Efecto de los decodificadores en la calidad de la solución para un problema de distribución de instalaciones UA-FLP

En este trabajo se propuso una comparación entre dos decodificadores diferentes para un problema de distribución de planta de áreas desiguales y dimensiones fijas UA-FLP; los decodificadores utilizados  son el decodificador en espiral y el decodificador en abanico. Para realizar este  trabajo se seleccionaron 6 instancias encontradas en la literatura y el problema se resolvió por medio de una metaheurística muy conocida en la comunidad científica como lo es el algoritmo genético básico. El objetivo principal de este estudio fue demostrar si existían diferencias en la calidad de la solución propuesta por cada uno de los decodificadores. Entre los resultados encontrados se evidencio que el decodificador en espiral ofrece mejores resultados en comparación con el decodificador  en abanico, en efecto  se logró demostrar que los  decodificadores tienen gran influencia  en la calidad de la  solución para este tipo de problemas.

Efecto de los decodificadores en la calidad de la solución para un problema de distribución de instalaciones UA-FLP

En este trabajo se propuso una comparación entre dos decodificadores diferentes para un problema de distribución de planta de áreas desiguales y dimensiones fijas UA-FLP; los decodificadores utilizados  son el decodificador en espiral y el decodificador en abanico. Para realizar este  trabajo se seleccionaron 6 instancias encontradas en la literatura y el problema se resolvió por medio de una metaheurística muy conocida en la comunidad científica como lo es el algoritmo genético básico. El objetivo principal de este estudio fue demostrar si existían diferencias en la calidad de la solución propuesta por cada uno de los decodificadores. Entre los resultados encontrados se evidencio que el decodificador en espiral ofrece mejores resultados en comparación con el decodificador  en abanico, en efecto  se logró demostrar que los  decodificadores tienen gran influencia  en la calidad de la  solución para este tipo de problemas.

Beating the SDP bound for the floor layout problem: A simple combinatorial idea

For many mixed-integer programming (MIP) problems, high-quality dual bounds can be obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through semi-definite programming (SDP) relaxation hierarchies. In this paper, we introduce an alternative bounding approach that exploits the ‘combinatorial implosion’ effect by solving portions of the original problem and aggregating this information to obtain a global dual bound. We apply this technique to the one-dimensional and two-dimensional floor layout problems and compare it with the bounds generated by both state-of-the-art MIP solvers and by SDP relaxations. Specifically, we prove that the bounds obtained through the proposed technique are at least as good as those obtained through SDP relaxations, and present computational results that these bounds can be significantly stronger and easier to compute than these alternative strategies, particularly for very difficult problem instances.United States. National Science Foundation. Graduate Research Fellowship Program (Grant 1122374)United States. National Science Foundation. Graduate Research Fellowship Program (Grant CMMI-1351619

Strong mixed-integer formulations for the floor layout problem

The floor layout problem (FLP) tasks a designer with positioning a collection of rectangular boxes on a fixed floor in such a way that minimizes total communication costs between the components. While several mixed integer programming (MIP) formulations for this problem have been developed, it remains extremely challenging from a computational perspective. This work takes a systematic approach to constructing MIP formulations and valid inequalities for the FLP that unifies and recovers all known formulations for it. In addition, the approach yields new formulations that can provide a significant computational advantage and can solve previously unsolved instances. While the construction approach focuses on the FLP, it also exemplifies generic formulation techniques that should prove useful for broader classes of problems.United States. National Science Foundation. Graduate Research Fellowship Program (Grant 1122374)United States. National Science Foundation. Graduate Research Fellowship Program (Grant CMMI-1351619

A convex optimisation framework for the unequal-areas facility layout problem

The unequal-areas facility layout problem is concerned with finding the optimal arrangement of a given number of non-overlapping indivisible departments with unequal area requirements within a facility. We present a convex-optimisation-based framework for efficiently finding competitive solutions for this problem. The framework is based on the combination of two mathematical programming models. The first model is a convex relaxation of the layout problem that establishes the relative position of the departments within the facility, and the second model uses semidefinite optimisation to determine the final layout. Aspect ratio constraints, frequently used in facility layout methods to restrict the occurrence of overly long and narrow departments in the computed layouts, are taken into account by both models. We present computational results showing that the proposed framework consistently produces competitive, and often improved, layouts for well-known large instances when compared with other approaches in the literature.Facility layout Semidefinite programming Convex programming Global optimisation

