Discrete-event Simulation and Optimization to Improve the Performance of a Healthcare System

Thesis (Ph.D.)--University of Washington, 2016-08

Motion Planning and Controls with Safety and Temporal Constraints

Motion planning, or trajectory planning, commonly refers to a process of converting high-level task specifications into low-level control commands that can be executed on the system of interest. For different applications, the system will be different. It can be an autonomous vehicle, an Unmanned Aerial Vehicle(UAV), a humanoid robot, or an industrial robotic arm. As human machine interaction is essential in many of these systems, safety is fundamental and crucial. Many of the applications also involve performing a task in an optimal manner within a given time constraint. Therefore, in this thesis, we focus on two aspects of the motion planning problem. One is the verification and synthesis of the safe controls for autonomous ground and air vehicles in collision avoidance scenarios. The other part focuses on the high-level planning for the autonomous vehicles with the timed temporal constraints. In the first aspect of our work, we first propose a verification method to prove the safety and robustness of a path planner and the path following controls based on reachable sets. We demonstrate the method on quadrotor and automobile applications. Secondly, we propose a reachable set based collision avoidance algorithm for UAVs. Instead of the traditional approaches of collision avoidance between trajectories, we propose a collision avoidance scheme based on reachable sets and tubes. We then formulate the problem as a convex optimization problem seeking control set design for the aircraft to avoid collision. We apply our approach to collision avoidance scenarios of quadrotors and fixed-wing aircraft. In the second aspect of our work, we address the high level planning problems with timed temporal logic constraints. Firstly, we present an optimization based method for path planning of a mobile robot subject to timed temporal constraints, in a dynamic environment. Temporal logic (TL) can address very complex task specifications such as safety, coverage, motion sequencing etc. We use metric temporal logic (MTL) to encode the task specifications with timing constraints. We then translate the MTL formulae into mixed integer linear constraints and solve the associated optimization problem using a mixed integer linear program solver. We have applied our approach on several case studies in complex dynamical environments subjected to timed temporal specifications. Secondly, we also present a timed automaton based method for planning under the given timed temporal logic specifications. We use metric interval temporal logic (MITL), a member of the MTL family, to represent the task specification, and provide a constructive way to generate a timed automaton and methods to look for accepting runs on the automaton to find an optimal motion (or path) sequence for the robot to complete the task.

Exact solutions for the agricultural and the two-dimensional packing problems

Objectives and study method: The objective of this study is to develop exact algorithms that can be used as management tools for the agricultural production planning and to obtain exact solutions for two of the most well known twodimensional packing problems: the strip packing problem and the bin packing problem. For the agricultural production planning problem we propose a new hierarchical scheme of three stages to improve the current agricultural practices. The objective of the first stage is to delineate rectangular and homogeneous management zones into the farmer’s plots considering the physical and chemical soil properties. This is an important task because the soil properties directly affect the agricultural production planning. The methodology for this stage is based on a new method called “Positions and Covering” that first generates all the possible positions in which the plot can be delineated. Then, we use a mathematical model of linear programming to obtain the optimal physical and chemical management zone delineation of the plot. In the second stage the objective is to determine the optimal crop pattern that maximizes the farmer’s profit taken into account the previous management zones delineation. In this case, the crop pattern is affected by both management zones delineation, physical and chemical. A mixed integer linear programming is used to solve this stage. The objective of the last stage is to determine in real-time the amount of water to irrigate in each crop. This stage takes as input the solution of the crop planning stage, the atmospheric conditions (temperature, radiation, etc.), the humidity level in plots, and the physical management zones of plots, just to name a few. This procedure is made in real-time during each irrigation period. A linear programming is used to solve this problem. A breakthrough happen when we realize that we could propose some adaptations of the P&C methodology to obtain optimal solutions for the two-dimensional packing problem and the strip packing. We empirically show that our methodologies are efficient on instances based on real data for both problems: agricultural and two-dimensional packing problems. Contributions and conclusions: The exact algorithms showed in this study can be used in the making-decision support for agricultural planning and twodimensional packing problems. For the agricultural planning problem, we show that the implementation of the new hierarchical approach can improve the farmer profit between 5.27% until 8.21% through the optimization of the natural resources. An important characteristic of this problem is that the soil properties (physical and chemical) and the real-time factors (climate, humidity level, evapotranspiration, etc.) are incorporated. With respect to the two-dimensional packing problems, one of the main contributions of this study is the fact that we have demonstrate that many of the best solutions founded in literature by others approaches (heuristics approaches) are the optimal solutions. This is very important because some of these solutions were up to now not guarantee to be the optimal solutions.

