A landscape-scale optimisation model to break the hazardous fuel continuum while maintaining habitat quality

Wildfires have demonstrated their destructive powers in several parts of the world in recent years. In an effort to mitigate the hazard of large catastrophic wildfires, a common practice is to reduce fuel loads in the landscape. This can be achieved through prescribed burning or mechanically. Prioritising areas to treat is a challenge for landscape managers. To help deal with this problem, we present a spatially explicit, multiperiod mixed integer programming model. The model is solved to yield a plan to generate a dynamic landscape mosaic that optimally fragments the hazardous fuel continuum while meeting ecosystem considerations. We demonstrate that such a multiperiod plan for fuel management is superior to a myopic strategy. We also show that a range of habitat quality values can be achieved without compromising the optimal fuel reduction objective. This suggests that fuel management plans should also strive to optimise habitat quality. We illustrate how our model can be used to achieve this even in the special case where a faunal species requires mature habitat that is also hazardous from a wildfire perspective. The challenging computational effort required to solve the model can be overcome with either a rolling horizon approach or lexicographically. Typical Australian heathland landscapes are used to illustrate the model but the approach can be implemented to prioritise treatments in any fire-prone landscape where preserving habitat connectivity is a critical constraint

Mathematical programming with uncertainty and multiple objectives for sustainable development and wildfire management

Mathematical Programming is a well-placed field of Operational Research to tackle problems as diverse as those that arise in Logistics and Disaster Management. The fundamental objective of Mathematical Programming is the selection of an optimal alternative that meets a series of restrictions. The criterion by which the alternatives are evaluated is traditionally only one (for example, minimizing cost), however it is also common for several objectives to want to be considered simultaneously, thus giving rise to the Multi-criteria Decision. If the conditions to be met by an alternative or the evaluation of said alternative depend on random (or unknown) factors, we are in an optimization context under uncertainty. In the first chapters of this thesis the fields of multicriteria decision and optimization with uncertainty are studied, in two applications in the context of sustainable development and disaster management. Optimization with uncertainty is introduced through an application to rural electrification. In rural areas, access to electricity through solar systems installed in consumers' homes is common. These systems have to be repaired when they fail, so the decision of how to size a maintenance network is affected by great uncertainty. A mathematical programming model is developed by treating uncertainty in an unexplained way, the objective of which is to obtain a maintenance network at minimum cost. This model is later used as a tool to obtain simple rules that can predict the cost of maintenance using little information. The model is validated using information from a real program implemented in Morocco. When studying Multicriteria Optimization it is considered a problem in forest fire management. To mitigate the effects of forest fires, it is common to modify forests, with what is known as fuel treatment. Through this practice, consisting of the controlled felling or burning of trees in selected areas, it is achieved that when fires inevitably occur, they are easier to control. Unfortunately, modifying the flora can affect the existing fauna, so it is sensible to look for solutions that improve the situation in the face of a fire but without great detriment to the existing species. In other words, there are several criteria to take into account when optimizing. A mathematical programming model is developed, which suggests which zones to burn and when, taking into account these competing criteria. This model is applied to a series of simulated realistic cases. The following is a theoretical study of the field of Multiobjective Stochastic Programming (MSP), in which problems that simultaneously have various criteria and uncertainty are considered. In this chapter, a new solution concept is developed for MSP problems with risk aversion, its properties are studied and a linear programming model capable of obtaining said solution is formulated. A computational study of the model is also carried out, applying it to a variation of the well-known backpack problem. Finally, the problem of controlled burning is studied again, this time considering the existing uncertainty as it is not possible to know with certainty how many controlled burns can be carried out in a year, due to the limited window of time in which these can be carried out. The problem is solved using the multi-criteria and stochastic methodology with risk aversion developed in the previous chapter. Finally, the resulting model is applied to a real case located in southern Spain

Mathematical programming with uncertainty and multiple objectives for sustainable development and wildfire management

