Solving Robust Variants of Integer Flow Problems with Uncertain Arc Capacities

This paper deals with robust optimization and network flows. Several robust variants of integer flow problems are considered. They assume uncertainty of network arc capacities as well as of arc unit costs (where applicable). Uncertainty is expressed by discrete scenarios. Since the considered variants of the maximum flow problem are easy to solve, the paper is mostly concerned with NP-hard variants of the minimum-cost flow problem, thus proposing an approximate algorithm for their solution. The accuracy of the proposed algorithm is verified by experiments

Random Neural Networks and Optimisation

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

Detecting resilient structures in stochastic networks: A two-stage stochastic optimization approach

We propose a two-stage stochastic programming framework for designing or identifying "resilient," or "reparable" structures in graphs whose topology may undergo a stochastic transformation. The reparability of a subgraph satisfying a given property is defined in terms of a budget constraint, which allows for a prescribed number of vertices to be added to or removed from the subgraph so as to restore its structural properties after the observation of random changes to the graph's set of edges. A two-stage stochastic programming model is formulated and is shown to be N P -complete for a broad range of graph-theoretical properties that the resilient subgraph is required to satisfy. A general combinatorial branch-and-bound algorithm is developed, and its computational performance is illustrated on the example of a two-stage stochastic maximum clique problem. © 2016 Wiley Periodicals, Inc. NETWORKS, 201

The Challenges of Credible Thermal Protection System Reliability Quantification

The paper discusses several of the challenges associated with developing a credible reliability estimate for a human-rated crew capsule thermal protection system. The process of developing such a credible estimate is subject to the quantification, modeling and propagation of numerous uncertainties within a probabilistic analysis. The development of specific investment recommendations, to improve the reliability prediction, among various potential testing and programmatic options is then accomplished through Bayesian analysis

Neural Networks for Flight Control

Neural networks are being developed at NASA Ames Research Center to permit real-time adaptive control of time varying nonlinear systems, enhance the fault-tolerance of mission hardware, and permit online system reconfiguration. In general, the problem of controlling time varying nonlinear systems with unknown structures has not been solved. Adaptive neural control techniques show considerable promise and are being applied to technical challenges including automated docking of spacecraft, dynamic balancing of the space station centrifuge, online reconfiguration of damaged aircraft, and reducing cost of new air and spacecraft designs. Our experiences have shown that neural network algorithms solved certain problems that conventional control methods have been unable to effectively address. These include damage mitigation in nonlinear reconfiguration flight control, early performance estimation of new aircraft designs, compensation for damaged planetary mission hardware by using redundant manipulator capability, and space sensor platform stabilization. This presentation explored these developments in the context of neural network control theory. The discussion began with an overview of why neural control has proven attractive for NASA application domains. The more important issues in control system development were then discussed with references to significant technical advances in the literature. Examples of how these methods have been applied were given, followed by projections of emerging application needs and directions

OPTIMIZATION MODELS AND METHODOLOGIES TO SUPPORT EMERGENCY PREPAREDNESS AND POST-DISASTER RESPONSE

This dissertation addresses three important optimization problems arising during the phases of pre-disaster emergency preparedness and post-disaster response in time-dependent, stochastic and dynamic environments. The first problem studied is the building evacuation problem with shared information (BEPSI), which seeks a set of evacuation routes and the assignment of evacuees to these routes with the minimum total evacuation time. The BEPSI incorporates the constraints of shared information in providing on-line instructions to evacuees and ensures that evacuees departing from an intermediate or source location at a mutual point in time receive common instructions. A mixed-integer linear program is formulated for the BEPSI and an exact technique based on Benders decomposition is proposed for its solution. Numerical experiments conducted on a mid-sized real-world example demonstrate the effectiveness of the proposed algorithm. The second problem addressed is the network resilience problem (NRP), involving an indicator of network resilience proposed to quantify the ability of a network to recover from randomly arising disruptions resulting from a disaster event. A stochastic, mixed integer program is proposed for quantifying network resilience and identifying the optimal post-event course of action to take. A solution technique based on concepts of Benders decomposition, column generation and Monte Carlo simulation is proposed. Experiments were conducted to illustrate the resilience concept and procedure for its measurement, and to assess the role of network topology in its magnitude. The last problem addressed is the urban search and rescue team deployment problem (USAR-TDP). The USAR-TDP seeks an optimal deployment of USAR teams to disaster sites, including the order of site visits, with the ultimate goal of maximizing the expected number of saved lives over the search and rescue period. A multistage stochastic program is proposed to capture problem uncertainty and dynamics. The solution technique involves the solution of a sequence of interrelated two-stage stochastic programs with recourse. A column generation-based technique is proposed for the solution of each problem instance arising as the start of each decision epoch over a time horizon. Numerical experiments conducted on an example of the 2010 Haiti earthquake are presented to illustrate the effectiveness of the proposed approach

