The effective maintenance scheduling of power system generators is very important to a power utility for the economical and reliable operation of a power system. Many mathematical methods have been implemented for generator maintenance scheduling (GMS). However, these methods have many limitations and require many approximations. Here a Genetic Algorithm is proposed for GMS problems in order to overcome some of the limitations of the conventional methods. This paper formulates a general GMS problem using a reliability criterion as an integer programming problem, and demonstrates the use of GAs with three different problem encodings: binary, binary for integer and integer. The GA performances for each of these representations are analysed and compared for a test problem based on a practical power system scenario. The effects of different GA parameters are also studied. The results show that the integer GA is a very effective method for GMS problems.

This research project examined the ability to combine spatial data analysis and mathematical programming techniques in developing a multiple-use land management plan for a public forest in northeastern Virginia. Linear programming-based timber management scheduling models were constructed utilizing the Model I formulation of Johnson and Scheurman (1977). The models were formulated as mixed strata-based, area-based models (Johnson and Stuart 1987) that maximized present net worth subject to a fixed timberland base, an ending inventory requirement, workload control restrictions, and harvest volume control restrictions. The linear programming-based models which incorporated spatial data analysis capabilities were solved using mixed-integer programming. The model was used to assess the costs of implementing spatial restrictions designed to address forest resource management concerns, in particular, timber production and reserve status acreage for wildlife habitat purposes. The impact of imposing alternative spatial stand allocation requirements and different levels of reserve status acreage was evaluated by measuring the cost in terms of reductions in the present net value (PNV) of timber benefits and timber harvest volumes. The results indicate that the optimal solution value is more sensitive to the level of reserve status acreage imposed on the model than to the spatial restrictions for stand allocations placed on the model. / Master of Science

This dissertation addresses the development of optimization models for hospital evacuation logistics, as well as the analyses of various resource management strategies in terms of the equity of evacuation plans generated. We first formulate the evacuation transportation problem of a hospital as an integer programming model that minimizes the total evacuation risk consisting of the threat risk necessitating evacuation and the transportation risk experienced en route. Patients, categorized based on medical conditions and care requirements, are allocated to a limited fleet of vehicles with various medical capabilities and capacities to be transported to receiving beds, categorized much like patients, at the alternative facilities. We demonstrate structural properties of the underlying transportation network that enables the model to be used for both strategic planning and operational decision making. Next, we examine the resource management and equity issues that arise when multiple hospitals in a region are evacuated. The efficiency and equity of the allocation of resources, including a fleet of vehicles, receiving beds, and each hospital\'s loading capacity, determine the performance of the optimal evacuation plan. We develop an equity modeling framework, where we consider equity among evacuating hospitals and among patients. The range of equity of optimal solutions is investigated and properties of optimal and equitable solutions based on risk-based utility functions are analyzed. Finally, we study the integration of the transportation problem with the preceding hospital building evacuation. Since, in practice, the transportation plan depends on the pace of building evacuation, we develop a model that would generate the transportation plan subject to the output of hospital building evacuation. The optimal evacuation plans are analyzed with respect to resource utilization and patient prioritization schemes. Parametric analysis of the resource constraints is provided along with managerial insights into the assessment of evacuation requirements and resource allocation. In order to demonstrate the performance of the proposed models, computational results are provided using case studies with real data obtained from the second largest hospital in Virginia. / Ph. D.

