Hamiltonian cycles and subsets of discounted occupational measures

We study a certain polytope arising from embedding the Hamiltonian cycle problem in a discounted Markov decision process. The Hamiltonian cycle problem can be reduced to finding particular extreme points of a certain polytope associated with the input graph. This polytope is a subset of the space of discounted occupational measures. We characterize the feasible bases of the polytope for a general input graph $G$, and determine the expected numbers of different types of feasible bases when the underlying graph is random. We utilize these results to demonstrate that augmenting certain additional constraints to reduce the polyhedral domain can eliminate a large number of feasible bases that do not correspond to Hamiltonian cycles. Finally, we develop a random walk algorithm on the feasible bases of the reduced polytope and present some numerical results. We conclude with a conjecture on the feasible bases of the reduced polytope.Comment: revised based on referees comment

Large Markov Decision Processes and Combinatorial Optimization

Markov decision processes continue to gain in popularity for modeling a wide range of applications ranging from analysis of supply chains and queuing networks to cognitive science and control of autonomous vehicles. Nonetheless, they tend to become numerically intractable as the size of the model grows fast. Recent works use machine learning techniques to overcome this crucial issue, but with no convergence guarantee. This note provides a brief overview of literature on solving large Markov decision processes, and exploiting them to solve important combinatorial optimization problems

Advances in Branch-and-Fix methods to solve the Hamiltonian cycle problem in manufacturing optimization

159 p.Esta tesis parte del problema de la optimización de la ruta de la herramienta donde se contribuye con unsistema de soporte para la toma de decisiones que genera rutas óptimas en la tecnología de FabricaciónAditiva. Esta contribución sirve como punto de partida o inspiración para analizar el problema del cicloHamiltoniano (HCP). El HCP consiste en visitar todos los vértices de un grafo dado una única vez odeterminar que dicho ciclo no existe. Muchos de los métodos propuestos en la literatura sirven paragrafos no dirigidos y los que se enfocan en los grafos dirigidos no han sido implementados ni testeados.Uno de los métodos para resolver el problema es el Branch-and-Fix (BF), un método exacto que utiliza latranformación del HCP a un problema continuo. El BF es un algoritmo de ramificación que consiste enconstruir un árbol de decisión donde en cada vértice dos problemas lineales son resueltos. Este método hasido testeado en grafos de tamaño pequeño y por ello, no se ha estudiado en profundidad las limitacionesque puede presentar. Por ello, en esta tesis se proponen cuatro contribuciones metodológicasrelacionadas con el HCP y el BF: 1) mejorar la enficiencia del BF en diferentes aspectos, 2) proponer unmétodo de ramificación global, 3) proponer un método del BF colapsado, 4) extender el HCP a unescenario multi-objetivo y proponer un método para resolverlo

HEALTH OUTCOMES AND OPTIMAL CHOICES IN URBAN AREAS IN RESPONSE TO ENVIRONMENTAL SHOCKS AND CHANGES IN FOREST AMENITIES

Forests and trees may play important roles in human health outcomes and choices made by individuals in urban areas. Disruptions to forest amenities and tree canopy coverage caused by shocks to the natural environment may affect urban air quality, behavioral decisions, time use habits, and environmental management. This work exploits two distinct and unrelated shocks to forests in the United States to investigate the environmental and health economic links in urban areas between people and trees, and a proposed deeply ingrained role for environmental health in how people live, interact, optimize in their communities. The first chapter argues that environmental quality and forest amenities are important determinants of health and behavioral patterns in urban areas. The conclusion is that further investigations into the indirect market and nonmarket effects of forests and trees on the urban economy are necessary to better guide self-investments in health and management of natural resources. Chapter 2 examines one mechanism through which shocks to the natural environment caused by forest fires in the Mountain West affect health in high-density communities distant from the flame zone. Using a case study wildfire event in eastern Arizona that brought smoke over Albuquerque, New Mexico in 2011, this chapter advances the methodology by which wildfire smoke damages are assessed by modifying a relatively new US EPA benefit transfer computer program, coupling it with original household survey data, and demonstrating how it can be applied to wildfire smoke events. This chapter concludes that not only are wildfire smoke events costly in urban areas, but that perhaps wildfire smoke is more toxic to health than conventional urban air pollution, necessitating more deliberate and nuanced choices by analysts tasked with estimating the damages of wildfire events. Chapter 3 exploits a different shock to forest cover, caused by the emerald ash borer (EAB), to investigate heterogeneity in urban invasive species management when health is directly accounted for by environmental managers and policymakers. Simulation results show that accounting for health impacts associated with lost tree cover increases net benefits of management by more than 1100% in a combined management model and leads to mortality reductions of 21 persons over 50 years and 5,500 cases of reduced morbidity over the same time period for a representative EAB infested county in the US. Additionally, results indicate that a one size fits all\u27 management approach may be inappropriate for responding to large-scale invasive species infestations due to heterogeneity in county demographics, underlying health incidence, and tree coverage. Chapter 4 further exploits the shock to forest and tree cover caused by EAB to examine behavioral changes in infested areas. Specifically, this chapter investigates how a shock to environmental quality caused by detection of EAB influences labor-leisure tradeoffs made by residents of infested areas using data from the nationally-representative American Time Use Survey. Econometric results from a variety of models indicate a negative relationship between EAB detection and daily outdoor leisure time in addition to a contemporaneous positive relationship between EAB detection and daily time spent on labor supply activities. These findings exist primarily along the extensive margin and persist after controlling for year and area fixed effects and daily weather conditions. Changes are persistent; lasting for 2 years and longer. The overall conclusion presented in chapter 5 is that forests and trees have economically meaningful impacts on health outcomes and individual behavioral patterns in urban areas as a result of shocks to environmental quality. It may be useful for policymakers and environmental managers to consider forest amenities, and disruption to forest quality in particular, when setting environmental and labor market policy. Accounting for the links between nature, health, and optimal choices, may lead to better informed policy, particularly in high-density populated areas where impacts of trees are perhaps the greatest

