Pooling Problems with Single-Flow Constraints

The pooling problem is a frequently studied extension of the traditional minimum cost flow problem, in which the composition of the flow is subject to restrictions. In a network consisting of three layers of nodes, the composition is given at the source layer. In the intermediate nodes, referred to as pools, the composition is a weighted average of the compositions in entering flow streams. The same is true at the sink layer, where upper bounds on the concentration of each component apply. Motivated by practical applications, and needs for heuristic methods for the standard pooling problem, the current work focuses on pooling problems where the flow graph is restricted to satisfy certain sparsity conditions. We consider in particular the requirements that each pool receives flow from at most one neighboring source, or sends flow to at most one neighboring sink. We prove that the pooling problem remains NP-hard after this and other similar extensions. It is also demonstrated how the single-flow constrained extensions can be modeled by means of mixed integer linear programming (MILP), without introducing bilinear terms. We also show that such MILP-models are useful for computing good feasible solutions to the original problem.acceptedVersio

Integer Programming Formulations for the Shared Multicast Tree Problem

We study the shared multicast tree (SMT) problem in wireless networks. To support a multicast session between a set of network nodes, SMT aims to establish a wireless connection between them, such that the total energy consumption is minimized. All destinations of the multicast message must be connected, while non-destinations are optional nodes that can be used to relay messages. The objective function reflecting power consumption distinguishes SMT clearly from the traditional minimum Steiner tree problem. We develop two integer programming formulations for SMT. Both models are subsequently extended and strengthened. Theorems on relations between the LP bounds corresponding to the models are stated and proved. As the number of variables in the strongest formulations is a polynomial of degree four in the number of network nodes, the models are impractical for computing lower bounds in instances beyond a fairly small size, and therefore a constraint generation scheme is developed. Results from computational experiments with the models demonstrate good promise of the approaches taken.acceptedVersio

Strategic optimization of offshore wind farm installation

This work describes logistical planning of offshore wind farm (OWF) installation through linear programming. A mixed integer linear programming (MILP) model is developed to analyze cost-effective port and vessel strategies for offshore installation operations. The model seeks to minimize total costs through strategic decisions, that is decisions on port and vessel fleet and mix. Different vessels, ports and weather restrictions over a fixed time horizon are considered in the model. Several deterministic test cases with historic weather data are implemented in AMPL, and run with the CPLEX solver. The results provide valuable insight into economic impact of strategic decisions. Numerical experiments on instances indicate that decision aid could be more reliable if large OWFs are considered in fractionated parts, alternatively by developing heuristics.acceptedVersio

Fixed cardinality stable sets

Given an undirected graph G=(V,E) and a positive integer k in {1, ..., |V|}, we initiate the combinatorial study of stable sets of cardinality exactly k in G. Our aim is to instigate the polyhedral investigation of the convex hull of fixed cardinality stable sets, inspired by the rich theory on the classical structure of stable sets. We introduce a large class of valid inequalities to the natural integer programming formulation of the problem. We also present simple combinatorial relaxations based on computing maximum weighted matchings, which yield dual bounds towards finding minimum-weight fixed cardinality stable sets, and particular cases which are solvable in polynomial time.publishedVersio

Optimization of reliable cyclic cable layouts in offshore wind farms

A novel approach for optimizing reliable cable layouts in offshore wind farms is presented. While optimization models traditionally are designed to suggest acyclic cable routes, those developed in this work recognize that cyclic layouts reduce the consequences of cable failures. The models under study take into account that cables cannot cross each other, which, particularly in instances with restrictive cable capacity, can make it attractive to let cables follow a joint trajectory, and visit turbines without connecting to them. A two-layered optimization process is developed. The outer layer is associated with an integer programming problem, which is subject to simultaneous generation of rows and columns representing cable paths. In the inner layer, a problem identifying feasible low cost paths is solved, guided by optimal dual variable values in the continuous relaxation of the former problem. Results from experimental applications to existing wind farms show good promise of the method.publishedVersio

Turning points in shaping choral conducting practice: six tales of Norwegian conductors’ professional development

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Kommunal ansatt og folkevalgt : ansatt med politisk makt eller folkevalgt med administrativ makt?