Mathematical Programming is a field of Operations Research well located for tackling problems as diverse as those arising in Logistics and Disaster Management. The main objective of Mathematical Programming is the selection of an optimal alternative satisfying a series of constraints. Traditionally alternatives are usually judged by a single criterion (for example, minimizing cost); however, it is also common that multiple objectives have to be considered simultaneously, leading to Multicriteria Decision Making. When the conditions to be satisfied by an alternative, or the evaluation of that alternative relies on random or unknown factors, there is a context of Optimization under uncertainty. The first chapters of this thesis study the field of Multicriteria Decision Making and Optimization under uncertainty, in two application in the context of sustainable development and disaster management. Optimization with uncertainty is presented with an application to rural electrification. It is common, especially in rural areas, that the access to electricity is provided via solar systems installed on the homes of the users. These systems have to be repaired when they malfunction. Consequently, the decision of how to size and locate a maintenance network is affected by uncertainty. A mathematical programming model is developed, treating the uncertainty in a non-explicit way, whose goal is to obtain a maintenance network at minimum cost. Such model is then used as a tool for obtaining more straightforward rules that are able to predict maintenance cost using limited information. The model is validated using information from a real program implemented in Morocco. When studying Multicriteria Decision Making a problem in wildfire management is considered. To mitigate the effect of wildfires, it is common the modification of forest, with what is known as fuel management. This technique, consisting in the felling or controlled burns of vegetation in selected areas, results on more manageable fires when they inevitably occur. Unfortunately, modifying flora can affect existing fauna, and thus it is sensible to search for solutions that improve the landscape wildfire-related, without substantial damage to existing species. That is, there are multiple criteria to take into account when optimizing. A mathematical programming model is developed, suggesting which areas to burn and when, taking into account the conflicting criteria. This model is applied to a series of realistic simulated cases. After that, a theoretical study of the field of Multiobjective Stochastic Programming (MSP) is performed, in which problems which simultaneously have multiple criteria and uncertainty are considered. In that chapter, a new concept of solution for MSP problems with risk-aversion is developed, its properties are studied, and a linear programming model is formulated for obtaining such a solution. A computational study of the model is also performed, applying it to a variant of the well-known knapsack problem. Finally, prescribed burning is studied again, considering this time the existing uncertainty due to not knowing how many prescribed burns can be completed within a year, caused by the limited time-window in which prescribed burns can be performed. The problem is solved using the risk-averse multiobjective stochastic methodology developed in the previous chapter. Lastly, the resulting model is applied to a real case located in the south of Spain

Managing ecological systems with unknown threshold locations

The optimal management of ecological systems is challenging because the locations of thresholds between desirable and undesirable regimes are generally unknown to the decision-maker. However, it is possible to learn about the resilience of an ecological system by intelligently perturbing the system using adaptive management (Arrow et al. 1995). Previous research has modelled optimal decisions in systems with hysteretic thresholds (Mäler et al. 2003), derived necessary conditions for optimal control when the locations of thresholds are unknown (Nævdal 2006; Nævdal and Oppenheimer 2007), and used stochastic dynamic programming to examine the effect of this form of uncertainty on risk averse behaviour (Brozovic and Schlenker 2011). This thesis extends previous research to model the effect on optimal decisions of learning about the locations of thresholds via a process of adaptive management. A dynamic programming framework is developed and applied to various ecological contexts, including numerical simulations of a shallow lake ecosystem, and used to demonstrate the role of learning. This thesis demonstrates that learning can be modelled by updating the prior probability distribution for a threshold’s location and by adjusting the boundary between the regions of a system’s state-space that could and could not contain the threshold. The model captures the trade-off faced by the decision-maker between the costs of crossing a threshold and shifting to an undesirable alternative regime, and the benefits of learning about the threshold location. Explicit consideration of the value of information means the decision-maker will generally make decisions that incur a greater risk of crossing the threshold in order to learn about its location. This finding is independent of the initial prior probability distribution used to model threshold location and the type of ecosystem dynamics considered. By explicitly modelling the value of information, this thesis better demonstrates the nature of optimal decision-making in the adaptive management of ecological systems