Hierarchical and Nesting Approaches for the Facility Layout Problem

The Facility Layout Problem (FLP) seeks to determine the dimensions, coordinates and arrangement of rectangular departments within a given facility. The goal is to minimize the cost of inter-department flow. It has several real-world applications, including the design of manufacturing and warehousing facilities and electronic chips. Despite being studied for several decades, the FLP is still very difficult to solve for facilities with thirty or more departments. Thus, many heuristic approaches have been developed to solve the problem in a reasonable time. One such approach tackles the problem in two stages. In the first, some decision, usually the relative positioning of the departments, is fixed. In the second, an easier restricted problem is solved. This thesis explores hierarchical and nesting approaches for the FLP in an attempt to leverage the fact that smaller instances of the FLP can be solved to optimality relatively quickly. The goal is to find ways in which the FLP can be decomposed into several smaller problems and recombined to form a high-quality solution to the original problem. Hierarchical approaches use clustering or related methods to generate a tree where the leaves are the original departments and the root is the facility. The intermediate nodes are super-departments within an overall layout. A new hierarchical approach for the FLP is presented which performs layouts down this tree in a manner that controls dead-space and generates high-quality solutions. The approach provides solutions competitive with the best-known solutions on benchmark instances from the literature, with up to 8% improvement. The success of the hierarchical approach provided the motivation for a new formulation that nests departments within super-departments. The resulting formulation is even more difficult to solve directly than the original FLP; however, it is suitable for a two-stage solution approach. The first stage determines the assignment of departments to super-departments and the relative positioning of the super-departments. In the second stage, the remainder of the formulation is solved. The approach is found to provide better solutions than the hierarchical approach. Solutions are found with up to 14% improvement over the best-known solutions from the literature

Transformation bestehender Gebäude: Ein Ansatz auf Basis von BIM-Technologien

Working on an existing building represents a complex design challenge that stimulates the development of new design approaches. Especially in the context of historical buildings redesign, it is possible to detect some “invariants”: in an historical layout, in fact, it is possible to “read” precise traces and specific rules of aggregation that does not vary across homogenous categories of building typology. Throughout a transformation, the building will maintain its native function or change it radically, keep the original distributive path or bring an alternative layout, preserve the existing structure or acquire new additional elements. In any case, the final result must balance respect for historical constraints alongside the creative process, whilst avoiding the violation of the principles of sustainable design. From this perspective comes the idea to study the potential and the limitations of the use of modern IT tools in the context of re-designing existing buildings. One possible approach is suggested by “Building Information Modeling”, which is becoming a new paradigm for the entire architectural, engineering and construction industries. Although an in-depth review of the literature shows a variety of design methods for new construction, the existing methods and tools for dealing with existing buildings are limited. BIM may be partially adopted in the context of an automated procedure of assessment: the existing building can be parameterized and then physically and mathematically analysed. This work proposes a method that integrates Graph Theory with the evaluative process, with particular reference to the circulation aspect within a distribution layout. Using a custom tool that can extract data from a BIM model (rooms and connections) and create a graph from this information, it was possible to measure parameters and define a minimum performance usage as a criterion to compare several design solutions.Die Arbeit an einem bestehendem Gebäude stellt eine komplexe Herausforderung dar, die zur Entwicklung neuer Entwurfsansätze anregt. Speziell im Kontext von Umplanungen historischer Bauten kann man „Invarianten“ erkennen: So ist es möglich, spezifische Spuren und Prinzipien der Fügung zu lesen, die innerhalb homogener Gebäudetypologien nicht variieren. Durch Transformation kann ein Gebäude seine ursprüngliche Funktion beibehalten oder radikal verändern. Sie kann das originäre Erschließungssystem erhalten oder durch ein neues Layout verändern; sie kann das bestehende Tragsystem respektieren oder neue, zusätzliche Elemente hinzufügen. In jedem Fall muss das Ergebnis die Balance zwischen dem Respekt vor dem historischen Zwängen und dem kreativen Prozessen wahren. Daher entstammt die Idee das Potential und die Grenzen von modernen IT-Werkzeugen im Kontext der Umgestaltung bestehender Gebäude zu untersuchen. Ein möglicher Ansatz legt das “Building Information Modeling” nah, welches sich zu einem neuen Paradigma für die gesamte Architektur-Ingenieur, und Bauindustrie entwickelt. Obschon eine tiefere Sichtung der Literatur eine Fülle von Entwurfsmethoden für Neubauten aufzeigt, sind die Methoden und Werkzeuge wie mit Bestandsbauten umzugehen sind, sehr eingeschränkt. BIM wird teilweise im Kontext automatisierter Prozeduren zur Datenerhebung eingesetzt: Gebäude werden parametrisiert und dann physisch und mathematisch analysiert. Mit dieser Arbeit wird nun eine Methode vorgeschlagen, die die Graphentheorie mit evaluierenden Prozessen vereint. Schwerpunkt ist dabei der Aspekt der Zirkulation innerhalb von Erschließungslayouts. Unter Einsatz eines speziellen Werkzeugs, welches Daten (Räume und Verbindungen) aus einem BIM-Modell zieht und daraus graphische Darstellungen generiert, ist es möglich Parameter zu erhalten und Minimalleistungen der Nutzung zu definieren, die als Kriterium zur Bewertung verschiedener Entwurfsvarianten herangezogen werden können