Diagnosing infeasibilities in network flow problems

"First Draft: June 13, 1994."Includes bibliographical references (p. 20-21).by Charu C. Aggarwal

A characterization of irreducible infeasible subsystems in flow networks

Infeasible network flow problems with supplies and demands can be characterized via violated cut-inequalities of the classical Gale-Hoffman theorem. Written as a linear program, irreducible infeasible subsystems (IISs) provide a different means of infeasibility characterization. In this article, we answer a question left open in the literature by showing a one-to-one correspondence between IISs and Gale-Hoffman-inequalities in which one side of the cut has to be weakly connected. We also show that a single max-flow computation allows one to compute an IIS. Moreover, we prove that finding an IIS of minimal cardinality in this special case of flow networks is strongly NP-hard

Matrix Methods for Optimal Manifesting of Multinode Space Exploration Systems

http://www1.aiaa.org/content.cfm?pageid=318, Presented at the AIAA Space 2010 Conference and ExhibitionAnaheim, CA, 30 August–2 September 2010.This paper presents matrix-based methods for determining optimal cargo manifests for space exploration. An exploration system is defined as a sequence of in-space and on-surface transports between multiple nodes coupled with demands for resources. The goal is to maximize value and robustness of exploration while satisfying logistical demands and physical constraints at all times. To reduce problem complexity, demands are abstracted to a single class of resources, and one metric (e.g., mass or volume) governs capacity limits. Matrices represent cargo carried by transports, cargo used to satisfy demands, and cargo transferred to other transports. A system of equations enforces flow conservation, demand satisfaction, and capacity constraints. Exploration system feasibility is evaluated by determining if a solution exists to a linear program or network-flow problem. Manifests are optimized subject to an objective function using linear or nonlinear programming techniques. In addition to modeling the manifesting problem, a few metrics such as the transport criticality index are formulated to enable analysis and interpretation. The proposed matrix manifest modeling methods are demonstrated with a notional lunar exploration system composed of 32 transports, including eight cargo and nine crewed landings at an outpost at the lunar south pole and several surface excursions to Malapert Crater and Schrödinger Basin. It is found that carry-along and prepositioning logistics strategies yield different manifesting solutions in which transport criticality varies. For the lunar scenario, transport criticality is larger for a prepositioning strategy (mean value of 3.02), as compared with an alternative carry-along case (mean value of 1.99)

Feature Selection with Support Vector Machines Applied on Tornado Detection

In this paper, a linear programming support vector machine which is based on L1-norm is applied to do feature selection in the tornado data set. The data is the ouputs of Weather Surveillance Radar 1998 Doppler (WSR-88D). The approach is evaluated based on the indices of probability of detection, false alarm rate, bias and Heidke skill. Tornado circulation attributes/variables derived largely from the National Severe Storms Laboratory Mesocyclone Detection Algorithm (MDA) have been investigated for their efficacy in distinguishing between mesocyclones that become tornadic from those which do not

Analysis and management of security constraints in overstressed power systems

Management of operational security constraints is one of the important tasks performed by system operators, which must be addressed properly for secure and economic operation. Constraint management is becoming an increasingly complex and challenging to execute in modern electricity networks for three main reasons. First, insufficient transmission capacity during peak and emergency conditions, which typically result in numerous constraint violations. Second, reduced fault levels, inertia and damping due to power electronic interfaced demand and stochastic renewable generation, which are making network more vulnerable to even small disturbances. Third, re-regulated electricity markets require the networks to operate much closer to their operational security limits, which typically result in stressed and overstressed operating conditions. Operational security constraints can be divided into static security limits (bus voltage and branch thermal limits) and dynamic security limits (voltage and angle stability limits). Security constraint management, in general, is formulated as a constrained, nonlinear, and nonconvex optimization problem. The problem is usually solved by conventional gradient-based nonlinear programming methods to devise optimal non-emergency or emergency corrective actions utilizing minimal system reserves. When the network is in emergency state with reduced/insufficient control capability, the solution space of the corresponding nonlinear optimization problem may be too small, or even infeasible. In such cases, conventional non-linear programming methods may fail to compute a feasible (corrective) control solution that mitigate all constraint violations or might fail to rationalize a large number of immediate post-contingency constraint violations into a smaller number of critical constraints. Although there exists some work on devising corrective actions for voltage and thermal congestion management, this has mostly focused on the alert state of the operation, not on the overstressed and emergency conditions, where, if appropriate control actions are not taken, network may lose its integrity. As it will be difficult for a system operator to manage a large number of constraint violations (e.g. more than ten) at one time, it is very important to rationalize the violated constraints to a minimum subset of critical constraints and then use information on their type and location to implement the right corrective actions at the right locations, requiring minimal system reserves and switching operations. Hence, network operators and network planners should be equipped with intelligent computational tools to “filter out” the most critical constraints when the feasible solution space is empty and to provide a feasible control solution when the solution space is too narrow. With an aim to address these operational difficulties and challenges, this PhD thesis presents three novel interdependent frameworks: Infeasibility Diagnosis and Resolution Framework (IDRF), Constraint Rationalization Framework (CRF) and Remedial Action Selection and Implementation Framework (RASIF). IDRF presents a metaheuristic methodology to localise and resolve infeasibility in constraint management problem formulations (in specific) and nonlinear optimization problem formulations (in general). CRF extends PIDRF and reduces many immediate post-contingency constraint violations into a small number of critical constraints, according to various operational priorities during overstressed operating conditions. Each operational priority is modelled as a separate objective function and the formulation can be easily extended to include other operational aspects. Based on the developed CRF, RASIF presents a methodology for optimal selection and implementation of the most effective remedial actions utilizing various ancillary services, such as distributed generation control, reactive power compensation, demand side management, load shedding strategies. The target buses for the implementation of the selected remedial actions are identified using bus active and reactive power injection sensitivity factors, corresponding to the overloaded lines and buses with excessive voltage violations (i.e. critical constraints). The RASIF is validated through both static and dynamic simulations to check the satisfiability of dynamic security constraints during the transition and static security constraints after the transition. The obtained results demonstrate that the framework for implementation of remedial actions allows the most secure transition between the pre-contingency and post-contingency stable equilibrium points

