243,192 research outputs found

    Dynamic Network Flows with Uncertain Costs belonging to Interval

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    This paper considers minimum cost flow problem in dynamic networks with uncertain costs. First, we present a short introduction of dynamic minimum cost flow. Then, we survey discrete and continuous dynamic minimum cost flow problems, their properties and relationships between them. After that, the minimum cost flow problem in discrete dynamic network with uncertainty in the cost vector is considered such that the arc cost can be changed within an interval. Finally, we propose an algorithm to find the optimal solution of the proposed model

    An Integrated Contraflow Strategy for Multimodal Evacuation

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    To improve the efficiency of multimodal evacuation, a network aggregation method and an integrated contraflow strategy are proposed in this paper. The network aggregation method indicates the uncertain evacuation demand on the arterial subnetwork and balances accuracy and efficiency by refining the local road subnetworks. The integrated contraflow strategy contains three arterial configurations: noncontraflow to shorten the strategy setup time, full-lane contraflow to maximize the evacuation network capacity, and bus contraflow to realize the transit cycle operation. The application of this strategy takes two steps to provide transit priority during evacuation: solve the transit-based evacuation problem with a minimum-cost flow model, firstly, and then address the auto-based evacuation problem with a bilevel network flow model. The numerical results from optimizing an evacuation network for a super typhoon justify the validness and usefulness of the network aggregation method and the integrated contraflow strategy

    Random Neural Networks and Optimisation

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    In this thesis we introduce new models and learning algorithms for the Random Neural Network (RNN), and we develop RNN-based and other approaches for the solution of emergency management optimisation problems. With respect to RNN developments, two novel supervised learning algorithms are proposed. The first, is a gradient descent algorithm for an RNN extension model that we have introduced, the RNN with synchronised interactions (RNNSI), which was inspired from the synchronised firing activity observed in brain neural circuits. The second algorithm is based on modelling the signal-flow equations in RNN as a nonnegative least squares (NNLS) problem. NNLS is solved using a limited-memory quasi-Newton algorithm specifically designed for the RNN case. Regarding the investigation of emergency management optimisation problems, we examine combinatorial assignment problems that require fast, distributed and close to optimal solution, under information uncertainty. We consider three different problems with the above characteristics associated with the assignment of emergency units to incidents with injured civilians (AEUI), the assignment of assets to tasks under execution uncertainty (ATAU), and the deployment of a robotic network to establish communication with trapped civilians (DRNCTC). AEUI is solved by training an RNN tool with instances of the optimisation problem and then using the trained RNN for decision making; training is achieved using the developed learning algorithms. For the solution of ATAU problem, we introduce two different approaches. The first is based on mapping parameters of the optimisation problem to RNN parameters, and the second on solving a sequence of minimum cost flow problems on appropriately constructed networks with estimated arc costs. For the exact solution of DRNCTC problem, we develop a mixed-integer linear programming formulation, which is based on network flows. Finally, we design and implement distributed heuristic algorithms for the deployment of robots when the civilian locations are known or uncertain

    Robust and stochastic approaches to network capacity design under demand uncertainty

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    This thesis considers the network capacity design problem with demand uncertainty using the stochastic, robust and distributionally robust stochastic optimization approaches (DRSO). Network modeling in itself has found wide areas of application in most fields of human endeavor. The network would normally consist of source (origin) and sink (destination) nodes connected by arcs that allow for flows of an entity from the origin to the destination nodes. In this thesis, a special type of the minimum cost flow problem is addressed, the multi-commodity network flow problem. Commodities are the flow types that are transported on a shared network. Offered demands are, for the most part, unknown or uncertain, hence a model that immune against this uncertainty becomes the focus as well as the practicability of such models in the industry. This problem falls under the two-stage optimization framework where a decision is delayed in time to adjust for the first decision earlier made. The first stage decision is called the "here and now", while the second stage traffic re-adjustment is the "wait and see" decision. In the literature, the decision-maker is often believed to know the shape of the uncertainty, hence we address this by considering a data-driven uncertainty set. The research also addressed the non-linearity of cost function despite the abundance of literature assuming linearity and models proposed for this. This thesis consist of four main chapters excluding the "Introduction" chapter and the "Approaches to Optimization under Uncertainty" chapter where the methodologies are reviewed. The first of these four, Chapter 3, proposes the two models for the Robust Network Capacity Expansion Problem (RNCEP) with cost non-linearity. These two are the RNCEP with fixed-charge cost and RNCEP with piecewise-linear cost. The next chapter, Chapter 4, compares the RNCEP models under two types of uncertainties in order to address the issue of usefulness in a real world setting. The resulting two robust models are also comapared with the stochastic optimization model with distribution mean. Chapter 5 re-examines the earlier problem using machine learning approaches to generate the two uncertainty sets while the last of these chapters, Chapter 6, investigates DRSO model to network capacity planning and proposes an efficient solution technique

