The petrochemical Industry is based upon the production of chemicals from petroleum and also deals with chemicals manufactured from the by products of petroleum refinery. At the preliminary stages of chemical plant development and design, the choice of chemical process route is the key design decision. In the past, economics were the most important criterion in choosing the chemical process route. Modified studies imply that the two of the important planning objectives for a petrochemical industry, environmental risk and the industrial safety involved in the development. For the economic evaluation of the industry, and for the proposed final chemicals products in the development, simple and clear economic indicators are needed to be able to indicate an overall economic gain in the development. Safety, as the second objective, is considered in this study as the risk of chemical plant accidents. Risk, when used as an objective function, has to have a simple quantitative form to be easily evaluated for a large number of possible plants in the petrochemical network. The simple quantitative form adopted is a safety index that enables the number of people affected by accidents resulting in chemical releases to be estimated. Environmental issues have now become important considerations due to the potential harmful impacts produced by chemical releases. In this study third objective of planning petrochemical industry was developed by involving environmental considerations and environmental risk index. Indiana Relative Chemical Hazard Score (IRCHS) was used to allow chemical industries routes to be ranked by environmental hazardous. The focus of this work is to perform early planning and decision-making for a petrochemical plants network for maximum economical gain, minimum risk to people from possible chemical accidents and minimum environmental risk. The three objectives, when combined with constraints describing the desired or the possible structure of the industry, will form an optimization model. For this study, the petrochemical planning model consists of a Mixed Integer Linear Programming (MILP) model to select the best routes from the basic feedstocks available in Kuwait -as a case study- to the desired final products with multiple objective functions. The economic, safety and environmental risk objectives usually have conflicting needs. The presence of several conflicting objectives is typical when planning. In many cases, where optimization techniques are utilized, the multiple objectives are simply aggregated into one single objective function. Optimization is then conducted to get one optimal result. This study, which is concerned with economic and risk objectives, leads to the identification of important factors that affecting the building-up of environmental management system for petrochemical industry. Moreover, the procedure of modelling and model solution can be used to simplify the decision-making for complex or large systems such as the petrochemical industry. It presents the use of simple multiple objective optimization tools within a petrochemical planning tool formulated as a mixed integer linear programming model. Such a tool is particularly useful when the decision-making task must be discussed and approved by officials who often have little experience with optimization theories

The petrochemical Industry is based upon the production of chemicals from petroleum and also deals with chemicals manufactured from the by products of petroleum refinery. At the preliminary stages of chemical plant development and design, the choice of chemical process route is the key design decision. In the past, economics were the most important criterion in choosing the chemical process route. Modified studies imply that the two of the important planning objectives for a petrochemical industry, environmental risk and the industrial safety involved in the development. For the economic evaluation of the industry, and for the proposed final chemicals products in the development, simple and clear economic indicators are needed to be able to indicate an overall economic gain in the development. Safety, as the second objective, is considered in this study as the risk of chemical plant accidents. Risk, when used as an objective function, has to have a simple quantitative form to be easily evaluated for a large number of possible plants in the petrochemical network. The simple quantitative form adopted is a safety index that enables the number of people affected by accidents resulting in chemical releases to be estimated. Environmental issues have now become important considerations due to the potential harmful impacts produced by chemical releases. In this study third objective of planning petrochemical industry was developed by involving environmental considerations and environmental risk index. Indiana Relative Chemical Hazard Score (IRCHS) was used to allow chemical industries routes to be ranked by environmental hazardous. The focus of this work is to perform early planning and decision-making for a petrochemical plants network for maximum economical gain, minimum risk to people from possible chemical accidents and minimum environmental risk. The three objectives, when combined with constraints describing the desired or the possible structure of the industry, will form an optimization model. For this study, the petrochemical planning model consists of a Mixed Integer Linear Programming (MILP) model to select the best routes from the basic feedstocks available in Kuwait -as a case study- to the desired final products with multiple objective functions. The economic, safety and environmental risk objectives usually have conflicting needs. The presence of several conflicting objectives is typical when planning. In many cases, where optimization techniques are utilized, the multiple objectives are simply aggregated into one single objective function. Optimization is then conducted to get one optimal result. This study, which is concerned with economic and risk objectives, leads to the identification of important factors that affecting the building-up of environmental management system for petrochemical industry. Moreover, the procedure of modelling and model solution can be used to simplify the decision-making for complex or large systems such as the petrochemical industry. It presents the use of simple multiple objective optimization tools within a petrochemical planning tool formulated as a mixed integer linear programming model. Such a tool is particularly useful when the decision-making task must be discussed and approved by officials who often have little experience with optimization theories

