Algorithm Engineering in Robust Optimization

Robust optimization is a young and emerging field of research having received a considerable increase of interest over the last decade. In this paper, we argue that the the algorithm engineering methodology fits very well to the field of robust optimization and yields a rewarding new perspective on both the current state of research and open research directions. To this end we go through the algorithm engineering cycle of design and analysis of concepts, development and implementation of algorithms, and theoretical and experimental evaluation. We show that many ideas of algorithm engineering have already been applied in publications on robust optimization. Most work on robust optimization is devoted to analysis of the concepts and the development of algorithms, some papers deal with the evaluation of a particular concept in case studies, and work on comparison of concepts just starts. What is still a drawback in many papers on robustness is the missing link to include the results of the experiments again in the design

Load allocation problem for optimal design of aircraft electrical power system

More and more electric systems are embedded in today aircraft. As a result, the complexity of electrical power system design is increasing and the need of generic and efficient design methods is today required. Among numerous design tasks, the allocation of electric systems on the busbars of the electrical power system is considered as an important one since it has a direct impact on the aircraft mass. But due to the high number of possible allocations and regarding the large diversity of potential sizing cases for the equipments, finding the optimal allocation of electric loads is a hard task. In this paper, the problem is formalized mathematically. Then, four stochastic optimization methods are assessed on complex load allocation problems. Based on this assessment, a genetic algorithm using niching method is considered as the most appropriate algorithm for solving this aircraft design proble

An Investigation Report on Auction Mechanism Design

Auctions are markets with strict regulations governing the information available to traders in the market and the possible actions they can take. Since well designed auctions achieve desirable economic outcomes, they have been widely used in solving real-world optimization problems, and in structuring stock or futures exchanges. Auctions also provide a very valuable testing-ground for economic theory, and they play an important role in computer-based control systems. Auction mechanism design aims to manipulate the rules of an auction in order to achieve specific goals. Economists traditionally use mathematical methods, mainly game theory, to analyze auctions and design new auction forms. However, due to the high complexity of auctions, the mathematical models are typically simplified to obtain results, and this makes it difficult to apply results derived from such models to market environments in the real world. As a result, researchers are turning to empirical approaches. This report aims to survey the theoretical and empirical approaches to designing auction mechanisms and trading strategies with more weights on empirical ones, and build the foundation for further research in the field

A methodology for company valuation

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis presents an approach for company valuation by a replication portfolio of traded assets in discrete time. The model allows us to value companies with an uncertain cash flow stream without having to revert to any discount rates including premia. Modelling of asset values can be achieved in two steps: (i) Choosing a suitable stochastic process and calibrating its parameters to fit the historical asset time series behaviour, and (ii) generating a state space transition graph to implement the stochastic process dynamics in discrete time. For company valuation, a selected number of "assets" (economic, financial, and other factors) should be captured that may reasonably be assumed to influence future cash flows of the company. Each vertex of the transition graph represents a "state of the world" and is accompanied with a corresponding cash flow caused by the sales (or other company activities) at that vertex. These possible future company cash flows can be "replicated" (without..

Real-time Container Transport Planning with Decision Trees based on Offline Obtained Optimal Solutions

Hinterland networks for container transportation require planning methods in order to increase efficiency and reliability of the inland road, rail and waterway connections. In this paper we aim to derive real-time decision rules for suitable allocations of containers to inland services by analysing the solution structure of a centralised optimisation method used offline on historic data. The decision tree can be used in a decision support system (DSS) for instantaneously allocating incoming orders to suitable services, without the need for continuous planning updates. Such a DSS is beneficial, as it is easy to implement in the current practice of container transportation. Earlier proposed centralised methods can find the optimal solution for the intermodal inland transportation problem in retrospect, but are not suitable when information becomes gradually available. The main contributions are threefold: firstly, a structured method for creating decision trees from optimal solutions is proposed. Secondly, an innovative method is used for obtaining multiple equivalent optimal solutions to prevent overfitting of the decision tree. And finally, a structured analysis of three error types is presented for assessing the quality of an obtained tree. A case study illustrates the method’s purpose by comparing the quality of the resulting plan with alternative methods

On parallel computing for stochastic optimization models and algorithms

167 p.Esta tesis tiene como objetivo principal la resolución de problemas de optimización bajo incertidumbre a gran escala, mediante la interconexión entre las disciplinas de Optimización estocástica y Computación en paralelo. Se describen algoritmos de descomposición desde la perspectivas de programación matemática y del aprovechamiento de recursos computacionales con el fin de resolver problemas de manera más rápida, de mayores dimensiones o/y obtener mejores resultados que sus técnicas homónimas en serie. Se han desarrollado dos estrategias de paralelización, denotadas como inner y outer. La primera de las cuales, realiza tareas en paralelo dentro de un esquema algorítmico en serie, mientras que la segunda ejecuta de manera simultánea y coordinada varios algoritmos secuenciales. La mayor descomposición del problema original, compartiendo el área de factibilidad, creando fases de sincronización y comunicación entre ejecuciones paralelas o definiendo condiciones iniciales divergentes, han sido claves en la eficacia de los diseños de los algoritmos propuestos. Como resultado, se presentan tanto algoritmos exactos como matheurísticos, que combinan metodologías metaheurísticas y técnicas de programación matemática. Se analiza la escalabilidad de cada algoritmo propuesto, y se consideran varios bancos de problemas de diferentes dimensiones, hasta un máximo de 58 millones de restricciones y 54 millones de variables (de las cuales 15 millones son binarias). La experiencia computacional ha sido principalmente realizada en el cluster ARINA de SGI/IZO-SGIker de la UPV/EHU