Studies in the areas of goal pursuit and well-being suggest that the goals people work toward in their daily lives are important contributors of well-being. However, research to date has focused primarily on aspects of the individual in goal pursuit even though goals are not pursued in isolation. In fact, there is evidence that this emphasis on the individual, particularly salient in Western cultures, has negative consequences at both the individual and community levels. With regard to well-being, data have indicated that it is best represented as two dimensional, including hedonic and eudaimonic well-being. However, the research on personal goals has primarily focused on hedonic well-being of the individual. Overall, hedonic well-being appears to be more related to affective experience, whereas eudaimonic well-being appears to be more comprehensive and related to topics like purpose in life, self-acceptance, and positive relations with others. The theoretical framework of Virtue Ethics posits that social affiliations are essential for human beings to flourish and experience eudaimonia, and this study examines that premise. A two-step approach to structural equation modeling was used to contribute to the extant literature on goal pursuit and well-being by 1) exploring the individual and interpersonal dimensions of goal pursuit and their relationships to hedonic and eudaimonic well-being and 2) exploring the interpersonal dimensions of goal pursuit as a mediator of the relationship between individual dimensions of goal pursuit and eudaimonic well-being. The retained structural model from the two-step approach included Efficacy (an Individual Dimension of Goal Pursuit) and Generativity (an Interpersonal Dimension of Goal Pursuit). Results demonstrated that Efficacy and Generativity were both significantly related to Hedonic and Eudaimonic Well-being; however, Generativity was more strongly related to Eudaimonic than Hedonic Well-being. These findings were consistent with the premise of Virtue theory, that those engaged in goal pursuit with or on behalf of others are more likely to experience higher levels of eudaimonic well-being. Future research should include further exploration of the Interpersonal Dimensions of Goal Pursuit and well-being specifically by focusing on improving measurement for the Interpersonal Dimensions of Goal Pursuit, Hedonic, and Eudaimonic Well-being.

Simulating large numbers of agents, performing complex behaviors in realistic environments is a difficult problem with applications in robotics, computer graphics and animation. A multi-agent system can be a useful tool for studying a range of situations in simulation in order to plan and train for actual events. Systems supporting such simulations can be used to study and train for emergency or disaster scenarios including search and rescue, civilian crowd control, evacuation of a building, and many other training situations. This work describes our approach to multi-agent systems which integrates a roadmap-based approach with agent-based systems for groups of agents performing a wide range of behaviors. The system that we have developed is highly customizable and allows us to study a variety of behaviors and scenarios. The system is tunable in the kinds of agents that can exist and parameters that describe the agents. The agents can have any number of behaviors which dictate how they react throughout a simulation. Aspects that are unique to our approach to multi-agent group behavior are the environmental encoding that the agents use when navigating and the extensive usage of the roadmap in our behavioral framework. Our roadmap-based approach can be utilized to encode both basic and very complex environments which include multi- level buildings, terrains and stadiums. In this work, we develop techniques to improve the simulation of multi-agent systems. The movement strategies we have developed can be used to validate agent movement in a simulated environment and evaluate building designs by varying portions of the environment to see the effect on pedestrian flow. The strategies we develop for searching and tracking improve the ability of agents within our roadmap-based framework to clear areas and track agents in realistic environments. The application focus of this work is on pursuit-evasion and evacuation planning. In pursuit-evasion, one group of agents, the pursuers, attempts to find and capture another set of agents, the evaders. The evaders have a goal of avoiding the pursuers. In evacuation planning, the evacuating agents attempt to find valid paths through potentially complex environments to a safe goal location determined by their environmental knowledge. Another group of agents, the directors may attempt to guide the evacuating agents. These applications require the behaviors created to be tunable to a range of scenarios so they can reflect real-world reactions by agents. They also potentially require interaction and coordination between agents in order to improve the realism of the scenario being studied. These applications illustrate the scalability of our system in terms of the number of agents that can be supported, the kinds of realistic environments that can be handled, and behaviors that can be simulated.