Integer Linear Programming for Sequence Problems: A general approach to reduce the problem size

Sequence problems belong to the most challenging interdisciplinary topics of the actuality. They are ubiquitous in science and daily life and occur, for example, in form of DNA sequences encoding all information of an organism, as a text (natural or formal) or in form of a computer program. Therefore, sequence problems occur in many variations in computational biology (drug development), coding theory, data compression, quantitative and computational linguistics (e.g. machine translation). In recent years appeared some proposals to formulate sequence problems like the closest string problem (CSP) and the farthest string problem (FSP) as an Integer Linear Programming Problem (ILPP). In the present talk we present a general novel approach to reduce the size of the ILPP by grouping isomorphous columns of the string matrix together. The approach is of practical use, since the solution of sequence problems is very time consuming, in particular when the sequences are long.

Coordinated Scheduling of Wind-Thermal Gencos in Day-Ahead Markets

This paper presents a stochastic mixed-integer linear programming approach for solving the self-scheduling problem of a price-taker thermal and wind power producer taking part in a pool-based electricity market. Uncertainty on electricity price and wind power is considered through a set of scenarios. Thermal units are modeled by variable costs, start-up costs and technical operating constraints, such as: ramp up/down limits and minimum up/down time limits. An efficient mixed-integer linear program is presented to develop the offering strategies of the coordinated production of thermal and wind energy generation, aiming to maximize the expected profit. A case study with data from the Iberian Electricity Market is presented and results are discussed to show the effectiveness of the proposed approach.

Scheduling techniques to optimise rail operations

In Australia, railway systems play a vital role in transporting the sugarcane crop from farms to mills. The sugarcane transport system is very complex and uses daily schedules, consisting of a set of locomotives runs, to satisfy the requirements of the mill and harvesters. The total cost of sugarcane transport operations is very high; over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. Efficient schedules for sugarcane transport can reduce the cost and limit the negative effects that this system can have on the raw sugar production system. There are several benefits to formulating the train scheduling problem as a blocking parallel-machine job shop scheduling (BPMJSS) problem, namely to prevent two trains passing in one section at the same time; to keep the train activities (operations) in sequence during each run (trip) by applying precedence constraints; to pass the trains on one section in the correct order (priorities of passing trains) by applying disjunctive constraints; and, to ease passing trains by solving rail conflicts by applying blocking constraints and Parallel Machine Scheduling. Therefore, the sugarcane rail operations are formulated as BPMJSS problem. A mixed integer programming and constraint programming approaches are used to describe the BPMJSS problem. The model is solved by the integration of constraint programming, mixed integer programming and search techniques. The optimality performance is tested by Optimization Programming Language (OPL) and CPLEX software on small and large size instances based on specific criteria. A real life problem is used to verify and validate the approach. Constructive heuristics and new metaheuristics including simulated annealing and tabu search are proposed to solve this complex and NP-hard scheduling problem and produce a more efficient scheduling system. Innovative hybrid and hyper metaheuristic techniques are developed and coded using C# language to improve the solutions quality and CPU time. Hybrid techniques depend on integrating heuristic and metaheuristic techniques consecutively, while hyper techniques are the complete integration between different metaheuristic techniques, heuristic techniques, or both.

Block models for improved earthwork allocation planning in linear infrastructure construction

Earthwork planning has been considered in this article and a generic block partitioning and modelling approach has been devised to provide strategic plans of various levels of detail. Conceptually this approach is more accurate and comprehensive than others, for instance those that are section based. In response to environmental concerns the metric for decision making was fuel consumption and emissions. Haulage distance and gradient are also included as they are important components of these metrics. Advantageously the fuel consumption metric is generic and captures the physical difficulties of travelling over inclines of different gradients, that is consistent across all hauling vehicles. For validation, the proposed models and techniques have been applied to a real world road project. The numerical investigations have demonstrated that the models can be solved with relatively little CPU time. The proposed block models also result in solutions of superior quality, i.e. they have reduced fuel consumption and cost. Furthermore the plans differ considerably from those based solely upon a distance based metric thus demonstrating a need for industry to reflect upon their current practices.