Under the envisioned smart city paradigm, there is an increasing demand for the coordinated operation of our infrastructure networks. In this context, this thesis puts forth a comprehensive toolbox for the optimization of electric power and water distribution networks. On the analytical front, the toolbox consists of novel mixed-integer (non)-linear program (MINLP) formulations; convex relaxations with optimality guarantees; and the powerful technique of McCormick linearization. On the application side, the developed tools support the operation of each of the infrastructure networks independently, but also towards their joint operation. Starting with water distribution networks, the main difficulty in solving any (optimal-) water flow problem stems from a piecewise quadratic pressure drop law. To efficiently handle these constraints, we have first formulated a novel MINLP, and then proposed a relaxation of the pressure drop constraints to yield a mixed-integer second-order cone program. Further, a novel penalty term is appended to the cost that guarantees optimality and exactness under pre-defined network conditions. This contribution can be used to solve the WF problem; the OWF task of minimizing the pumping cost satisfying operational constraints; and the task of scheduling the operation of tanks to maximize the water service time in an area experiencing electric power outage. Regarding electric power systems, a novel MILP formulation for distribution restoration using binary indicator vectors on graph properties alongside exact McCormick linearization is proposed. This can be used to minimize the restoration time of an electric system under critical operational constraints, and to enable a coordinated response with the water utilities during outages. / Master of Science / The advent of smart cities has promoted research towards interdependent operation of utilities such as water and power systems. While power system analysis is significantly developed due to decades of focused research, water networks have been relying on relatively less sophisticated tools. In this context, this thesis develops Advanced efficient computational tools for the analysis and optimization for water distribution networks. Given the consumer demands, an optimal water flow (OWF) problem for minimizing the pump operation cost is formulated. Developing a rigorous analytical framework, the proposed formulation provides significant computational improvements without compromising on the accuracy. Explicit network conditions are provided that guarantee the optimality and feasibility of the obtained OWF solution. The developed formulation is next used to solve two practical problems: the water flow problem, that solves the complex physical equations yielding nodal pressures and pipeline flows given the demands/injections; and an OWF problem that finds the best operational strategy for water utilities during power outages. The latter helps the water utility to maximize their service time during power outages, and helps power utilities better plan their restoration strategy. While the increased instrumentation and automation has enabled power utilities to better manage restoration during outages, finding an optimal strategy remains a difficult problem. The operational and coordination requirements for the upcoming distributed resources and microgrids further complicate the problem. This thesis develops a computationally fast and reasonably accurate power distribution restoration scheme enabling optimal coordination of different generators with optimal islanding. Numerical tests are conducted on benchmark water and power networks to corroborate the claims of the developed formulations.

The sponsor of the thesis is the Composite Unit of AIRBUS Nantes plant, which manufactures aircraft composite. The basic process to manufacture composite parts is to lay-up raw composite material on a tool and involves very costly means and raw material. This process can be modeled as a two-stage hybrid flow shop problem with specific constraints, particularly prescription constraints on the jobs. This thesis restates the practical problem as a scheduling problem by doing hypotheses and restrictions. Then, it designs a mathematical model based on time-indexed variables. This model has been implemented in an IP solver to solve real based scenarios. A heuristic algorithm is developed for obtaining good solutions quickly. Finally, the heuristic is used to increase the execution speed of the IP solver. This thesis concludes by a discussion on the advantages and disadvantages of each option (IP solver vs. heuristic software) for the sponsor. / Master of Science