Managing ecological systems with unknown threshold locations

The optimal management of ecological systems is challenging because the locations of thresholds between desirable and undesirable regimes are generally unknown to the decision-maker. However, it is possible to learn about the resilience of an ecological system by intelligently perturbing the system using adaptive management (Arrow et al. 1995). Previous research has modelled optimal decisions in systems with hysteretic thresholds (Mäler et al. 2003), derived necessary conditions for optimal control when the locations of thresholds are unknown (Nævdal 2006; Nævdal and Oppenheimer 2007), and used stochastic dynamic programming to examine the effect of this form of uncertainty on risk averse behaviour (Brozovic and Schlenker 2011). This thesis extends previous research to model the effect on optimal decisions of learning about the locations of thresholds via a process of adaptive management. A dynamic programming framework is developed and applied to various ecological contexts, including numerical simulations of a shallow lake ecosystem, and used to demonstrate the role of learning. This thesis demonstrates that learning can be modelled by updating the prior probability distribution for a threshold’s location and by adjusting the boundary between the regions of a system’s state-space that could and could not contain the threshold. The model captures the trade-off faced by the decision-maker between the costs of crossing a threshold and shifting to an undesirable alternative regime, and the benefits of learning about the threshold location. Explicit consideration of the value of information means the decision-maker will generally make decisions that incur a greater risk of crossing the threshold in order to learn about its location. This finding is independent of the initial prior probability distribution used to model threshold location and the type of ecosystem dynamics considered. By explicitly modelling the value of information, this thesis better demonstrates the nature of optimal decision-making in the adaptive management of ecological systems

A risk-averse solution for the prescribed burning problem

Hazard reduction is a complex task involving important efforts to prevent and mitigate the consequences of disasters. Many countries around the world have experienced devastating wildfires in recent decades and risk reduction strategies are now more important than ever. Reducing contiguous areas of high fuel load through prescribed burning is a fuel management strategy for reducing wildfire hazard. Unfortunately, this has an impact on the habitat of fauna and thus constrains a prescribed burning schedule which is also subject to uncertainty. To address this problem a mathematical programming model is proposed for scheduling prescribed burns on treatment units on a landscape over a planning horizon. The model takes into account the uncertainty related to the conditions for performing the scheduled prescribed burns as well as several criteria related to the safety and quality of the habitat. This multiobjective stochastic problem is modelled from a riskaverse perspective whose aim is to minimize the worst achievement of the criteria on the different scenarios considered. This model is applied to a real case study in Andalusia (Spain) comparing the solutions achieved with the risk-neutral solution provided by the simple weighted aggregated average. The results obtained show that our proposed approach outperforms the risk-neutral solution in worst cases without a significant loss of quality in the global set of scenarios

Operations research for decision support in wildfire management

The February 2009 ‘Black Saturday’ bushfires resulted in 173 fatalities, caused AUD$4 billion in damage and provided a stark reminder of the destructive potential of wildfire. Globally, wildfire-related destruction appears to be worsening with observed increases in fire occurrence and severity. Wildfire management is a difficult undertaking and involves a complex mix of interrelated components operating across varying temporal and spatial scales. This thesis explores how operations research methods may be employed to provide decision support to wildfire managers so as to reduce the harmful impacts of wildfires on people, communities and natural resources. Some defining challenges of wildfire management are identified, namely complexity, multiple conflicting objectives and uncertainty. A range of operations research methods that can resolve these difficulties are then presented together with illustrative examples from the wildfire and disaster operations research literature. Three mixed integer programming models are then proposed to address specific real-world wildfire management problems. The first model incorporates the complementray effects of fuel treatment and supression preparedness decisions within an integrated framework. The second model schedules fuel treatments across multiple time periods to maintain fire resistant landscape patterns while satisfying various ecological and operational requirements. The third model aggregates fuel treatment units to minimise total perimeter requiring management