Growth and species interactions of Eucalyptus pellita in a mixed and monoculture plantation in the humid tropics of north Queensland

This study investigated whether mixed-species designs can increase the growth of a tropical eucalypt when compared to monocultures. Monocultures of Eucalyptus pellita (E) and Acacia peregrina (A) and mixtures in various proportions (75E:25A, 50E:50A, 25E:75A) were planted in a replacement series design on the Atherton Tablelands of north Queensland, Australia. High mortality in the establishment phase due to repeated damage by tropical cyclones altered the trial design. Effects of experimental designs on tree growth were estimated using a linear mixed-effects model with restricted maximum likelihood analysis (REML). Volume growth of individual eucalypt trees were positively affected by the presence of acacia trees at age 5 years and this effect generally increased with time up to age 10 years. However, the stand volume and basal area increased with increasing proportions of E. pellita, due to its larger individual tree size. Conventional analysis did not offer convincing support for mixed-species designs. Preliminary individual-based modelling using a modified Hegyi competition index offered a solution and an equation that indicates acacias have positive ecological interactions (facilitation or competitive reduction) and definitely do not cause competition like a eucalypt. These results suggest that significantly increased in growth rates could be achieved with mixed-species designs. This statistical methodology could enable a better understanding of species interactions in similarly altered experiments, or undesigned mixed-species plantations.

An integrated model of an open-pit coal mine: Improving energy efficiency decisions

This article contributes an original integrated model of an open-pit coal mine for supporting energy-efficient decisions. Mixed integer linear programming is used to formulate a general integrated model of the operational energy consumption of four common open-pit coal mining subsystems: excavation and haulage, stockpiles, processing plants and belt conveyors. Mines are represented as connected instances of the four subsystems, in a flow sheet manner, which are then fitted to data provided by the mine operators. Solving the integrated model ensures the subsystems’ operations are synchronised and whole-of-mine energy efficiency is encouraged. An investigation on a case study of an open-pit coal mine is conducted to validate the proposed methodology. Opportunities are presented for using the model to aid energy-efficient decision-making at various levels of a mine, and future work to improve the approach is described.

Optimising the operational energy efficiency of an open-pit coal mine system

This thesis investigates factors that impact the energy efficiency of a mining operation. An innovative mathematical framework and solution approach are developed to model, solve and analyse an open-pit coal mine. A case study in South East Queensland is investigated to validate the approach and explore the opportunities for using it to aid long, medium and short term decision makers.

Optimal design of multiproduct batch chemical plant using NSGA-II

The optimal design of a multiproduct batch chemical plant is formulated as a multiobjective optimization problem, and the resulting constrained mixed-integer nonlinear program (MINLP) is solved by the nondominated sorting genetic algorithm approach (NSGA-II). By putting bounds on the objective function values, the constrained MINLP problem can be solved efficiently by NSGA-II to generate a set of feasible nondominated solutions in the range desired by the decision-maker in a single run of the algorithm. The evolution of the entire set of nondominated solutions helps the decision-maker to make a better choice of the appropriate design from among several alternatives. The large set of solutions also provides a rich source of excellent initial guesses for solution of the same problem by alternative approaches to achieve any specific target for the objective functions

