Each year the Railway Applications Section (RAS) of the Institution for Operations Research and the Management Sciences (INFORMS) posits a research problem to the world in the form of a competition. For 2012, the contest involved solving the Train Dispatching Problem (TDP) on a realistic 85 edge network for three different sets of input data. This work is an independent attempt to match or improve upon the results of the top three finishers in the contest using mixed integer programming (MIP) techniques while minimizing the use of heuristics. The primary focus is to partition the network in a manner that reduces the number of binary variables in the formulation as much as possible without compromising the ability to satisfy any of the contest requirements. This resulted in the ability to optimally solve this model for RAS Data Set 1 in 29 seconds without any problem-specific heuristics, variable restrictions, or variable fixing. Applying some assumptions about train movements allowed the same Data Set 1 solution to be found in 5.4 seconds. After breaking the larger Data Sets 2 and 3 into smaller sub-problems, solutions for Data Sets 2 and 3 were 28% and 1% better, respectively, than those of the competition winner. The time to obtain solutions for Data Sets 2 and 3 was 90 and 318 seconds, respectively.

<p dir="ltr">This thesis presents a comprehensive exploration of advanced optimization strategies for addressing mixed-integer optimal control problems (MIOCPs) in aerospace applications, emphasizing the enhancement of convergence robustness, computational efficiency, and accuracy. The research develops a broad spectrum of optimization methodologies, including multi-phase approaches, parallel computing, reinforcement learning (RL), and distributed algorithms, to tackle complex MIOCPs characterized by highly nonlinear dynamics, intricate constraints, and discrete control variables.</p><p dir="ltr">Through discretization and reformulation, MIOCPs are transformed into general quadratically constrained quadratic programming (QCQP) problems, which are then equivalently converted into rank-one constrained semidefinite programs problems. To address these, iterative algorithms are developed specifically for solving such problems. Initially, two iterative search methods are introduced to achieve convergence: one is a hybrid alternating direction method of multipliers (ADMM) designed for large-scale QCQP problems, and the other is an iterative second-order cone programming (SOCP) algorithm developed to achieve global convergence. Moreover, to facilitate the convergence of these iterative algorithms and to enhance their solution quality, a multi-phase strategy is proposed. This strategy integrates with both the iterative ADMM and SOCP algorithms to optimize the solving of QCQP problems, improving both the convergence rate and the optimality of the solutions. To validate the effectiveness and improved computational performance of the proposed multi-phase iterative algorithms, the proposed algorithms were applied to several aerospace optimization problems, including six-degree-of-freedom (6-DoF) entry trajectory optimization, fuel-optimal powered descent, and multi-point precision landing challenges in a human-Mars mission. Theoretical analyses of convergence properties along with simulation results have been conducted, demonstrating the efficiency, robustness, and enhanced convergence rate of the optimization framework.</p><p dir="ltr">However, the iteration based multi-phase algorithms primarily guarantee only local optima for QCQP problems. This research introduces a novel approach that integrates a distributed framework with stochastic search techniques to overcome this limitation. By leveraging multiple initial guesses for collaborative communication among computation nodes, this method not only accelerates convergence but also enhances the exploration of the solution space in QCQP problems. Additionally, this strategy extends to tackle general nonlinear programming (NLP) problems, effectively steering optimization toward more globally promising directions. Numerical simulations and theoretical proofs validate these improvements, marking significant advancements in solving complex optimization challenges.</p><p dir="ltr">Following the use of multiple agents in QCQP problems, this research expand this advantage to address more general rank-constrained semidefinite programs (RCSPs). This research developed a method that decomposes matrices into smaller submatrices for parallel processing by multiple agents within a distributed framework. This approach significantly enhances computational efficiency and has been validated in applications such as image denoising, showcasing substantial improvements in both efficiency and effectiveness.</p><p dir="ltr">Moreover, to address uncertainties in applications, a learning-based algorithm for QCQPs with dynamic parameters is developed. This method creates high-performing initial guesses to enhance iterative algorithms, specifically applied to the iterative rank minimization (IRM) algorithm. Empirical evaluations show that the RL-guided IRM algorithm outperforms the original, delivering faster convergence and improved optimality, effectively managing the challenges of dynamic parameters.</p><p dir="ltr">In summary, this thesis introduces advanced optimization strategies that significantly enhance the resolution of MIOCPs and extends these methodologies to more general issues like NLP and RCSP. By integrating multi-phase approaches, parallel computing, distributed techniques, and learning methods, it improves computational efficiency, convergence, and solution quality. The effectiveness of these methods has been empirically validated and theoretically confirmed, representing substantial progress in the field of optimization.</p>

Road traffic dominates in domestic Swedish transportation and is highly dependent on fossil fuels, petrol and diesel. Currently, the use of renewable fuels in transportation accounts for less than 6% of the total energy use in transport. The demand for bioethanol to fuel transportation is growing and cannot be met through current domestic production alone. Lignocellulosic ethanol derived from agricultural crop residues may be a feasible alternative source of ethanol for securing a consistent regional fuel supply in Swedish climatic conditions.  This licentiate thesis focuses on regional transport fuel supply by considering local small-scale ethanol production from straw. It presents the results of investigations of regional transport fuel supply with respect to minimising regional CO2 emissions, cost estimates for transport fuel supply, and the availability of lignocellulosic resources for small-scale ethanol production. Regional transport fuel demand between the present and 2020 is also estimated. The results presented here show that significant bioethanol can be produced from the straw and Salix available in the studied regions and that this is sufficient to meet the regions’ current ethanol fuel demand.  A cost optimisation model for regional transport fuel supply is developed and applied for two cases in one study region, one when the ethanol production plant is integrated with an existing CHP plant (polygeneration), and one with a standalone ethanol production plant. The results of the optimisation model show that in both cases the changes in ethanol production costs have the biggest influence on the cost of supplying the regional passenger car fleet with transport fuel, followed by the petrol price and straw production costs.  By integrating the ethanol production process with a CHP plant, the costs of supplying regional passenger car fleet with transport fuel can be reduced by up to a third. Moreover, replacing petrol fuel with ethanol can cut regional CO2 emissions from transportation by half.

In this thesis, two methods are proposed in order to rank units: Target-direction-set value efficiency analysis (TDSVEA) and mixed integer programming (MIP) technique. Besides its ranking ability based on preferences of a decision maker (DM), TDSVEA, which modifies the targeted projection approach of Value Efficiency Analysis (VEA) and Data Envelopment Analysis (DEA), provides important information to analyzer: targets and distances of units from these targets, proposed input allocations in order to project these targets, the lack of harmony between the DM and the manager of the unit etc. In MIP technique, units select weights of the criteria from a feasible weight space in order to outperform maximum number of other units. Units are then ranked according to their outperforming ability. Mixed integer programs in this technique are simplified by domination and weight-domination relations. This simplification procedure is further simplified using transitivity between relations. Both TDSVEA and MIP technique are applied to rank research universities and these rankings are compared to those of other ranking techniques.

This thesis analyzes the mean variance optimization problem with respect to cardinalityconstraints. The aim of this thesis is to figure out how much of an impact transactionchanges has on the profit and risk of a portfolio. We solve the problem by implementingmixed integer programming (MIP) and solving the problem by using the Gurobi solver.In doing this, we create a mathematical model that enforces the amount of transactionchanges from the initial portfolio. Our results is later showed in an Efficient Frontier,to see how the profit and risk are changing depending on the transaction changes.Overall, this thesis demonstrates that the application of MIP is an effective approachto solve the mean variance optimization problem and can lead to improved investmentoutcomes.