This thesis presents novel approaches that use interior point concepts in solving mixed integer programs. Particularly, we use the analytic center cutting plane method to improve three of the main components of the branch-and-bound algorithm: cutting planes, heuristics, and branching. First, we present an interior point branch-and-cut algorithm for structured integer programs based on Benders decomposition. We explore using Benders decomposition in a branch-and-cut framework where the Benders cuts are generated using the analytic center cutting plane method. The algorithm is tested on two classes of problems: the capacitated facility location problem and the multicommodity capacitated fixed charge network design problem. For the capacitated facility location problem, the proposed approach was on average 2.5 times faster than Benders-branch-and-cut and 11 times faster than classical Benders decomposition. For the multicommodity capacitated fixed charge network design problem, the proposed approach was 4 times faster than Benders-branch-and-cut while classical Benders decomposition failed to solve the majority of the tested instances. Second, we present a heuristic algorithm for mixed integer programs based on interior points. As integer solutions are typically in the interior, we use the analytic center cutting plane method to search for integer feasible points within the interior of the feasible set. The algorithm searches along two line segments that connect the weighted analytic center and two extreme points of the linear programming relaxation. Candidate points are rounded and tested for feasibility. Cuts aimed to improve the objective function and restore feasibility are then added to displace the weighted analytic center until a feasible integer solution is found. The algorithm is composed of three phases. In the first, points along the two line segments are rounded gradually to find integer feasible solutions. Then in an attempt to improve the quality of the solutions, the cut related to the bound constraint is updated and a new weighted analytic center is found. Upon failing to find a feasible integer solution, a second phase is started where cuts related to the violated feasibility constraints are added. As a last resort, the algorithm solves a minimum distance problem in a third phase. For all the tested instances, the algorithm finds good quality feasible solutions in the first two phases and the third phase is never called. Finally, we present a new approach to generate good general branching constraints based on the shape of the polyhedron. Our approach is based on approximating the polyhedron using an inscribed ellipsoid. We use Dikin's ellipsoid which we calculate using the analytic center. We propose to use the disjunction that has a minimum width on the ellipsoid. We use the fact that the width of the ellipsoid in a given direction has a closed form solution in order to formulate a quadratic problem whose optimal solution is a thin direction of the ellipsoid. While solving a quadratic problem at each node of the branch-and-bound tree is impractical, we use a local search heuristic for its solution. Computational testing conducted on hard integer problems from MIPLIB and CORAL showed that the proposed approach outperforms classical branching.

The Discrete Wavelet Transform (DWT) is a popular tool in the field of image and video compression applications. Because of its multi-resolution representation capability, the DWT has been used effectively in applications such as transient signal analysis, computer vision, texture analysis, cell detection, and image compression. Daubechies wavelets are one of the popular transforms in the wavelet family. Daubechies filters provide excellent spatial and spectral locality-properties which make them useful in image compression.<p> In this thesis, we present an efficient implementation of a shared hardware core to compute two 8-point Daubechies wavelet transforms. The architecture is based on a new two-level folded mapping technique, an improved version of the Algebraic Integer Quantization (AIQ). The scheme is developed on the factorization and decomposition of the transform coefficients that exploits the symmetrical and wrapping structure of the matrices. The proposed architecture is parallel, pipelined, and multiplexed. Compared to existing designs, the proposed scheme reduces significantly the hardware cost, critical path delay and power consumption with a higher throughput rate.<p> Later, we have briefly presented a new mapping scheme to error-freely compute the Daubechies-8 tap wavelet transform, which is the next transform of Daubechies-6 in the Daubechies wavelet series. The multidimensional technique maps the irrational transformation basis coefficients with integers and results in considerable reduction in hardware and power consumption, and significant improvement in image reconstruction quality.

