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Opis: The paper presents the Mixed-Integer Non-linear Programming (MINLP) approach to the synthesis of trusses. The solution of continuous/discrete non-convex and non-linear optimization problems is discussed with respect to the simultaneous topology, shape and discrete sizing optimization of trusses. A truss MINLP superstructure of different topology and design alternatives has been generated, and a special MINLP model formulation for trusses has been developed. In the optimization model, a mass objective function of the structure has been defined and subjected to design, load and dimensioning constraints. The MINLP problems are solved using the Modified Outer-Approximation/Equality-Relaxation (OA/ER) algorithm. Multi-level MINLP strategies are introduced to accelerate the convergence of the algorithm. The Modified Two-Phase and the Sequential Two-Phase MINLP strategies are proposed in order to solve highly combinatorial topology, shape and discrete sizing optimization problems. The importance of local buckling constraints on topology optimization is also discussed. Some simple numerical examples are shown at the end of the paper to demonstrate the suitability and efficiency of the proposed method.
Ključne besede: structural synthesis, topology optimization, discrete sizing optimization, mixed-integer non-linear programming, MINLP, modified OA/ER algorithm, multi-level MINLP strategies, steel structures, trusses
Objavljeno v DKUM: 11.03.2025; Ogledov: 0; Prenosov: 12
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Opis: We present an algorithm that determines the prime factors of connected graphs with respect to the Cartesian product in linear time and space. This improves a result of Aurenhammer et al. [Cartesian graph factorization at logarithmic cost per edge, Comput. Complexity 2 (1992) 331-349], who compute the prime factors in ▫$O(mlog n)$▫ time, where ▫$m$▫ denotes the number of vertices of ▫$G$▫ and ▫$n$▫ the number of edges. Our algorithm is conceptually simpler. It gains its efficiency by the introduction of edge-labellings.
Ključne besede: matematika, teorija grafov, kartezični produkt grafov, linearni algoritem, razcep, mathematics, graph theory, Cartesian product graphs, linear algorithm, decomposition
Objavljeno v DKUM: 10.07.2015; Ogledov: 1727; Prenosov: 139
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Opis: We consider two classical problems from location theory which may serve as theoretical models for several logistic problems where one wants to assign elements of a set A to elements of a set B such that some linear or quadratic function attains its minimum. It turns out that linear objective function yields a linear assignment problem, which can be solved easily by several primal-dual methods like Hungarian method, Shortest augmenting path method etc. On the other hand, taking quadratic objective function into account makes the problem much harder. The resulting quadratic assignment problem is a very useful model but also very tough problem from theoretical and practical point of view. We list several well-known applications of these models and also the most effective methods to solve the problem. However, it is still a challenging task to solve this problem to optimality when the size of underlying sets A and B is greater than 25 and currently impossible task when the size is greater than 35.
Ključne besede: quadratic assignment problem, linear assignment problem, branch and bound algorithm, heuristics
Objavljeno v DKUM: 05.06.2012; Ogledov: 2051; Prenosov: 145
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