In this dissertation, a distribution system operator (DSO) framework is proposed to optimally coordinate distributed energy resources (DER) aggregators' comprehensive participation in the retail energy market as well as wholesale energy and regulation markets. Various types of DER aggregators, including energy storage aggregators (ESAGs), dispatchable distributed generation aggregators (DDGAGs), electric vehicles charging stations (EVCSs), and demand response aggregators (DRAGs), are modeled in the proposed DSO framework. An important characteristic of a DSO is being capable of handling uncertainties in the system operation. An appropriate method for a market operator to cover uncertainties is using two-stage stochastic programming. To handle comprehensive retail and wholesale markets participation of distributed energy resource (DER) aggregators under uncertainty, a two-stage stochastic programming model for the DSO is proposed. To handle unbalanced distribution grids with single-phase aggregators, A DSO framework is proposed for unbalanced distribution networks based on a linearized unbalanced power flow which coordinates with wholesale market clearing process and ensures the DSO's non-profit characteristic. When proposing a DSO, coordination with the ISO is important. A framework is proposed to coordinate the operation of the independent system operator (ISO) and distribution system operator (DSO). The framework is compatible with current practice of the U.S. wholesale market to enable massive distributed energy resources (DERs) to participate in the wholesale market. The DSO builds a bid-in cost function to be submitted to the ISO market through parametric programming. A pricing problem for the DSO is proposed. In pricing problem, after ISO clears the wholesale market, the locational marginal price (LMP) of the ISO-DSO coupling substation is determined, the DSO utilizes this price to solve the DSO pricing problem. The DSO pricing problem determines the distribution LMP (D-LMP) in the distribution system and calculates the payment to each aggregator. An efficient algorithm is proposed to solve the ISO-DSO coordination parametric programming problem. Notably, our proposed algorithm significantly improves the computational efficiency of solving the parametric programming DSO problem which is computationally intensive. Various case studies are performed to analyze the market outcome of the proposed DSO framework and coordination with the ISO.

Networks are a versatile modeling tool for the cyber and physical infrastructure that characterize society. They can be used to describe system spatiotemporal dynamics, including distribution of commodities, movement of agents, and data transmission. This flexibility has resulted in the widespread use of network optimization techniques for decision-making in telecommunications, transportation, commerce, among other systems. However, realistic network problems are typically large-scale and require the use of integer variables to incorporate design or logical system constraints. This makes such problems hard to solve and precludes their wide applicability in the solution of applied problems. This dissertation studies four large-scale optimization problems with underlying network structure in different domain applications, including wireless sensor networks, wastewater monitoring, and scheduling. The problems of interest are formulated using mixed-integer optimization formulations. The proposed solution approaches in this dissertation include branch-and-cut and heuristic algorithms, which are enhanced with network-based valid inequalities and network reduction techniques. The first chapter studies a relay node placement problem in wireless sensor networks, with and without the presence of transmission obstacles in the deployment region. The proposed integer linear programming approach leverages the underlying network structure to produce valid inequalities and network reduction heuristics, which are incorporated in the branch-and-bound exploration. The solution approach outperforms the equivalent nonlinear model and solves instances with up to 1000 sensors within reasonable time. The second chapter studies the continuous version of the maximum capacity (widest) path interdiction problem and introduces the first known polynomial time algorithm to solve the problem using a combination of binary search and the discrete version of the Newton’s method. The third chapter explores the service agent transport interdiction problem in autonomous vehicle systems, where an agent schedules service tasks in the presence of an adversary. This chapter proposes a single stage branch-and-cut algorithm to solve the problem, along with several enhancement techniques to improve scalability. The last chapter studies the optimal placement of sensors in a wastewater network to minimize the maximum coverage (load) of placed sensors. This chapter proposes a branch-and-cut algorithm enhanced with network reduction techniques and strengthening constraints.

The rank aggregation problem has ubiquitous applications in operations research, artificial intelligence, computational social choice, and various other fields. Generally, rank aggregation is utilized whenever a set of judges (human or non-human) express their preferences over a set of items, and it is necessary to find a consensus ranking that best represents these preferences collectively. Many real-world instances of this problem involve a very large number of items, include ties, and/or contain partial information, which brings a challenge to decision-makers. This work makes several contributions to overcoming these challenges. Most attention on this problem has focused on an NP-hard distance-based variant known as Kemeny aggregation, for which solution approaches with provable guarantees that can handle difficult large-scale instances remain elusive. Firstly, this work introduces exact and approximate methodologies inspired by the social choice foundations of the problem, namely the Condorcet criterion, to decompose the problem. To deal with instances where exact partitioning does not yield many subsets, it proposes Approximate Condorcet Partitioning, which is a scalable solution technique capable of handling large-scale instances while providing provable guarantees. Secondly, this work delves into the rank aggregation problem under the generalized Kendall-tau distance, which contains Kemeny aggregation as a special case. This new problem provides a robust and highly-flexible framework for handling ties. First, it derives exact and heuristic solution methods for the generalized problem. Second, it introduces a novel social choice property that encloses existing variations of the Condorcet criterion as special cases. Thirdly, this work focuses on top-k list aggregation. Top-k lists are a special form of item orderings wherein out of n total items only a small number of them, k, are explicitly ordered. Top-k lists are being increasingly utilized in various fields including recommendation systems, information retrieval, and machine learning. This work introduces exact and inexact methods for consolidating a collection of heterogeneous top- lists. Furthermore, the strength of the proposed exact formulations is analyzed from a polyhedral point of view. Finally, this work identifies the top-100 U.S. universities by consolidating four prominent university rankings to assess the computational implications of this problem.