    Robust optimization with incremental recourse

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    In this paper, we consider an adaptive approach to address optimization problems with uncertain cost parameters. Here, the decision maker selects an initial decision, observes the realization of the uncertain cost parameters, and then is permitted to modify the initial decision. We treat the uncertainty using the framework of robust optimization in which uncertain parameters lie within a given set. The decision maker optimizes so as to develop the best cost guarantee in terms of the worst-case analysis. The recourse decision is ``incremental"; that is, the decision maker is permitted to change the initial solution by a small fixed amount. We refer to the resulting problem as the robust incremental problem. We study robust incremental variants of several optimization problems. We show that the robust incremental counterpart of a linear program is itself a linear program if the uncertainty set is polyhedral. Hence, it is solvable in polynomial time. We establish the NP-hardness for robust incremental linear programming for the case of a discrete uncertainty set. We show that the robust incremental shortest path problem is NP-complete when costs are chosen from a polyhedral uncertainty set, even in the case that only one new arc may be added to the initial path. We also address the complexity of several special cases of the robust incremental shortest path problem and the robust incremental minimum spanning tree problem

    Robust optimization models with mixed-integer uncertainty sets

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    In many real-world decision-making problems, some parameters are uncertain and decision-makers have to solve optimization models under uncertainty. In this study, we address two specific classes of problems with uncertain parameters and we are interested in solutions that are robust under any realization of uncertainty. The first one is a class of minimum-cost flow problems where the arcs are subject to multiple ripple-effect disruptions that increase their usage cost. The locations of the disruptions' epicenters are uncertain, and the decision-maker seeks a flow that minimizes cost assuming the worst-case realization of the disruptions. We evaluate the damage to each arc using different methods in which the arcs’ costs post-disruptions are represented with a mixed-integer feasible region. In the second class, we propose a novel problem that considers a decision-maker (a government agency or a public-private consortium) who seeks to efficiently allocate resources in retrofitting and recovery strategies to minimize social vulnerability under an uncertain tornado. As tornado paths cannot be forecast reliably, we model the problem using a two-stage robust optimization problem with a mixed-integer nonlinear uncertainty set that represents the tornado damage.In this study, our primary objective is to develop a mathematical and algorithmic framework for modeling and solving these specific problems. To accomplish this goal, we utilize robust optimization to formulate these problems; develop decomposition algorithms inspired by methods of mixed-integer optimization; and exploit the geometrical characteristics of the uncertainty sets to enhance the formulations and algorithms. We test our proposed approaches over real datasets and synthetic instances. The numerical experiments show that our methods provide sound decision-making strategies under uncertainty and achieve orders of magnitude improvements in computational times over standard approaches from the literature

    On robust network coding subgraph construction under uncertainty

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    We consider the problem of network coding subgraph construction in networks where there is uncertainty about link loss rates. For a given set of scenarios specified by an uncertainty set of link loss rates, we provide a robust optimization-based formulation to construct a single subgraph that would work relatively well across all scenarios. We show that this problem is coNP-hard in general for both objectives: minimizing cost of subgraph construction and maximizing throughput given a cost constraint. To solve the problem tractably, we approximate the problem by introducing path constraints, which results in polynomial time-solvable solution in terms of the problem size. The simulation results show that the robust optimization solution is better and more stable than the deterministic solution in terms of worst-case performance. From these results, we compare the tractability of robust network design problems with different uncertain network components and different problem formulations
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