Intermodal Network Design and Expansion for Freight Transportation

Over the last 50 years, international trade has grown considerably, and this growth has strained the global supply chains and their underlying support infrastructures. Consequently, shippers and receivers have to look for more efficient ways to transport their goods. In recent years, intermodal transport is becoming an increasingly attractive alternative to shippers, and this trend is likely to continue as governmental agencies are considering policies to induce a freight modal shift from road to intermodal to alleviate highway congestion and emissions. Intermodal freight transport involves using more than one mode, and thus, it is a more complex transport process. The factors that affect the overall efficiency of intermodal transport include, but not limited to: 1) cost of each mode, 2) trip time of each mode, 3) transfer time to another mode, and 4) location of that transfer (intermodal terminal). One of the reasons for the inefficiencies in intermodal freight transportation is the lack of planning on where to locate intermodal facilities in the transportation network and which infrastructure to expand to accommodate growth. This dissertation focuses on the intermodal network design problem and it extends previous works in three aspects: 1) address competition among intermodal service providers, 2) incorporate uncertainty of demand and supply in the design, and 3) incorporate multi-period planning into investment decisions. The following provides an overview of the works that have been completed in this dissertation. This work formulated robust optimization models for the problem of finding near-optimal locations for new intermodal terminals and their capacities for a railroad company, which operates an intermodal network in a competitive environment with uncertain demands. To solve the robust models, a Simulated Annealing (SA) algorithm was developed. Experimental results indicated that the SA solutions (i.e. objective function values) are comparable to those obtained using GAMS, but the SA algorithm can obtain solutions faster and can solve much larger problems. Also, the results verified that solutions obtained from the robust models are more effective in dealing with uncertain demand scenarios. In a second study, a robust Mixed-Integer Linear Program (MILP) was developed to assist railroad operators with intermodal network expansion decisions. Specifically, the objective of the model was to identify critical rail links to retrofit, locations to establish new terminals, and existing terminals to expand, where the intermodal freight network is subject to demand and supply uncertainties. Addition considerations by the model included a finite overall budget for investment, limited capacities on network links and at intermodal terminals, and due dates for shipments. A hybrid genetic algorithm was developed to solve the proposed MILP. It utilized a column generation algorithm for freight flow assignment and a shortest path labeling algorithm for routing decisions. Experimental results indicated that the developed algorithm can produce optimal solutions efficiently for both small-sized and large-sized intermodal freight networks. The results also verified that the developed model outperformed the traditional network design model with no uncertainty in terms of total network cost. The last study investigated the impact of multi-period approach in intermodal network expansion and routing decisions. A multi-period network design model was proposed to find when and where to locate new terminals, expand existing terminals and retrofit weaker links of the network over an extended planning period. Unlike the traditional static model, the planning horizon was divided into multiple periods in the multi-period model with different time scales for routing and design decisions. Expansion decisions were subject to budget constraints, demand uncertainty and network disruptions. A hybrid Simulated Annealing algorithm was developed to solve this NP-hard model. Model and algorithm’s application were investigated with two numerical case studies. The results verified the superiority of the multi-period model versus the single-period one in terms of total transportation cost and capacity utilization