Design of logical topologies for wavelength-routed optical networks

his paper studies the problem of designing a logical topology over a wavelength-routed all-optical network (AON) physical topology, The physical topology consists of the nodes and fiber links in the network, On an AON physical topology, we can set up lightpaths between pairs of nodes, where a lightpath represents a direct optical connection without any intermediate electronics, The set of lightpaths along with the nodes constitutes the logical topology, For a given network physical topology and traffic pattern (relative traffic distribution among the source-destination pairs), our objective is to design the logical topology and the routing algorithm on that topology so as to minimize the network congestion while constraining the average delay seen by a source-destination pair and the amount of processing required at the nodes (degree of the logical topology), We will see that ignoring the delay constraints can result in fairly convoluted logical topologies with very long delays, On the other hand, in all our examples, imposing it results in a minimal increase in congestion, While the number of wavelengths required to imbed the resulting logical topology on the physical all optical topology is also a constraint in general, we find that in many cases of interest this number can be quite small, We formulate the combined logical topology design and routing problem described above (ignoring the constraint on the number of available wavelengths) as a mixed integer linear programming problem which we then solve for a number of cases of a six-node network, Since this programming problem is computationally intractable for larger networks, we split it into two subproblems: logical topology design, which is computationally hard and will probably require heuristic algorithms, and routing, which can be solved by a linear program, We then compare the performance of several heuristic topology design algorithms (that do take wavelength assignment constraints into account) against that of randomly generated topologies, as well as lower bounds derived in the paper.

Trade determination in multi-attribute exchanges

Electronic exchanges are double-sided marketplaces that allow multiple buyers to trade with multiple sellers, with aggregation of demand and supply across the bids to maximize the revenue in the market. Two important issues in the design of exchanges are (1) trade determination (determining the number of goods traded between any buyer-seller pair) and (2) pricing. In this paper we address the trade determination issue for one-shot, multi-attribute exchanges that trade multiple units of the same good. The bids are configurable with separable additive price functions over the attributes and each function is continuous and piecewise linear. We model trade determination as mixed integer programming problems for different possible bid structures and show that even in two-attribute exchanges, trade determination is NP-hard for certain bid structures. We also make some observations on the pricing issues that are closely related to the mixed integer formulations.

Optimum steering input determination and path-tracking of all-wheel steer vehicles on uneven terrains based on constrained optimization

In this paper we propose a framework for optimum steering input determination of all-wheel steer vehicles (AWSV) on rough terrains. The framework computes the steering input which minimizes the tracking error for a given trajectory. Unlike previous methodologies of computing steering inputs of car-like vehicles, the proposed methodology depends explicitly on the vehicle dynamics and can be extended to vehicle having arbitrary number of steering inputs. A fully generic framework has been used to derive the vehicle dynamics and a non-linear programming based constrained optimization approach has been used to compute the steering input considering the instantaneous vehicle dynamics, no-slip and contact constraints of the vehicle. All Wheel steer Vehicles have a special parallel steering ability where the instantaneous centre of rotation (ICR) is at infinity. The proposed framework automatically enables the vehicle to choose between parallel steer and normal operation depending on the error with respect to the desired trajectory. The efficacy of the proposed framework is proved by extensive uneven terrain simulations, for trajectories with continuous or discontinuous velocity profile.

Design, specification, and synthesis of aircraft electric power systems control logic

Cyber-physical systems integrate computation, networking, and physical processes. Substantial research challenges exist in the design and verification of such large-scale, distributed sensing, ac- tuation, and control systems. Rapidly improving technology and recent advances in control theory, networked systems, and computer science give us the opportunity to drastically improve our approach to integrated flow of information and cooperative behavior. Current systems rely on text-based spec- ifications and manual design. Using new technology advances, we can create easier, more efficient, and cheaper ways of developing these control systems. This thesis will focus on design considera- tions for system topologies, ways to formally and automatically specify requirements, and methods to synthesize reactive control protocols, all within the context of an aircraft electric power system as a representative application area.

This thesis consists of three complementary parts: synthesis, specification, and design. The first section focuses on the synthesis of central and distributed reactive controllers for an aircraft elec- tric power system. This approach incorporates methodologies from computer science and control. The resulting controllers are correct by construction with respect to system requirements, which are formulated using the specification language of linear temporal logic (LTL). The second section addresses how to formally specify requirements and introduces a domain-specific language for electric power systems. A software tool automatically converts high-level requirements into LTL and synthesizes a controller.

The final sections focus on design space exploration. A design methodology is proposed that uses mixed-integer linear programming to obtain candidate topologies, which are then used to synthesize controllers. The discrete-time control logic is then verified in real-time by two methods: hardware and simulation. Finally, the problem of partial observability and dynamic state estimation is ex- plored. Given a set placement of sensors on an electric power system, measurements from these sensors can be used in conjunction with control logic to infer the state of the system.