoulos in his MSc thesis titled “Structural Optimization using Game Theory” [1]. Structural optimization is a procedure of compromises between the desired structural attributes, that is, safety and functionality on the one side, and cost effectiveness on the other. Game theory, as purely strategic analysis theory, provides with valuable advice regarding the evaluation of conditions and decision making. It is therefore possible for game theory, if used in an appropriate way, to become a useful tool in the hands of an engineer, both in structural optimization and in other applications that require calculated decisions. The remaining work is organized as follows: In Chapter 1 an introduction to game theory is taking place, so that the readers can familiarize themselves with its objective. At first, a series of basic games is displayed, that present the logic of Game Theory in a simple and comprehensible way. Subsequently, the most basic concepts are explained, such as utility and Nash Equilibrium. This chapter’s exclusive aim is to get the reader accustomed to the basic concepts of game theory. Chapter 2 is more mathematically oriented. In this chapter, the various ways to discover a Nash Equilibrium are presented. The covered methods, are the iterative deletion of dominated alternatives and the backward induction, as far as pure strategy equilibria are concerned. In Chapter 3 the structural optimization problem addressed in the present thesis is discussed and after that the methodology used is described, named Maximization of Minimum Utility Method. This method allows a wider choice of objective function, surpassing the limits of the classic problem of the most economic design, while at the same time allowing the usage of limitations regarding any design variable, funding included. According to the Maximization of Minimum Utility Method, the discrete problem of structural optimization is simulated as a game, played by the defending player, who “defends” the structure, managing the cross sections at hand, and the attacking player, who decides upon the way to attack the structure, by choosing among some predefined load combinations, usually described by code regulations. Furthermore, the method defines the utility value of each player, depending on the results (in terms of stresses, displacements, plastic collapse load factor and funding) of their combined decisions. The game is simulated as a zero sum game, in order to make it fully competitive, excluding any possibility of cooperation between the players. The game is then solved using game theory and the backward induction method. In this way both the optimal design of the given structure and the critical loading case at Nash Equilibrium are simultaneously identified. Chapter 4 refers to difficulties presented due to the great size of most problems and suggests heuristic algorithms as a solution. The inherent problem of the method lies in the combinatorial explosion of the set of the possible alternatives that define the solution space, the accurate analysis of which demands huge computational time and computer memory, rendering the method inefficient. This flaw is due to the fact that even in small scale problems, the number of possible strategies available to the defending player is just too big to handle. Game theory requires sequential analysis of each and every strategy, which renders inefficient the above method in its classic form. For this reason two heuristic algorithms are being used, aiming to identify the optimal solution by examining only a small fraction of the solution space in a short time period. This comes at the cost of giving up the certainty of finding the mathematically optimal solution, but preserving sufficient conditions for finding satisfactory solutions in the area of the theoretically optimal solution. The first of the algorithms in use is the well-known Simulated Annealing algorithm, whereas the second is the Gradual Reduction algorithm. In case of the latter algorithm, some changes took place in order to improve its efficiency, while a series of technics was developed that aim to enhance its effectiveness. By combining the maximization of minimum utility method with heuristic algorithms, a powerful discrete optimization tool emerges, which is capable of solving numerous kinds of optimization problems. A code is written in Java, containing both the maximization of minimum utility method and the heuristic algorithms employed. The code was used in order to solve a number of structural optimization problems, which are discussed in chapter 5. These problems regard weight minimization considering either elastic or plastic analysis, topology optimization or displacement minimization with budget constraints. The validity of the suggested method is verified by solving already known problems from references. In Chapter 6 the conclusions of the thesis are presented, as well as some ideas for future work. Both the maximization of minimum utility method and the heuristic algorithms employed to accelerate the method have worked successfully. The suggested methodology can be applied to any kind of structural optimization problem. The attempt to improve the speed of both algorithms as well as the effectiveness of the Gradual Reduction algorithm by using techniques developed, is considered successful judging by the results. The suggested method can be applied in any kind of structure, trusses, frames or any other structure, provided that the corresponding solver is available. Moreover, the method can also apply to structures with several loading cases.	en
heal.advisorName	ΚΟΥΜΟΥΣΗΣ, ΒΛΑΣΗΣ	el
heal.committeeMemberName	ΠΑΠΑΔΟΠΟΥΛΟΣ, ΒΗΣΣΑΡΙΩΝ	el
heal.committeeMemberName	ΛΑΓΑΡΟΣ, ΝΙΚΟΛΑΟΣ	el
heal.committeeMemberName	ΚΟΥΜΟΥΣΗΣ, ΒΛΑΣΗΣ	el
heal.academicPublisher	Σχολή Πολιτικών Μηχανικών	el
heal.academicPublisherID	ntua
heal.numberOfPages	114
heal.fullTextAvailability	true