We present versions of the Frank-Wolfe method for linearly constrained convex programs, in which consecutive search directions are made conjugate. Preliminary computational studies in a MATLAB environment applying pure Frank-Wolfe, Conjugate direction Frank-Wolfe (CFW), Bi-conjugate Frank-Wolfe (BFW) and ”PARTANized” Frank-Wolfe methods to some classical Traffic Assignment Problems show that CFW and BFW compare favorably to the other methods. This spurred a more detailed study, comparing our methods to Bar-Gera’s origin-based algorithm. This study indicates that our methods are competitive for accuracy requirements suggested by Boyce et al. We further show that CFW is globally convergent. We moreover point at independent studies by other researchers that show that our methods compare favourably with recent bush-based and gradient projection algorithms on computers with several cores. / <p>Updated from "E-publ" to published. QC 20130625</p>

Successful future surface combatants in the US Navy must embrace the growing integration and interdependency of propulsive and combat systems. Traditionally, the development of Hull, Mechanical and Electrical systems has been segregated from the development of weapons and sensors. However, with the incorporation of high energy weapons into future ship configurations, ship design processes must evolve to embrace the concept of a System of Systems being the only way to achieve affordable capability in our future fleets. This thesis bridges the gap between the physical architecture of components within a ship and the way in which they are logically connected to model the energy flow through a representative design and provide insight into sizing requirements of both system components and their connections using an Architecture Flow Optimization (AFO). This thesis presents a unique method and tool to optimize naval ship system logical and physical architecture considering necessary operational conditions and possible damage scenarios. The particular and unique contributions of this thesis are: 1) initially only energy flow is considered without explicit consideration of commodity flow (electric, mechanical, chilled water, etc.), which is calculated in post-processing; 2) AFO is applied to a large and complex naval surface combatant system of systems, demonstrating its scalability; 3) data necessary for the AFO is extracted directly from a naval ship synthesis model at a concept exploration level of detail demonstrating its value in early stage design; and 4) it uses network-based methods which make it adaptable to future knowledge-based network analysis methods and approaches. / Master of Science / The US Navy faces a future where their ships will be required to perform a greater number and increasingly more diverse mission set while the resources provided to them dwindle. Traditionally, propulsive, electrical and weapons systems onboard ships have been segregated in their development, however, with the incorporation of high energy weapons into future ship configurations, the ship design processes must evolve to incorporate these interdependent power consumers. To take advantage of emerging technologies in a resource constrained environment, the future fleet of the US Navy must incorporate the concept of a “System of Systems” early in the ship design process. This thesis correlates the energy available onboard a ship to how it can be distributed to components in the execution of required missions. Additionally, this thesis provides insight into the sizing requirements of intermediary and auxiliary components using an Architecture Flow Optimization (AFO) by only analyzing energy flow without considering the commodity flow (electricity, mechanical power, chilled water, etc.) which can be calculated post optimization. Using network-based methods allows the AFO to be adaptable to future knowledge-based network analysis methods and approaches while using data directly from a naval ship synthesis model enables the AFO to be scaled to incorporate a large and complex system of systems proving its value to early stage design.

Norrmejerier står inför förändringar vad gäller både mjölkkonsumtion och flytt av produktionen från Luleå mejeri till Umeå mejeri inom en snar framtid. Det har gett behov av ett verktyg för att snabbt kunna fatta beslut om systemet kan hantera en ökad mängd volym och antal produktkategorier. För att ta fram ett sådant verktyg skapades en matematisk optimeringsmodell uppbyggd i programvaran Python som gör det möjligt att köra programmet för olika scenarion. Modellen använder optimeringslösaren Pulp för att hitta en lösning på problemet. Den matematiska modellen baseras på Multi Commodity Flow Problem med tidsvariabel i kombination med Flow-shop scheduling och har modifierats efter systemet på Umeå mejeri. Det är en pessimistisk modell baserat på de antaganden som gjorts i rapporten. Programmet baseras på ett dygns produktion och avgör, genom att minimera den totala tiden det tar för flödet genom processen, om det finns kapacitet för en ökad produktion. Systemet i projektet är uppdelat i två subnätverk på grund av tidskomplexiteten och resultaten visar att implementering av en ytterligare produktkategori kan hanteras av båda subnätverken. En ökad volym med 10% av den befintliga kan endast hanteras av den första delen av nätverket. Det betyder att det finns tekniska begränsningar i det andra subnätverket. Genom tillägg av extra noder som kan användas till en viss straffkostnad kunde flaskhalsar identifieras och det visade sig att pastör 2P1 är en uppenbar flaskhals i systemet. Om man ökar produktionen ytterligare kan även silosarna behöva utökas för att hantera flödet. / Norrmejerier is facing changes in terms of both milk consumption and a move of the production from Luleå dairy to Umeå dairy in the near future. This has given rise to the need of a tool that quickly can make descisions about whether the system can handle an increased amount of volume and number of product categories. To produce such a tool a mathematical optimization model was created in Python which makes it possible to run the program for different scenarios. The model uses the optimization solver Pulp. The mathematical model is based on Multi Commodity Flow Problem with time variable combined with Flow-shop scheduling and has been modified according to the system at Umeå dairy. Based on the assumptions made in the report it is a pessimistic model. The program is based on one day's production and determines by minimizing the total time it takes for the flow to pass through the system, to see if there is enough capacity for increased production. The system in the project is divided into two subnetworks due to the time complexity and the results show that implementation of an additional product category can be handled by both subnetworks. An increased volume of 10% of the existing volume can only be handled by the first part of the network. This means that there are technical limitations in the second subnetwork. By adding extra nodes that can be used for a certain penalty cost, bottlenecks could be identified and it turned out that Pasteur 2P1 is an obvious bottleneck in the system. If the production increases further the silos may also need to be expanded to handle the flow in the system.

A multi-commodity flow problem consists of moving several commodities from their respective sources to their sinks through a network where each edge has different costs and capacity constraints. This paper explores different linear programming algorithms and their performance regarding finding an optimal solution for multi-commodity flow problems. By testing several of different network constraints, we examine which algorithms are most suitable for specific network and problem structures. Furthermore, we implement our own multi-commodity solver and compare its performance against state-of-the-art linear programming solvers. The results show that for the methods we tested it is difficult to discern which class of linear programming methods are optimal solvers for multi-commodity flow problems and that their performance depends on how the network and commodities are structured.