Masteroppgave ledelse ORG917 - Universitetet i Agder 201

Towards stronger Lagrangean bounds for stable spanning trees

Given a graph G=(V,E) and a set C of unordered pairs of edges regarded as being in conflict, a stable spanning tree in G is a set of edges T inducing a spanning tree in G, such that for each {e_i, e_j} in C, at most one of the edges e_i and e_j is in T. The existing work on Lagrangean algorithms to the NP-hard problem of finding minimum weight stable spanning trees is limited to relaxations with the integrality property. We have recently initiated the combinatorial and polyhedral study of fixed cardinality stable sets [see https://doi.org/10.1016/j.dam.2021.01. 019], which motivates a new formulation for stable spanning trees based on Lagrangean Decomposition. By optimizing over the spanning tree polytope of G and the fixed cardinality stable set polytope of the conflict graph H=(E,C) in the subproblems, we are able to determine stronger Lagrangean bounds (equivalent to dualizing exponentially-many subtour elimination constraints), while limiting the number of multipliers in the dual problem to |E|. This naturally asks for more sophisticated dual algorithms, requiring the fewest iterations possible, and we derive a collection of Lagrangean dual ascent directions to this end.publishedVersio

Word Neighbor Priming in Bilingual Sentence Reading: Evidence from Eye Movements

Master's thesis English EN501 - University of Agder 2018This study investigates English sentence reading processes in Norwegian-English bilinguals. It aims to explore the effects of word form overlap and its connection to second-language (L2) English proficiency. We recorded eye movements of Norwegian-English bilinguals while they read single sentences on screen. The experiment was a replication of Frisson, Koole, Hughes, Olson and Wheeldon, (2014), who investigated the effects of form similarity between words (orthographic and phonological, both separate and combined) on sentence reading in English monolinguals. They also investigated the effects of distance between prime and target words, and found that words that overlap in both orthography and phonology cause inhibition (longer gaze durations) when the distance between prime and target was 3 words. Interestingly only skilled readers showed the same effect when distance between prime and target was 9 words. Our study aimed to investigate whether the same inhibitory effects occur in Norwegian- English bilinguals and to determine if aspects of L2 proficiency modulated the effect. In our experiment, the sentences contained a prime word (related) or matched control word (unrelated) and a target word. In the related conditions, the prime and target overlapped both orthographically and phonetically in the end (e.g. fork-pork) or the beginning (e.g. rail-raid). We also examined the effects of distance between prime and target. In order to investigate effects of individual differences in bilingual language profile and proficiency, the results were then correlated with factors of a bilingual profile established using data from a revised LEAPQuestionnaire from a sister project. We found that proficient L2 users show more inhibition when there is phonological and orthographic overlap. Generally, there is inhibition in end overlap items, and facilitation in begin overlap items, but only when the distance is about 3 words. When prime and target is separated by 9 words, the effect disappears. We also found that there is a significant correlation between L2 proficiency and the effects of overlap. The more proficient the bilingual is in their L2, the more native-like the inhibition effects. We conclude that proficient L2 readers are more likely to be affected by word overlap priming, and that skilled L2 readers are negatively impacted by word overlap to a higher degree than less skilled L2 readers are. These findings suggest that, similar to L1 readers, skilled L2 readers maintain word-form information for longer when reading than less skilled readers

Modelling overfow using mixed integer programming in short‑term hydropower scheduling

Short-term hydropower scheduling seeks to find a production schedule that maximizes profit, but must also consider the hydrological balance and risk of overflow. Overflow is by nature a non-linear and non-convex phenomenon. Common approximations and relaxations may cause non-physical results such as overflow from reservoirs that are not full. This paper presents a mixed-integer linear programming formulation that can be used to prevent non-physical overflow behaviour, but that comes at a cost of significant higher solving time. To achieve an acceptable solving time, we propose a heuristic to provide tight upper bounds on the overflow variables in each time step. When applied on the model of the Fossdal watercourse in Norway, the proposed method reduces the solving time with more than 90% compared to using a conservative fixed coefficient for all time steps.Modelling overfow using mixed integer programming in short‑term hydropower schedulingpublishedVersio