Programación matemática con incertidumbre y múltiples objetivos para desarrollo sostenible y gestión de incendios forestales

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, leída el 27-01-2020Mathematical Programming is a well-placed field of Operational Research to tackle problems as diverse as those that arise in Logistics and Disaster Management. The fundamental objective of Mathematical Programming is the selection of an optimal alternative that meets a series of restrictions. The criterion by which the alternatives are evaluated is traditionally only one (for example, minimizing cost), however it is also common for several objectives to want to be considered simultaneously, thus giving rise to the Multi-criteria Decision. If the conditions to be met by an alternative or the evaluation of said alternative depend on random (or unknown) factors, we are in an optimization context under uncertainty. In the first chapters of this thesis the fields of multicriteria decision and optimization with uncertainty are studied, in two applications in the context of sustainable development and disaster management. Optimization with uncertainty is introduced through an application to rural electrification. In rural areas, access to electricity through solar systems installed in consumers' homes is common. These systems have to be repaired when they fail, so the decision of how to size a maintenance network is affected by great uncertainty. A mathematical programming model is developed by treating uncertainty in an unexplained way, the objective of which is to obtain a maintenance network at minimum cost. This model is later used as a tool to obtain simple rules that can predict the cost of maintenance using little information. The model is validated using information from a real program implemented in Morocco. When studying Multicriteria Optimization it is considered a problem in forest fire management. To mitigate the effects of forest fires, it is common to modify forests, with what is known as fuel treatment. Through this practice, consisting of the controlled felling or burning of trees in selected areas, it is achieved that when fires inevitably occur, they are easier to control. Unfortunately, modifying the flora can affect the existing fauna, so it is sensible to look for solutions that improve the situation in the face of a fire but without great detriment to the existing species. In other words, there are several criteria to take into account when optimizing. A mathematical programming model is developed, which suggests which zones to burn and when, taking into account these competing criteria. This model is applied to a series of simulated realistic cases. The following is a theoretical study of the field of Multiobjective Stochastic Programming (MSP), in which problems that simultaneously have various criteria and uncertainty are considered. In this chapter, a new solution concept is developed for MSP problems with risk aversion, its properties are studied and a linear programming model capable of obtaining said solution is formulated. A computational study of the model is also carried out, applying it to a variation of the well-known backpack problem. Finally, the problem of controlled burning is studied again, this time considering the existing uncertainty as it is not possible to know with certainty how many controlled burns can be carried out in a year, due to the limited window of time in which these can be carried out. The problem is solved using the multi-criteria and stochastic methodology with risk aversion developed in the previous chapter. Finally, the resulting model is applied to a real case located in southern Spain.La Programación Matemática es un campo de la Investigación Operativa bien situado para abordar problemas tan diversos como aquellos que surgen en Logística y en Gestión de Desastres. El objetivo fundamental de la Programación Matemática es la selección de una alternativa óptima que cumpla una serie de restricciones. El criterio por el cual se evalúan las alternativas es tradicionalmente uno solo (por ejemplo minimizar coste), sin embargo es también común que varios objetivos quieran ser considerados simultáneamente, dando así lugar a la Decisión Multicriterio. En caso de que las condiciones que ha de cumplir una alternativa o la evaluación de dicha alternativa dependan de factores aleatorios (o desconocidos) nos encontramos en un contexto de optimización bajo incertidumbre. En los primeros capítulos de esta tesis se estudian los campos de decisión multicriterio y optimización con incertidumbre, en dos aplicaciones en el contexto del desarrollo sostenible y la gestión de desastres. La optimización con incertidumbre se introduce mediante una aplicación a electrificación rural. En zonas rurales es común el acceso a la electricidad mediante sistemas solares instalados en las casas de los consumidores. Estos sistemas han de ser reparados cuando fallen, por lo que la decisión de cómo dimensionar una red de mantenimiento se ve afectada por una gran incertidumbre. Un modelo de programación matemática es desarrollado tratando la incertidumbre de forma no explícita, cuyo objetivo es obtener una red de mantenimiento a mínimo coste. Dicho modelo es posteriormente utilizado como herramienta para la obtención de reglas simples que puedan predecir el coste de mantenimiento utilizando poca información. El modelo es validado mediante información de un programa real implementado en Marruecos. Al estudiar la Optimización Multicriterio se considera un problema en gestión de incendios forestales. Para mitigar los efectos de los incendios forestales es común la modificación de los bosques, con lo que se conoce como tratamiento de combustible. Mediante esta práctica, consistente en la tala o quema controlada de árboles en zonas seleccionadas, se consigue que al producirse inevitablemente incendios estos sean más fáciles de controlar. Desafortunadamente el modificar la flora puede afectar a la fauna existente, con lo que es sensato buscar soluciones que mejoren la situación de cara a un incendio pero sin gran detrimento de las especies existentes. Es decir, hay varios criterios a tener en cuenta a la hora de optimizar. Se desarrolla un modelo de programación matemática, el cual sugiere qué zonas quemar y cuándo, teniéndose en cuenta estos criterios enfrentados. Este modelo es aplicado a una serie de casos realistas simulados. A continuación se llega a un estudio teórico del campo de Programación Estocástica Multiobjetivo (MSP, Multiobjective Stochastic Programming), en el que son considerados problemas que simultáneamente tienen varios criterios e incertidumbre. En ese capítulo se desarrolla un nuevo concepto de solución para problemas MSP con aversión al riesgo, se estudian sus propiedades y se formula un modelo de programación lineal capaz de obtener dicha solución. También se lleva a cabo un estudio computacional del modelo, aplicándolo a una variación del conocido problema de la mochila. Finalmente se estudia de nuevo el problema de las quemas controladas, considerando esta vez la incertidumbre existente al no ser posible saber con certeza cuántas quemas controladas pueden ser realizadas en un año, debido a la limitada ventana de tiempo en que estas pueden realizarse. El problema es resuelto mediante la metodología multicriterio y estocástica con aversión al riesgo desarrollada en el capítulo anterior. Por último, el modelo resultante es aplicado a un caso real situado en el sur de España.Fac. de Ciencias MatemáticasTRUEunpu