An adaptive group theoretic algorithm for integer programming problems

At head of title: Preliminary draft

CONSTRAINED MULTI-GROUP PROJECT ALLOCATION USING MAHALANOBIS DISTANCE

Optimal allocation is one of the most active research areas in operation research using binary integer variables. The allocation of multi constrained projects among several options available along a given planning horizon is an especially significant problem in the general area of item classification. The main goal of this dissertation is to develop an analytical approach for selecting projects that would be most attractive from an economic point of view to be developed or allocated among several options, such as in-house engineers and private contractors (in transportation projects). A relevant limiting resource in addition to the availability of funds is the in-house manpower availability. In this thesis, the concept of Mahalanobis distance (MD) will be used as the classification criterion. This is a generalization of the Euclidean distance that takes into account the correlation of the characteristics defining the scope of a project. The desirability of a given project to be allocated to an option is defined in terms of its MD to that particular option. Ideally, each project should be allocated to its closest option. This, however, may not be possible because of the available levels of each relevant resource. The allocation process is formulated mathematically using two Binary Integer Programming (BIP) models. The first formulation maximizes the dollar value of benefits derived by the traveling public from those projects being implemented subject to a budget, total sum of MD, and in-house manpower constraints. The second formulation minimizes the total sum of MD subject to a budget and the in-house manpower constraints. The proposed solution methodology for the BIP models is based on the branchand- bound method. In particular, one of the contributions of this dissertation is the development of a strategy for branching variables and node selection that is consistent with allocation priorities based on MD to improve the branch-and-bound performance level as well as handle a large scale application. The suggested allocation process includes: (a) multiple allocation groups; (b) multiple constraints; (c) different BIP models. Numerical experiments with different projects and options are considered to illustrate the application of the proposed approach

Generalized conflict learning for hybrid discrete/linear optimization

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2005.Includes bibliographical references (p. 73-76).Conflict-directed search algorithms have formed the core of practical, model-based reasoning systems for the last three decades. In many of these applications there is a series of discrete constraint optimization problems and a conflict-directed search algorithm, which uses conflicts in the forward search step to focus search away from known infeasibilities and towards the optimal solution. In the arena of model-based autonomy, discrete systems, like deep space probes, have given way to more agile systems, such as coordinated vehicle control, which must robustly control their continuous dynamics. Controlling these systems requires optimizing over continuous, as well as discrete variables, using linear and non-linear as well as logical constraints. This paper explores the development of algorithms for solving hybrid discrete/linear optimization problems that use conflicts in the forward search direction, generalizing from the conflict-directed search algorithms of model-based reasoning. We introduce a novel algorithm called Generalized Conflict-directed Branch and Bound (GCD-BB). GCD-BB extends traditional Branch and Bound (B&B), by first constructing conflicts from nodes of the search tree that are found to be infeasible or sub-optimal, and then by using these conflicts to guide the forward search away from known infeasible and sub-optimal states. We evaluate GCD-BB empirically on a range of test problems of coordinated air vehicle control. GCD-BB demonstrates a substantial improvement in performance compared to a traditional B&B algorithm, applied to either disjunctive linear programs or an equivalent binary integer program encoding.by Hui Li.S.M

Integration of process design and control: A review

There is a large variety of methods in literature for process design and control, which can be classified into two main categories. The methods in the first category have a sequential approach in which, the control system is designed, only after the details of process design are decided. However, when process design is fixed, there is little room left for improving the control performance. Recognizing the interactions between process design and control, the methods in the second category integrate some control aspects into process design. With the aim of providing an exploration map and identifying the potential areas of further contributions, this paper presents a thematic review of the methods for integration of process design and control. The evolution paths of these methods are described and the advantages and disadvantages of each method are explained. The paper concludes with suggestions for future research activities