Finding robust solutions against environmental changes

Many real world problems can be formalized as optimisation problems. Yet, the environment in the real world is mostly changing over time, which makes the optimisation problems change over time. This thesis is dedicated to the problem of finding robust solutions in changing environments. By robustness, we mean that a solution not only is good for the current environment but also maintains its performance after future environmental changes. The problem of finding such robust solutions repeatedly over time is termed as Robust Optimisation Over Time (ROOT). The first contribution of this thesis is a formal definition of ROOT problems and two robustness definitions of solutions to ROOT. The second contribution of this thesis is two benchmarks developed for ROOT. The third contribution of this thesis is an algorithm framework for finding solutions repeatedly over time to ROOT problems. Finally, the fourth contribution of this thesis is a dynamic handling strategy, which is used to initialise a population of solutions right after an environmental change when evolutionary algorithms are used for ROOT problems

Robust optimisation of urban drought security for an uncertain climate

Abstract Recent experience with drought and a shifting climate has highlighted the vulnerability of urban water supplies to “running out of water” in Perth, south-east Queensland, Sydney, Melbourne and Adelaide and has triggered major investment in water source infrastructure which ultimately will run into tens of billions of dollars. With the prospect of continuing population growth in major cities, the provision of acceptable drought security will become more pressing particularly if the future climate becomes drier. Decision makers need to deal with significant uncertainty about future climate and population. In particular the science of climate change is such that the accuracy of model predictions of future climate is limited by fundamental irreducible uncertainties. It would be unwise to unduly rely on projections made by climate models and prudent to favour solutions that are robust across a range of possible climate futures. This study presents and demonstrates a methodology that addresses the problem of finding “good” solutions for urban bulk water systems in the presence of deep uncertainty about future climate. The methodology involves three key steps: 1) Build a simulation model of the bulk water system; 2) Construct replicates of future climate that reproduce natural variability seen in the instrumental record and that reflect a plausible range of future climates; and 3) Use multi-objective optimisation to efficiently search through potentially trillions of solutions to identify a set of “good” solutions that optimally trade-off expected performance against robustness or sensitivity of performance over the range of future climates. A case study based on the Lower Hunter in New South Wales demonstrates the methodology. It is important to note that the case study does not consider the full suite of options and objectives; preliminary information on plausible options has been generalised for demonstration purposes and therefore its results should only be used in the context of evaluating the methodology. “Dry” and “wet” climate scenarios that represent the likely span of climate in 2070 based on the A1F1 emissions scenario were constructed. Using the WATHNET5 model, a simulation model of the Lower Hunter was constructed and validated. The search for “good” solutions was conducted by minimizing two criteria, 1) the expected present worth cost of capital and operational costs and social costs due to restrictions and emergency rationing, and 2) the difference in present worth cost between the “dry” and “wet” 2070 climate scenarios. The constraint was imposed that solutions must be able to supply (reduced) demand in the worst drought. Two demand scenarios were considered, “1.28 x current demand” representing expected consumption in 2060 and “2 x current demand” representing a highly stressed system. The optimisation considered a representative range of options including desalination, new surface water sources, demand substitution using rainwater tanks, drought contingency measures and operating rules. It was found the sensitivity of solutions to uncertainty about future climate varied considerably. For the “1.28 x demand” scenario there was limited sensitivity to the climate scenarios resulting in a narrow range of trade-offs. In contrast, for the “2 x demand” scenario, the trade-off between expected present worth cost and robustness was considerable. The main policy implication is that (possibly large) uncertainty about future climate may not necessarily produce significantly different performance trajectories. The sensitivity is determined not only by differences between climate scenarios but also by other external stresses imposed on the system such as population growth and by constraints on the available options to secure the system against drought. Recent experience with drought and a shifting climate has highlighted the vulnerability of urban water supplies to “running out of water” in Perth, south-east Queensland, Sydney, Melbourne and Adelaide and has triggered major investment in water source infrastructure which ultimately will run into tens of billions of dollars. With the prospect of continuing population growth in major cities, the provision of acceptable drought security will become more pressing particularly if the future climate becomes drier. Decision makers need to deal with significant uncertainty about future climate and population. In particular the science of climate change is such that the accuracy of model predictions of future climate is limited by fundamental irreducible uncertainties. It would be unwise to unduly rely on projections made by climate models and prudent to favour solutions that are robust across a range of possible climate futures. This study presents and demonstrates a methodology that addresses the problem of finding “good” solutions for urban bulk water systems in the presence of deep uncertainty about future climate. The methodology involves three key steps: 1) Build a simulation model of the bulk water system; 2) Construct replicates of future climate that reproduce natural variability seen in the instrumental record and that reflect a plausible range of future climates; and 3) Use multi-objective optimisation to efficiently search through potentially trillions of solutions to identify a set of “good” solutions that optimally trade-off expected performance against robustness or sensitivity of performance over the range of future climates. A case study based on the Lower Hunter in New South Wales demonstrates the methodology. It is important to note that the case study does not consider the full suite of options and objectives; preliminary information on plausible options has been generalised for demonstration purposes and therefore its results should only be used in the context of evaluating the methodology. “Dry” and “wet” climate scenarios that represent the likely span of climate in 2070 based on the A1F1 emissions scenario were constructed. Using the WATHNET5 model, a simulation model of the Lower Hunter was constructed and validated. The search for “good” solutions was conducted by minimizing two criteria, 1) the expected present worth cost of capital and operational costs and social costs due to restrictions and emergency rationing, and 2) the difference in present worth cost between the “dry” and “wet” 2070 climate scenarios. The constraint was imposed that solutions must be able to supply (reduced) demand in the worst drought. Two demand scenarios were considered, “1.28 x current demand” representing expected consumption in 2060 and “2 x current demand” representing a highly stressed system. The optimisation considered a representative range of options including desalination, new surface water sources, demand substitution using rainwater tanks, drought contingency measures and operating rules. It was found the sensitivity of solutions to uncertainty about future climate varied considerably. For the “1.28 x demand” scenario there was limited sensitivity to the climate scenarios resulting in a narrow range of trade-offs. In contrast, for the “2 x demand” scenario, the trade-off between expected present worth cost and robustness was considerable. The main policy implication is that (possibly large) uncertainty about future climate may not necessarily produce significantly different performance trajectories. The sensitivity is determined not only by differences between climate scenarios but also by other external stresses imposed on the system such as population growth and by constraints on the available options to secure the system against drought. Please cite this report as: Mortazavi, M, Kuczera, G, Kiem, AS, Henley, B, Berghout, B,Turner, E, 2013 Robust optimisation of urban drought security for an uncertain climate. National Climate Change Adaptation Research Facility, Gold Coast, pp. 74