Evaluating connectivity and ecological linkages between Perth’s protected areas to support biodiversity

While protected areas in urban environments provide island refuges for species survival within a hostile urban matrix, linkages between them are necessary to sustain biodiversity. This is especially important for cities such as Perth situated in Western Australia’s global ‘biodiversity hotspot’, where there is high species richness with many now endangered. This research estimated the degree of connectivity for ‘formal’ and ‘semi-formal’ protected area networks of the Perth and Peel region of WA. Four metrics providing alternative patch and landscape level perspectives were used to estimate and validate the degree of connectivity. Least-cost path modelling was then used to identify effective placement of ecological linkages for species of different dispersal capabilities, testing a range of ecological distance thresholds (EDT) between 50-1500m. Connectivity between protected areas within the region was low. For example, connectivity for species with an EDT of 1500m, such as the threatened Calyptorhynchus latirostris, was at ~0.0005 (range 0-1) for formally protected areas, increasing to 0.0016 when ‘semi-formal’ areas were included, and much lower for lower EDTs. The importance of ‘semi-formal’ areas (especially Bush Forever sites) in connectivity was further highlighted with the number of isolated protected areas dropping from 50% to 25% at 50m EDT and the number of protected areas within the largest linked network increasing from ~25% to ~80% at 1000m EDT, when they were included. This lack of connectivity highlights the need of biodiversity conservation planning decisions to be based on ecological information that enhances species movement. The least-cost path modelling identified routes of potential ecological linkages between protected areas through the urban matrix. Analysis of these detailed maps highlighted a suite of strategies to enhance connectivity, including where to break barriers to movement, enhance green spaces, and provide protection for native vegetation. This provides a resource to enable land managers and planners to make appropriate biodiversity conservation actions