The rapid technological advancement in the past century resulted in a decreased life cycle of a large number of products and, consequently, increased the rate of technological obsolescence. The disposal of obsolete products has resulted in rapid landfilling and now poses a major environmental threat. The governments in many countries around the world have started imposing regulations to curb uncontrolled product disposal. The consumers, too, are now aware of adverse effects of product disposal on environment and increasingly favor environmentally benign products. In the wake of imminent stringent government regulations and the consumer awareness about ecosystem-friendly products, the manufacturers need to think about the alternatives to product disposal. One way to deal with this problem is to disassemble an obsolete product and utilize some of its components/subassemblies in the manufacturing of new products. This seems to be a promising solution because products now-a-days are made in accordance with the highest quality standards and, although an obsolete product may not be in the required functional state as a whole, it is possible that several of its components or subassemblies are still in near perfect condition. However, product disassembly is a complex task requiring human labor as well as automated processes and, consequently, a huge amount of monetary investment. This research addresses a disassembly optimization problem, which aims at minimizing the costs associated with the disassembly process (namely, the costs of breaking the joints and the sequence dependent set-up cost associated with disassembly operations), while maximizing the benefits resulting from recovery of components/subassemblies from a product. We provide a mathematical abstraction of the disassembly optimization problem in the form of integer-programming models. One of our formulations includes a new way of modeling the subtour elimination constraints (SECs), which are usually encountered in the well-known traveling salesman problems. Based on these SECs, a new valid formulation for asymmetric traveling salesman problem (ATSP) was developed. The ATSP formulation was further extended to obtain a valid formulation for the precedence constrained ATSP. A detailed experimentation was conducted to compare the performance of the proposed formulations with that of other well-known formulations discussed in the literature. Our results indicate that in comparison to other well-known formulations, the proposed formulations are quite promising in terms of the LP relaxation bounds obtained and the number of branch and bound nodes explored to reach an optimal integer solution. These new formulations along with the results of experimentation are presented in Appendix A. To solve the disassembly optimization problem, a three-phase iterative solution procedure was developed that can determine optimal or near optimal disassembly plans for complex assemblies. The first phase helps in obtaining an upper bound on our maximization problem through an application of a Lagrangian relaxation scheme. The second phase helps to further improve this bound through addition of a few valid inequalities in our models. In the third phase, we fix some of our decision variables based on the solutions obtained in the iterations of phases 1 and 2 and then implement a branch and bound scheme to obtain the final solution. We test our procedure on several randomly generated data sets and identify the factors that render a problem to be computationally difficult. Also, we establish the practical usefulness of our approach through case studies on the disassembly of a computer processor and a laser printer. / Master of Science

<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>

This paper explores strategies in portfolio optimization, focusing on integrating mean-variance optimization (MVO) frameworks with cardinality constraints to enhance investment decision-making. Using a combination of quadratic programming and mixed-integer linear programming, the Gurobi optimizer handles complex constraints and achieves computational solutions. The study compares two mathematical formulations of the cardinality constraint: the Complementary Model and the Big M Model. As cardinality increased, risk decreased exponentially, converging at higher cardinalities. This behavior aligns with the theory of risk reduction through diversification. Additionally, despite initial expectations, both models performed similarly in terms of root relaxation risk and execution time due to Gurobi's presolve transformation of the Complementary Model into the Big M Model. Root relaxation risks were identical while execution times varied slightly without a consistent trend, underscoring the Big M Model's versatility and highlighting the limitations of the Complementary Model.

The effect of structural optimization on control of stiffened laminated composite structures is considered. The structural optimization considered here, is the maximization of structural frequencies of the structure subject to maximum weight and frequency separation constraints and an upper bound on weight. The number of plies with a given orientation and the stiffener areas form the two sets of design variables. As the number of plies is restricted to integer values, the optimization problem considered belongs to the class of nonlinear mixed integer problems (NMIP). Several efficiency measures are proposed to reduce the computational cost for solution of the optimization problem. Savings in computer time due to each of the measures is discussed. The control problem is solved using the independent modal space control technique. This technique greatly simplifies the evaluation of the sensitivity of the performance index with respect to the individual frequencies. The effect of different optimization schemes on the control performance is considered. To reduce the probability, that conclusions drawn from numerical results, are purely coincidental, a large number of cases has been studied. It has been concluded that sufficient improvement in control performance can be achieved through structural optimization. / Ph. D.

Recognizing the complexity of coal mining management, e.g., the scarcity of financial resources and the high level of uncertainty, a mixed binary programming model has been developed as an aid for generating production schedules which maximize the associated net present value. Defining the mine layout as a precedence network, with the nodes representing mining blocks, a solution procedure is developed, based on Benders' partitioning scheme. That is, the procedure iterates between two problems, namely, the master (primal) problem, solved by a combination of heuristic and exact methods, and the subproblem (dual problem), solved partly by inspection and partly as a minimal cost network flow problem. The heuristic methods are based on improvements of existing algorithms for scheduling precedence-related jobs on m processors. Computational experiences are presented and the procedure is demonstrated on a mining case. / Ph. D.