Based on the recent successes in stochastic linear programming and mixed integer programming, in this thesis we combine these two important areas of mathematical programming; specifically we study stochastic integer programming. We first study a simple and important stochastic integer programming problem, called stochastic uncapacitated lot-sizing (SLS), which is motivated by production planning under uncertainty. We describe a multi-stage stochastic integer programming formulation of the problem and develop a family of valid inequalities, called the (Q, S) inequalities. We establish facet-defining conditions and show that these inequalities are sufficient to describe the convex hull of integral solutions for two-period instances. A separation heuristic for (Q, S) inequalities is developed and incorporated into a branch-and-cut algorithm. A computational study verifies the usefulness of the inequalities as cuts. Then, motivated by the polyhedral study of (Q, S) inequalities for SLS, we analyze the underlying integer programming scheme for general stochastic integer programming problems. We present a scheme for generating new valid inequalities for mixed integer programs by taking pair-wise combinations of existing valid inequalities. The scheme is in general sequence-dependent and therefore leads to an exponential number of inequalities. For some special cases, we identify combination sequences that lead to a manageable set of all non-dominated inequalities. For the general scenario tree case, we identify combination sequences that lead to non-dominated inequalities. We also analyze the conditions such that the inequalities generated by our approach are facet-defining and describe the convex hull of integral solutions. We illustrate the framework for some deterministic and stochastic integer programs and we present computational results which show the efficiency of adding the new generated inequalities as cuts.

Classification, the development of rules for the allocation of observations to one or more groups, is a fundamental problem in machine learning and has been applied to many problems in medicine and business. We consider aspects of a classification model developed by Gallagher, Lee, and Patterson that is based on a result by Anderson. The model seeks to maximize the probability of correct G-group classification, subject to limits on misclassification probabilities. The mixed-integer programming formulation of the model is an empirical method for estimating the parameters of an optimal classification rule, which are identified as coefficients of linear functions by Anderson. The model is shown to be a consistent method for estimating the parameters of the optimal solution to the problem of maximizing the probability of correct classification subject to limits on inter-group misclassification probabilities. A polynomial time algorithm is described for two-group instances. The method is NP-complete for a general number of groups, and an approximation is formulated as a mixed-integer program (MIP). The MIP is difficult to solve due to the formulation of constraints wherein certain variables are equal to the maximum of a set of linear functions. These constraints are conducive to an ill-conditioned coefficient matrix. Methods for generating edges of the conflict graph and conflict hypergraphs are discussed. The conflict graph is employed for finding cuts in a branch-and-bound framework. This technique and others lead to improvement in solution time over industry-standard software on instances generated by real-world data. The classification accuracy of the model in relation to standard classification methods on real-world and simulated data is also noted.

The purpose of this study was to develop and test an optimization model that will provide a deployment plan of emission reduction technologies to reduce emissions from non-road equipment. The focus of the study was on the counties of Texas that have nonattainment (NA) and near-nonattainment (NNA) status. The objective of this research was to develop methodologies that will help to deploy emission reduction technologies for non-road equipment of TxDOT to reduce emissions in a cost effective and optimal manner. Three technologies were considered for deployment in this research, (1) hydrogen enrichment (HE), (2) selective catalytic reduction (SCR) and (3) fuel additive (FA). Combinations of technologies were also considered in the study, i.e. HE with FA, and SCR with FA. Two approaches were investigated in this research. The first approach was "Method 1" in which all the technologies, i.e. FA, HE and SCR were deployed in the NA counties at the first stage. In the second stage the same technologies were deployed in the NNA counties with the remaining budget, if any. The second approach was called "Method 2" in which all the technologies, i.e. FA, HE and SCR were deployed in the NA counties along with deploying only FA in the NNA counties at the first stage. Then with the remaining budget, SCR and HE were deployed in the NNA counties in the second stage. In each of these methods, 2 options were considered, i.e. maximizing NOx reduction with and without fuel economy consideration in the objective function. Thus, the four options investigated each having different mixes of emission reduction technologies include Case 1A: Method 1 with fuel economy consideration; Case 1B: Method 1 without fuel economy consideration; Case 2A: Method 2 with fuel economy consideration; and Case 2B: Method 2 without fuel economy consideration and were programmed with Visual C++ and ILOG CPLEX. These four options were tested for budget amounts ranging from $500 to $1,183,000 and the results obtained show that for a given budget one option representing a mix of technologies often performed better than others. This is conceivable because for a given budget the optimization model selects an affordable option considering the cost of technologies involved while at the same time maximum emission reduction, with and without fuel economy consideration, is achieved. Thus the alternative options described in this study will assist the decision makers to decide about the deployment preference of technologies. For a given budget, the decision maker can obtain the results for total NOx reduction, combined diesel economy and total combined benefit using the four models mentioned above. Based on their requirements and priorities, they can select the desired model and subsequently obtain the required deployment plan for deploying the emission reduction technologies in the NA and NNA counties.