Motivational support intervention to reduce smoking and increase physical activity in smokers not ready to quit: the TARS RCT.

BACKGROUND: Physical activity can support smoking cessation for smokers wanting to quit, but there have been no studies on supporting smokers wanting only to reduce. More broadly, the effect of motivational support for such smokers is unclear. OBJECTIVES: The objectives were to determine if motivational support to increase physical activity and reduce smoking for smokers not wanting to immediately quit helps reduce smoking and increase abstinence and physical activity, and to determine if this intervention is cost-effective. DESIGN: This was a multicentred, two-arm, parallel-group, randomised (1 : 1) controlled superiority trial with accompanying trial-based and model-based economic evaluations, and a process evaluation. SETTING AND PARTICIPANTS: Participants from health and other community settings in four English cities received either the intervention (n = 457) or usual support (n = 458). INTERVENTION: The intervention consisted of up to eight face-to-face or telephone behavioural support sessions to reduce smoking and increase physical activity. MAIN OUTCOME MEASURES: The main outcome measures were carbon monoxide-verified 6- and 12-month floating prolonged abstinence (primary outcome), self-reported number of cigarettes smoked per day, number of quit attempts and carbon monoxide-verified abstinence at 3 and 9 months. Furthermore, self-reported (3 and 9 months) and accelerometer-recorded (3 months) physical activity data were gathered. Process items, intervention costs and cost-effectiveness were also assessed. RESULTS: The average age of the sample was 49.8 years, and participants were predominantly from areas with socioeconomic deprivation and were moderately heavy smokers. The intervention was delivered with good fidelity. Few participants achieved carbon monoxide-verified 6-month prolonged abstinence [nine (2.0%) in the intervention group and four (0.9%) in the control group; adjusted odds ratio 2.30 (95% confidence interval 0.70 to 7.56)] or 12-month prolonged abstinence [six (1.3%) in the intervention group and one (0.2%) in the control group; adjusted odds ratio 6.33 (95% confidence interval 0.76 to 53.10)]. At 3 months, the intervention participants smoked fewer cigarettes than the control participants (21.1 vs. 26.8 per day). Intervention participants were more likely to reduce cigarettes by ≥ 50% by 3 months [18.9% vs. 10.5%; adjusted odds ratio 1.98 (95% confidence interval 1.35 to 2.90] and 9 months [14.4% vs. 10.0%; adjusted odds ratio 1.52 (95% confidence interval 1.01 to 2.29)], and reported more moderate-to-vigorous physical activity at 3 months [adjusted weekly mean difference of 81.61 minutes (95% confidence interval 28.75 to 134.47 minutes)], but not at 9 months. Increased physical activity did not mediate intervention effects on smoking. The intervention positively influenced most smoking and physical activity beliefs, with some intervention effects mediating changes in smoking and physical activity outcomes. The average intervention cost was estimated to be £239.18 per person, with an overall additional cost of £173.50 (95% confidence interval -£353.82 to £513.77) when considering intervention and health-care costs. The 1.1% absolute between-group difference in carbon monoxide-verified 6-month prolonged abstinence provided a small gain in lifetime quality-adjusted life-years (0.006), and a minimal saving in lifetime health-care costs (net saving £236). CONCLUSIONS: There was no evidence that behavioural support for smoking reduction and increased physical activity led to meaningful increases in prolonged abstinence among smokers with no immediate plans to quit smoking. The intervention is not cost-effective. LIMITATIONS: Prolonged abstinence rates were much lower than expected, meaning that the trial was underpowered to provide confidence that the intervention doubled prolonged abstinence. FUTURE WORK: Further research should explore the effects of the present intervention to support smokers who want to reduce prior to quitting, and/or extend the support available for prolonged reduction and abstinence. TRIAL REGISTRATION: This trial is registered as ISRCTN47776579. FUNDING: This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 27, No. 4. See the NIHR Journals Library website for further project information