Optimal management of bio-based energy supply chains under parametric uncertainty through a data-driven decision-support framework

This paper addresses the optimal management of a multi-objective bio-based energy supply chain network subjected to multiple sources of uncertainty. The complexity to obtain an optimal solution using traditional uncertainty management methods dramatically increases with the number of uncertain factors considered. Such a complexity produces that, if tractable, the problem is solved after a large computational effort. Therefore, in this work a data-driven decision-making framework is proposed to address this issue. Such a framework exploits machine learning techniques to efficiently approximate the optimal management decisions considering a set of uncertain parameters that continuously influence the process behavior as an input. A design of computer experiments technique is used in order to combine these parameters and produce a matrix of representative information. These data are used to optimize the deterministic multi-objective bio-based energy network problem through conventional optimization methods, leading to a detailed (but elementary) map of the optimal management decisions based on the uncertain parameters. Afterwards, the detailed data-driven relations are described/identified using an Ordinary Kriging meta-model. The result exhibits a very high accuracy of the parametric meta-models for predicting the optimal decision variables in comparison with the traditional stochastic approach. Besides, and more importantly, a dramatic reduction of the computational effort required to obtain these optimal values in response to the change of the uncertain parameters is achieved. Thus the use of the proposed data-driven decision tool promotes a time-effective optimal decision making, which represents a step forward to use data-driven strategy in large-scale/complex industrial problems.Peer ReviewedPostprint (published version

Optimisation of the weighting functions of an H_∞ controller using genetic algorithms and structured genetic algorithms

In this paper the optimisation of the weighting functions for an H<sub>∞</sub> controller using genetic algorithms and structured genetic algorithms is considered. The choice of the weighting functions is one of the key steps in the design of an H<sub>∞</sub> controller. The performance of the controller depends on these weighting functions since poorly chosen weighting functions will provide a poor controller. One approach that can solve this problem is the use of evolutionary techniques to tune the weighting parameters. The paper presents the improved performance of structured genetic algorithms over conventional genetic algorithms and how this technique can assist with the identification of appropriate weighting functions' orders

A Hierarchal Planning Framework for AUV Mission Management in a Spatio-Temporal Varying Ocean

The purpose of this paper is to provide a hierarchical dynamic mission planning framework for a single autonomous underwater vehicle (AUV) to accomplish task-assign process in a limited time interval while operating in an uncertain undersea environment, where spatio-temporal variability of the operating field is taken into account. To this end, a high level reactive mission planner and a low level motion planning system are constructed. The high level system is responsible for task priority assignment and guiding the vehicle toward a target of interest considering on-time termination of the mission. The lower layer is in charge of generating optimal trajectories based on sequence of tasks and dynamicity of operating terrain. The mission planner is able to reactively re-arrange the tasks based on mission/terrain updates while the low level planner is capable of coping unexpected changes of the terrain by correcting the old path and re-generating a new trajectory. As a result, the vehicle is able to undertake the maximum number of tasks with certain degree of maneuverability having situational awareness of the operating field. The computational engine of the mentioned framework is based on the biogeography based optimization (BBO) algorithm that is capable of providing efficient solutions. To evaluate the performance of the proposed framework, firstly, a realistic model of undersea environment is provided based on realistic map data, and then several scenarios, treated as real experiments, are designed through the simulation study. Additionally, to show the robustness and reliability of the framework, Monte-Carlo simulation is carried out and statistical analysis is performed. The results of simulations indicate the significant potential of the two-level hierarchical mission planning system in mission success and its applicability for real-time implementation