The goal of this dissertation was to examine how people pursue their personal goals in the context of an intimate relationship. Two studies were conducted; a daily diary study of dating partners’ joint activities and a longitudinal study of newly dating couples. In the daily diary study, people reported on their daily joint activities with their dating partners regarding whether their goals were met and how they were feeling during the given activity. The results showed that when people’s goals were met in an activity, their partners were able to accurately perceive that their goals were being met. However, when their goals were not met in the activity, their partners’ accuracy regarding their goals was only at chance levels. The partners’ overall levels of goal congruence did not predict the proportion of goal-congruent activities the partners participated in. However, the partners’ level of goal congruence predicted increases in life satisfaction, relationship commitment, and relationship satisfaction, as well as decreases in negative affect over time. In the longitudinal study, newly dating couples filled out measures of their goals, well-being, and relationship quality during their initial session. Three months later, the couples filled out measures of these same constructs again and answered questions about the goals that they reported pursuing during their initial session. Results showed that concurrently, the partners’ levels of goal congruence were associated with greater ability to make goal progress and higher relationship satisfaction, both of which, in turn, were associated with higher subjective well-being. Longitudinally, initial levels of goal congruence did not predict changes in goal progress and relationship quality over time. However, analysis of the individual goals indicated that people adjusted their goal pursuits based on the level of goal conflict between their own goals and their partners’ goals, such that people were more likely to stop pursuing or devalue goals that conflicted with their partners’ goals over time. Furthermore, the tendency to adjust goals over time was associated with increasing relationship commitment. The results of these studies show that conflict between relationship partners’ goals has important consequences for their relationship, goal progress, and personal well-being.

Graph searching problems are described as games played on graphs, between a set of searchers and a fugitive. Variants of the game restrict the abilities of the searchers and the fugitive and the corresponding search number (the least number of searchers that have a winning strategy) is related to several well-known parameters in graph theory. One popular variant is called the Cops and Robber game, where the searchers (cops) and the fugitive (robber) move in rounds, and in each round they move to an adjacent vertex. This game, defined in late 1970's, has been studied intensively. The most famous open problem is Meyniel's conjecture, which states that the cop number (the minimum number of cops that can always capture the robber) of a connected graph on n vertices is O(sqrt n). We consider a version of the Cops and Robber game, where the robber is faster than the cops, but is not allowed to jump over the cops. This version was first studied in 2008. We show that when the robber has speed s, the cop number of a connected n-vertex graph can be as large as Omega(n^(s/s+1)). This improves the Omega(n^(s-3/s-2)) lower bound of Frieze, Krivelevich, and Loh (Variations on Cops and Robbers, J. Graph Theory, to appear). We also conjecture a general upper bound O(n^(s/s+1)) for the cop number, generalizing Meyniel's conjecture. Then we focus on the version where the robber is infinitely fast, but is again not allowed to jump over the cops. We give a mathematical characterization for graphs with cop number one. For a graph with treewidth tw and maximum degree Delta, we prove the cop number is between (tw+1)/(Delta+1) and tw+1. Using this we show that the cop number of the m-dimensional hypercube is between c1 n / m sqrt(m) and c2 n / m for some constants c1 and c2. If G is a connected interval graph on n vertices, then we give a polynomial time 3-approximation algorithm for finding the cop number of G, and prove that the cop number is O(sqrt(n)). We prove that given n, there exists a connected chordal graph on n vertices with cop number Omega(n/log n). We show a lower bound for the cop numbers of expander graphs, and use this to prove that the random G(n,p) that is not very sparse, asymptotically almost surely has cop number between d1 / p and d2 log (np) / p for suitable constants d1 and d2. Moreover, we prove that a fixed-degree regular random graph with n vertices asymptotically almost surely has cop number Theta(n).

Pursuit and evasion games have garnered much research attention since the class of problems was first posed over a half century ago. With wide applicability to both civilian and military problems, the study of pursuit and evasion games showed much early promise. Early work generally focused on analytical solutions to games involving a single pursuer and a single evader. These solutions generally assumed simple system dynamics to facilitate convergence to a solution. More recently, numerical techniques have been utilized to solve more difficult problems. While many sophisticated numerical tools exist for standard optimization and optimal control problems, developing a more complete set of numerical tools for pursuit and evasion games is still a developing topic of research. This thesis extends the current body of numeric solution tools in two ways. First, an existing approach that modifies sophisticated optimization tools to solve two player pursuer and evasion games is extended to incorporate a class of state inequality constraints. Several classical problems are solved to illustrate the e±cacy of the new approach. Second, a new cooperation metric is introduced into the system objective function for multi-player pursuit and evasion games. This new cooperation metric encourages multiple pursuers to surround and then proceed to capture an evader. Several examples are provided to demonstrate this new cooperation metric.