71 
Developing Innovative Designs with Manufacturing Capability Using the Level Set MethodBaradaran Nakhjavani, Omid 05 September 2012 (has links)
This thesis discusses how to use topology and shape optimization, specifically the level set method, for innovative design. The level set method is a numerical algorithm that simulates the expansion of dynamic implicit surfaces. In this research, the equations for manufacturability are generated and solved through use of the level set method joined with the COMSOL multiphysics package. Specific constraints are added to make the optimization practical for engineering design. The resulting method was applied to design the best underlying support structure, conforming to both curvature and manufacturability constraints, for the longerons used with the International Space Station solar panels.

72 
Probabilistic Choice Models for Product Pricing Using Reservation PricesHui, Betsy January 2007 (has links)
The problem of pricing a product line to maximize profits is an important challenge faced by many companies. To address this problem, we discuss four different probabilistic choice models that are based on reservation prices: the Uniform Distribution Model, the Weighted Uniform Model, the ShareofSurplus Model, and the Price Sensitive Model. They are formulated as convex mixedinteger mathematical programs. We explore the properties and additional valid inequalities of these formulations. We also compare their optimal solutions on a set of inputs.
In general, the Uniform Distribution, Weighted Uniform, and Price Sensitive Models have the same optimal solution while the ShareofSurplus Model gives a different solution in many cases.
We develop a few heuristics for finding good feasible solutions. These simple and efficient heuristics perform well and help to improve the solution time.
Computational results of solving problem instances of various sizes are shown.

73 
Geometry of convex sets arising from hyperbolic polynomialsMyklebust, Tor Gunnar Josefsson Jay 29 August 2008 (has links)
This thesis focuses on convex sets and convex cones defined using hyperbolic polynomials.
We first review some of the theory of convex sets in $\R^d$ in general. We then review some classical algebraic theorems concerning polynomials in a single variable, as well as presenting a few more modern results about them. We then discuss the theory of hyperbolic polynomials in several variables and their associated hyperbolicity cones. We survey various ways to build and decompose hyperbolic cones and we prove that every nontrivial hyperbolic cone is the intersection of its derivative cones. We conclude with a brief discussion of the set of extreme rays of a hyperbolic cone.

74 
Exact, Approximate, and Online Algorithms for Optimization Problems Arising in DVD AssignmentPearson, James Ross January 2009 (has links)
Zip.ca is an online DVD rental company that faces two major operational problems:
calculation of the assignment of DVDs to customers every thirty minutes
throughout the day and purchasing of new inventory in regular intervals.
In this thesis, we model these two problems and develop algorithms to solve
them. In doing so, we encounter many theoretical problems that are both applicable
to Zip’s operations and intrinsically interesting problems independent of the
application.
First, we note that the assignment problem facing Zip is inherently in an online
setting. With returns of DVDs being processed throughout the day, the dataset
is constantly changing. Although the ideal solution would be to wait until the
end of the day to make decisions, physical work load capacities prevent this. For
this reason we discuss two online problems, online 01 budgeted matching and
the budgeted Adwords auction. We present a 1/(2 w_max/w_min)competitive algorithm for the online 01 budgeted matching problem, and prove that this is the best possible
competitive ratio possible for a wide class of algorithms. We also give a (1− (S+1)/(S+e) )competitive algorithm for the budgeted Adwords auction as the size of the bids
and cost get small compared to the budgets, where S is the ratio of the highest and
lowest ratios of bids to costs.
We suggest a linear programming approach to solve Zip’s assignment problem.
We develop an integer program that models the Bmatching instance with additional
constraints of concern to Zip, and prove that this integer program belongs to
a larger class of integer programs that has totally unimodular constraint matrices.
Thus, the assignment problem can be solved to optimality every thirty minutes.
We additionally create a test environment to check daily performance, and provide
realtime implementation results, showing a marked improvement over Zip’s old
algorithm.
We show that Zip’s purchasing problem can be modeled by the matching augmentation
problem defined as follows. Given a graph with vertex capacities and
costs, edge weights, and budget C, find a purchasing of additional node capacity of
cost at most C that admits a Bmatching of maximum weight. We give a PTAS for
this problem, and then present a special case that is polynomial time solvable that
still models Zip’s purchasing problem, under the assumption of uniform costs.
We then extend the augmentation idea to matroids and present matroid augmentation,
matroid knapsack, and matroid intersection knapsack, three NPhard
problems. We give an FPTAS for matroid knapsack by dynamic programming,
PTASes for the other two, and demonstrate applications of these problems.