Supply chain network design (SCND) identifies the production and distribution resources essential to maximizing a network’s profit. Once implemented, a SCND impacts a network’s performance for the long-term. This dissertation extends the SCND literature both in terms of model scope and solution approach. The SCND problem can be more realistically modeled to improve design decisions by including: the location, capacity, and technology attributes of a resource; the effect of the economies of scale on the cost structure; multiple products and multiple levels of supply chain hierarchy; stochastic, dynamic, and correlated demand; and the gradually unfolding uncertainty. The resulting multistage stochastic mixed-integer program (MSMIP) has no known general purpose solution methodology. Two decomposition approaches—end-of-horizon (EoH) decomposition and nodal decomposition—are applied. The developed EoH decomposition exploits the traditional treatment of the end-of-horizon effect. It rests on independently optimizing the SCND of every node of the last level of the scenario-tree. Imposing these optimal configurations before optimizing the design decisions of the remaining nodes produces a smaller and thus easier to solve MSMIP. An optimal solution results when the discount rate is 0 percent. Otherwise, this decomposition deduces a bound on the optimality-gap. This decomposition is neither SCND nor MSMIP specific; it pertains to any application sensitive to the EoH-effect and to special cases of MSMIP. To demonstrate this versatility, additional computational experiments for a two-stage mixed-integer stochastic program (SMIP) are included. This dissertation also presents the first application of nodal decomposition in both SCND and MSMIP. The developed column generation heuristic optimizes the nodal sub-problems using an iterative procedure that provides a restricted master problem’s columns. The heuristic’s computational efficiency rests on solving the sub-problems independently and on its novel handling of the master problem. Conceptually, it reformulates the master problem to avoid the duality-gap. Technologically, it provides the first application of Leontief substitution flow problems in MSMIP and thereby shows that hypergraphs lend themselves to loosely coupled MSMIPs. Computational results demonstrate superior performance of the heuristic approach and also show how this heuristic still applies when the SCND problem is modeled as a SMIP where the restricted master problem is a shortest-path problem.

Modern system-on-chip consists of an increasing number of highly complex modules. The quality of the interfaces and throughput of communication connections between these components are crucial to the performance of the system, since communication is often the main bottleneck in modern application domains like multimedia. In this thesis, a bus-based communication architecture synthesis approach is proposed. Given the result of hardware/software partitioning and pipelined scheduling, the proposed approach constructs a communication topology which meets the constraints. We begin with the minimum number of AHB and an APB, each time we add an AHB and do some transformation such as merging or setting local buses. Our goal is to find the bus architecture which has minimum area. We use integer programming to construct a bus architecture each time, until the bus architecture with the minimum area are found. By this approach, we can save a lot of time required to design the communication architecture manually.

The primary design goal of many embedded systems for multimedia applications is usually meeting the performance requirement at a minimum cost. In this thesis, we proposed two different ILP based approaches for hardware/software (HW/SW) partitioning and pipelined scheduling of embedded systems for multimedia applications. One ILP approach solves the HW/SW partitioning and pipelined scheduling problem simultaneously. Another ILP approach separates the HW/SW partitioning and pipelined scheduling problem into two phases. The first phase is focusing on the HW/SW partitioning and mapping problem. Second phase is used to solve the pipelined scheduling problem. The two ILP approaches not only partition and map each computation task of a particular multimedia application onto a component of the heterogeneous multiprocessor architecture, but also schedules and pipelines the execution of these computation tasks while considering communication time. For the first ILP model, the objective is to minimize the total component cost and the number of pipeline stages subject to the throughput constraint. In the second ILP approach, the objective of the first phase and second phase is to minimize the total component cost and the number of pipeline stages subject to the throughput constraint, respectively. Finally, experiments on three real multimedia applications (JPEG Encoder, MP3 Decoder, Wavelet Video Encoder) are used to demonstrate the effectiveness of the proposed approaches.