Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2008. / Includes bibliographical references (p. 47-48). / We solve the periodic boundary value problem for a mode-locked laser cavity using a specially preconditioned matrix-implicit Newton-Krylov solver. Solutions are obtained at least an order of magnitude faster than with dynamic simulation, the standard method. Our method is demonstrated experimentally on a one-dimensional temporal model of an eight femtosecond mode-locked laser operating in the dispersion-managed soliton regime. Our solver is applicable to finding the steady-state solution of any nonlinear optical cavity with moderate self phase modulation, such as those of solid state lasers, and requires only a model for the round-trip action of the cavity. We conclude by proposing avenues of future work to improve the method's convergence and expand its applicability to lasers with higher degrees of cavity nonlinearity. Our approach can be extended to spatio-temporal cavity models, potentially allowing for the first feasible simulation of the full dynamics of Kerr-lens mode locking. / by Jonathan R. Birge. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009. / This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. / Cataloged from student submitted PDF version of thesis. / Includes bibliographical references (p. 85-91). / A high-order Galerkin Least-Squares (GLS) finite element discretization is combined with massively parallel implicit solvers. The stabilization parameter of the GLS discretization is modified to improve the resolution characteristics and the condition number for the high-order interpolation. The Balancing Domain Decomposition by Constraints (BDDC) algorithm is applied to the linear systems arising from the two-dimensional, high-order discretization of the Poisson equation, the advection-diffusion equation, and the Euler equation. The Robin-Robin interface condition is extended to the Euler equation using the entropy-symmetrized variables. The BDDC method maintains scalability for the high-order discretization for the diffusion-dominated flows. The Robin-Robin interface condition improves the performance of the method significantly for the advection-diffusion equation and the Euler equation. The BDDC method based on the inexact local solvers with incomplete factorization maintains the scalability of the exact counterpart with a proper reordering. / by Masayuki Yano. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2010. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 99). / We discuss the conditions that are necessary for a given banded matrix to have a banded inverse. Although a generic requirement is known from previous studies, we tend to focus on the ranks of the block matrices that are present in the banded matrix. We consider mainly the two factor 2-by- 2 block matrix and the three factor 2-by-2 block matrix cases. We prove that the ranks of the blocks in the larger banded matrix need to necessarily conform to a particular order. We show that for other orders, the banded matrix in question may not even be invertible. We are then concerned with the factorization of the banded matrix into simpler factors. Simpler factors that we consider are those that are purely block diagonal. We show how we can obtain the different factors and develop algorithms and codes to solve for them. We do this for the two factor 2-by-2 and the three factor 2-by-2 matrices. We perform this factorization on both the Toeplitz and non-Toeplitz case for the two factor case, while we do it only for the Toeplitz case in the three factor case. We then look at extending our results when the banded matrix has elements at its corners. We show that this case is not very different from the ones analyzed before. We end our discussion with the solution for the factors of the circulant case. Appendix A deals with a conjecture about the minimum possible rank of a permutation matrix. Appendices B & C deal with some of the miscellaneous properties that we obtain for larger block matrices and from extending some of the previous work done by Strang in this field. / by Venugopalan Srinivasa Gopala Raghavan. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2009. / "September 2009." Cataloged from PDF version of thesis. / Includes bibliographical references (p. 150-157). / This thesis develops a framework for constructing an Evolutionary Design Model (EDM) that would enhance the design of complex systems through an efficient process. The framework proposed is generic and suggests a group of systematic methodologies that eventually lead to a fully realized and integrated design model. Within this model, complexities of the design are handled and the uncertainties of the design evolution are managed. Using the framework, vast design spaces can be searched while solutions are intelligently modified, their performance evaluated, and their results aggregated into a compatible set for design decisions. The EDM is composed of several design states as well as design evolving processes. A design state describes a design at a particular point in time and maps the system's object to the system's requirements and identifies its relation to the context in which the system will operate. A design evolving process involves many sub-processes which include formulation, decomposition, modeling, and integration. These sub-processes are not always carried out in a sequential manner, but rather a continuous move back and forth to previous and subsequent stages is expected. The resulting design model is described as an evolutionary model that moves a system's design from simple abstract states to more complex and detailed states throughout its evolution. / (cont.) The framework utilizes system modeling methodologies that include both logical and mathematical modeling methods. The type of model used within the EDM's evolving processes is highly dependent on and driven by design needs of each process. As the design progresses a shift from logical models to mathematical models occurs within the EDM. Finally, a partial EDM is implemented within the context of a computational design system for Masdar city to demonstrate the application of the proposed framework. / By Anas Alfaris. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2014. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 63-66). / This thesis focuses on visualizing high-dimensional design spaces for early-stage design problems in structural engineering and related disciplines. The design space, which is defined as the n + 1-dimensional surface that relates n design variables to a performance metric, contains all possible solutions to a formulated design problem. Graphical views of the design space are highly useful for designers because they organize a wide range of design possibilities in a compact, intuitive, and logical manner, illuminating global patterns, variable behaviors and relationships, and the nature of paths taken during iterative design processes. Design problems with two or fewer variables can easily be visualized in Euclidian space, through a curve or surface, but high-dimensional problems are difficult to display graphically. This is the key challenge addressed in this thesis. The thesis includes a critical review of existing methods for high-dimensional design space visualization, highlighting the unmet needs across a range of approaches. In response to these needs, the thesis makes a key contribution in the form of a new design space visualization method, called isoperforming parallel coordinate clusters (IPC clusters), that overcomes the issues of previous techniques. The IPC cluster approach is demonstrated on several conceptual structural design problems, and its application in optimization, directed exploration, and related design strategies is illustrated. Finally, the thesis concludes with a discussion of applications, impact, and future research directions. Key words: design space visualization, conceptual design, structural design, structural optimization / by Caitlin T. Mueller. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2013. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 138-140). / In the airline industry, spill refers to passenger demand turned away from a flight because demand has exceeded capacity. The accurate estimation of spill and the lost revenue it implies is an important parameter in airline fleet assignment models, where improved estimates lead to more profitable assignments. Previous models for spill estimation did not take into account the effects of passenger choice and airline revenue management. Since revenue management systems protect seats for later-arriving higher fare passengers, revenue management controls will influence the number of spilled passengers and their value because they will restrict availability to lower fare passengers even if seats on the aircraft are available. This thesis examines the effect of various revenue management systems and fare structures on spill, and, in turn, the marginal value of incremental capacity. The Passenger Origin Destination Simulator is used to simulate realistic passenger booking scenarios and to measure the value of spilled demand. A major finding of the research is that in less restricted fare structures and with traditional revenue management systems, increasing capacity on a flight leads to buy-down which can result in negative marginal revenues and therefore revenue losses. This behavior is contrary to conventional wisdom and is not considered in existing spill models. On the other hand, marginal revenues at low capacities are greater than would be predicted by first-choice-only spill models because some passengers will sell-up to higher fares to avoid spilling out. Additionally, because of passenger recapture between flights, adding capacity to one flight can lead to revenue losses on another. Therefore, the marginal value of incremental capacity is not always positive. Negative marginal revenues and associated revenue losses with increasing capacity can at least be partially mitigated by using more advanced revenue management forecasting and optimization algorithms which take into account passenger willingness to pay. The thesis also develops a heuristic analytical method for estimating spill costs which takes into account the effects of passenger sell-up, where previous models tend to underestimate the spill cost by only modeling passengers' first choices. The heuristic demonstrates improved estimates of passenger spill: in particular, in restricted fare structures and for moderate amounts of spill, the model exhibits approximate relative errors on the order of 5%, a factor of two improvement over previous models. / by Michael Abramovich. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2016. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 49-50). / Microgrids and distributed generation are predicted to become extremely dominant in developing nations, and will be largely beneficial to both electricity suppliers and consumers. With the penetration of renewable energy into the electricity supply, to maintain a balance between power supply and demand is becoming more difficult. Nevertheless, it is quite feasible that large electrical storage systems such as batteries can efficiently mitigate problems caused by the intermittency of renewables, and thus enable stable adoption of such power sources. In order to understand how the energy capacity and power characteristics of batteries should be specified to optimize economic or socioeconomic benefits, an optimizing strategy for battery usage in microgrids energy scheduling was constructed. This strategy is based on the past power consumption, predictions of day-ahead power consumption, and historical trends of seasonal and daily trends, which gives a nonlinear, discontinuous and high dimensional objective function. Optimizing such an objective function is found to be very computational intensive and complex. In this paper, the nature of this large-scale optimization problem is studied. For real time dispatch, four optimization methods including active-set, interior-point method, sequential quadratic programming (SQP) and trust-region-reflective are discussed and compared to find the relatively fast and robust optimization algorithm. The computation was implemented by using the MATLAB nonlinear programming solver 'fmincon'. Three main objectives are carried out to improve the efficiency of solving this optimization problem: (1) determination of the mathematical& physical definitions of tolerances and discussion on convergence criteria with the corresponding tolerances; (2) Study and comparison on influences of the initial condition and the behavior of the objective function (highly related to peak demand charge); and (3) suggestions on modification of the model to achieve reduction of the computation time whilst maintain acceptable accuracy. / by Lutao Xie. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2010. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 55). / This project aims to improve the operation and planning of a specific type of manufacturing system, a serial flow line that entails a sequence of process stages. The objective is to investigate inventory policy, raw material ordering policy, production planning and scheduling policy, in the face of demand uncertainty, raw material arrival uncertainty and in-process failure. The tactics being explored include segmenting the serial flow line with decoupling buffers to protect against demand and raw material arrival uncertainty, and production smoothing to reduce production-related costs and the variance in upstream processes. Key policies for each segment include a work release policy from the decoupling buffer before the segment, and a production control policy to manage work-in-process inventory level within the segment and to meet inventory targets in each downstream decoupling buffer. We also explore raw material ordering policy with fixed ordering times, long lead-times and staggered deliveries in a make-to-order setting. A tactical model has been developed to capture the key uncertainties and to determine the operating tactics through analysis and optimization. This study also includes extensive numerical tests to validate the output of the tactical model as well as to gain a better understanding of how the tactical model reacts to different parameter variations. / by Bin Huang. / S.M.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2017. / Cataloged from PDF version of thesis. / Includes bibliographical references (pages 109-110). / This thesis studies the effects of heterogeneous information on traffic equilibria and the resulting travel costs (both individual and social) when commuters make departure time choices to cross an unreliable bottleneck link. Increasing adoption and improved predictive abilities of Traveler Information Systems (TIS) enable commuters to plan their trips; however, there are inherent heterogeneities in information access and TIS accuracies, which can significantly affect commuters' choices and the equilibrium level of congestion. Our work addresses the open problem raised in Arnott et al. (1991) about the need to consider asymmetrically informed commuters in the bottleneck model of traffic congestion. We consider a Bayesian game with two heterogeneous commuter populations: one population is privately informed of the realized network state while the other only knows the public information about the distribution of states. We characterize the equilibrium of the game, in which each population chooses a departure rate function over time to minimize its expected cost based on its private belief about the state and the behavior of the other population. We provide a full equilibrium characterization for the complete range of values of link reliability, incident probability, and information penetration. This uncovers a rich structure of population strategies, which can broadly be categorized into two distinct regimes. Specifically, when information penetration is above a certain threshold, the populations' equilibrium strategies are non-unique, and the relative value of information (Vol) is 0, i.e. the two populations face the same cost. However, the aggregate departure rate function is unique and remains unchanged as more commuters gain access to information. On the other hand, when information penetration is below the threshold, equilibrium is unique, and Vol is positive and decreasing in information penetration. Importantly, we find that the lowest social cost is always achieved when a certain fraction of commuters are uninformed. The more unreliable the link, the higher the optimal information penetration that achieves this minimum. We define the Value of Heterogeneity (VoH) as the difference between the optimal social cost and the cost under complete information penetration, and find that it is significant (upto 20%) under practically relevant conditions. / by Zaid S. Khan. / S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2013. / Cataloged from PDF version of thesis. / Includes bibliographical references (p. 73-75). / In this research we model a job shop that produces a set of discrete parts in a make-to-stock setting. The intent of the research is to develop a planning model to determine the optimal operating tactics that minimize the relevant manufacturing costs subject to workload variability and capacity limits. We model the interplay of three key components in the job shop, namely, the production frequency for each part, the variability of production at each work station, and the level of parts inventory. We consider two operating tactics (decision variables): the production lot size for each part and the planned lead time for each work station. We model the relevant manufacturing costs, entailing production overtime costs and inventory-related costs (finished parts, work-in-process, and raw materials), as functions of these decision variables. We formulate a non-linear optimization model and implement it in the Excel Spreadsheet. We solve the model with the premium Excel Solver to determine the minimum-cost operating tactics. We test the model with both hypothetical and actual factory data from our research sponsor. The target factory processes 133 product parts on 59 work stations. The results are consistent with our intuition and demonstrate the potential value from optimizing over these tactics; these tests also provide some managerial insights on the application of these operating tactics. / by Rong Yuan. / S.M.