75 
Probabilistic Choice Models for Product Pricing Using Reservation PricesHui, Betsy January 2007 (has links)
The problem of pricing a product line to maximize profits is an important challenge faced by many companies. To address this problem, we discuss four different probabilistic choice models that are based on reservation prices: the Uniform Distribution Model, the Weighted Uniform Model, the ShareofSurplus Model, and the Price Sensitive Model. They are formulated as convex mixedinteger mathematical programs. We explore the properties and additional valid inequalities of these formulations. We also compare their optimal solutions on a set of inputs.
In general, the Uniform Distribution, Weighted Uniform, and Price Sensitive Models have the same optimal solution while the ShareofSurplus Model gives a different solution in many cases.
We develop a few heuristics for finding good feasible solutions. These simple and efficient heuristics perform well and help to improve the solution time.
Computational results of solving problem instances of various sizes are shown.

76 
Geometry of convex sets arising from hyperbolic polynomialsMyklebust, Tor Gunnar Josefsson Jay 29 August 2008 (has links)
This thesis focuses on convex sets and convex cones defined using hyperbolic polynomials.
We first review some of the theory of convex sets in $\R^d$ in general. We then review some classical algebraic theorems concerning polynomials in a single variable, as well as presenting a few more modern results about them. We then discuss the theory of hyperbolic polynomials in several variables and their associated hyperbolicity cones. We survey various ways to build and decompose hyperbolic cones and we prove that every nontrivial hyperbolic cone is the intersection of its derivative cones. We conclude with a brief discussion of the set of extreme rays of a hyperbolic cone.

77 
Exact, Approximate, and Online Algorithms for Optimization Problems Arising in DVD AssignmentPearson, James Ross January 2009 (has links)
Zip.ca is an online DVD rental company that faces two major operational problems:
calculation of the assignment of DVDs to customers every thirty minutes
throughout the day and purchasing of new inventory in regular intervals.
In this thesis, we model these two problems and develop algorithms to solve
them. In doing so, we encounter many theoretical problems that are both applicable
to Zip’s operations and intrinsically interesting problems independent of the
application.
First, we note that the assignment problem facing Zip is inherently in an online
setting. With returns of DVDs being processed throughout the day, the dataset
is constantly changing. Although the ideal solution would be to wait until the
end of the day to make decisions, physical work load capacities prevent this. For
this reason we discuss two online problems, online 01 budgeted matching and
the budgeted Adwords auction. We present a 1/(2 w_max/w_min)competitive algorithm for the online 01 budgeted matching problem, and prove that this is the best possible
competitive ratio possible for a wide class of algorithms. We also give a (1− (S+1)/(S+e) )competitive algorithm for the budgeted Adwords auction as the size of the bids
and cost get small compared to the budgets, where S is the ratio of the highest and
lowest ratios of bids to costs.
We suggest a linear programming approach to solve Zip’s assignment problem.
We develop an integer program that models the Bmatching instance with additional
constraints of concern to Zip, and prove that this integer program belongs to
a larger class of integer programs that has totally unimodular constraint matrices.
Thus, the assignment problem can be solved to optimality every thirty minutes.
We additionally create a test environment to check daily performance, and provide
realtime implementation results, showing a marked improvement over Zip’s old
algorithm.
We show that Zip’s purchasing problem can be modeled by the matching augmentation
problem defined as follows. Given a graph with vertex capacities and
costs, edge weights, and budget C, find a purchasing of additional node capacity of
cost at most C that admits a Bmatching of maximum weight. We give a PTAS for
this problem, and then present a special case that is polynomial time solvable that
still models Zip’s purchasing problem, under the assumption of uniform costs.
We then extend the augmentation idea to matroids and present matroid augmentation,
matroid knapsack, and matroid intersection knapsack, three NPhard
problems. We give an FPTAS for matroid knapsack by dynamic programming,
PTASes for the other two, and demonstrate applications of these problems.

78 
Green Petroleum Refining  Mathematical Models for Optimizing Petroleum Refining Under Emission ConstraintsAli Yusuf, Yusuf 07 August 2013 (has links)
Petroleum refining processes provide the daily requirements of energy for the global market. Each refining process produces wastes that have the capacity to harm the environment if not properly disposed of. The treatment of refinery waste is one of the most complex issues faced by refinery managers. Also, the hazardous nature of these wastes makes them rather costly to dispose of for the refineries. In this thesis, system analysis tools are used to design a program that allows for the selection of the optimal control, minimization and treating options for petroleum refinery waste streams. The performance of the developed model is demonstrated via a case study. Optimal mitigation alternatives to meet the emission reduction targets were studied by evaluating their relative impact on the profitable operation of the given facility. It was found that the optimal mitigation steps was to reduce emission precursors by conducting feed switches at the refinery. In all cases, the optimal solution did not include a capital expansion of the emission control facilities and equipment.

79 
Short horizon optimal control of nonlinear systems via discrete state space realizationFoley, Dawn Christine 05 1900 (has links)
No description available.

80 
A method to identify movelimits in structural optimizationCimtalay, Selçuk 12 1900 (has links)
No description available.

Page generated in 0.1119 seconds