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All sourcesNASA NTRSDOE OSTI
NASA NTRS2010

Integrated Analysis of Airport Capacity and Environmental Constraints

LMI conducted an integrated analysis of airport capacity and environmental constraints. identifying and ranking the key factors limiting achievement of NextGen capacity goals. The primary metric used was projected throughput, which was estimated for the years 2015 and 2025 based on the unconstrained demand forecast from the Federal Aviation Administration, and planned improvements including those proposed in the NextGen plan. A set of 310 critical airports was identified.. collectively accounting for more than 99 percent of domestic air traffic volume; a one-off analytical approach was used to isolate the constraint being assessed. The study considered three capacity constraints (runway.. taxiway, and gate) and three environmental constraints (fuel, NO(x) emissions, and noise). For the ten busiest airports, runway and noise are the primary and secondary constraints in both 2015 and 2025. For the OEP 35 airports and overall for the remaining airports, the most binding constraint is noise. Six of the 10 busiest airports, will face runway constraints in 2025, and 95 will face gate constraints. Nearly every airport will be subject to constraints due to emissions and NOx. Runway and taxi constraints are more concentrated in the large airports: environmental constraints are present at almost every airport regardless of size.

Hasan, Shahab↗
DOE OSTI2020

Energy Master Planning: Identifying Framing Constraints that Scope Your Technology Options

This paper addresses the framing constraints for building and community energy projects that must be considered when energy master planning (EMP) is conducted. The constraints cover emissions, sustainability, resilience, regulations and directives, and regional and local limitations such as available energy types, local conditions, and project requirements. The paper reflects development results from participants in an International Energy Agency project on energy master planning and in a U.S. Department of Defense project on technology integration to achieve resilient, low-energy use military installations. It identifies a comprehensive list of framing constraints categorized into locational threats, locational resources, energy and water distribution and storage systems, building and facility, indoor environmental, and equipment in buildings and district systems constraints. In addition, it identifies limits for these constraints that exist in seven participating countries. Some framing constraints can profoundly impact technology selection while others impact the installation of technologies (as in hardening) and have little to no impact on technology selection. Furthermore, framing constraints can be assessed in different ways and there are resources available to help EMP stakeholders evaluate them. Finally, a case is made that identifying and applying framing constraints early in EMP can bring efficiencies and better focus to the EMP process. We come to the conclusion that (1) for holistic energy planning, it is essential to identify and assess the framing constraints that bound an optimized EMP solution, (2) framing constraints limits should be evaluated as either hard or soft or promising technologies may fall out of an EMP analysis, (3) to maintain consistent quality in the EMP process, the identification of framing constraints and their limits, and perhaps their evaluation, should be standardized, (4) a standardized approach could establish a baseline that can be used, built upon, and improved, (5) as automated EMP tools are improved or developed, the resources in this paper could possibly contribute to their interworkings relative to technology screening, and (6) continued climate change and resulting aggressive goal setting will likely drive a continued and strong emphasis on EMP.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2023

Vibro-impact analysis and characterization of pipeline conveying fluids with multi-segmented motion-limiting constraints

Previous studies of the cantilevered pipeline conveying fluid system have included motion-limiting constraints in the form of trilinear springs. While this is desirable in experimental scenarios, it may not be representative of real-world applications. Therefore, here, this study focuses on multi-segmented motion-limiting constraints. As this type of motion-limiting constraint has not been investigated with a cantilevered pipeline system, a wide variety of outer and inner constraint stiffness and constraint gap sizes are investigated in this study to gain a comprehensive understanding of how the multi-segmented constraints affect the dynamics of the cantilevered pipeline. In this effort, bifurcation diagrams, phase portraits, Poincare maps, time histories, and power spectra are used to investigate the dynamics of the system, and the fluid flow speeds where dynamic characteristics are considered. In general, it is found that critical flow speeds like when the pipe sticks in the constraints are reduced as the constraint stiffnesses are increased. Additionally, the sticking flow speed occurred at lower flow speeds as the gap sizes of the inner and outer constraints decrease, and a larger constraint offset results in a smaller inner gap size leading to critical behaviors occurring at earlier flow speeds.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Combining Emergent Constraints for Climate Sensitivity

A method is proposed for combining information from several emergent constraints into a probabilistic estimate for a climate sensitivity proxy Y such as equilibrium climate sensitivity (ECS). The method is based on fitting a multivariate Gaussian PDF for Y and the emergent constraints using an ensemble of global climate models (GCMs); it can be viewed as a form of multiple linear regression of Y on the constraints. The method accounts for uncertainties in sampling this multidimensional PDF with a small number of models, for observational uncertainties in the constraints, and for overconfidence about the correlation of the constraints with the climate sensitivity. Its general form (Method C) accounts for correlations between the constraints. Method C becomes less robust when some constraints are too strongly related to each other; this can be mitigated using regularization approaches such as ridge regression. An illuminating special case, Method U, neglects any correlations between constraints except through their mutual relationship to the climate proxy; it is more robust to small GCM sample size and is appealingly interpretable. These methods are applied to ECS and the climate feedback parameter using a previously published set of 11 possible emergent constraints derived from climate models in the Coupled Model Intercomparison Project (CMIP). The ±2σ posterior range of ECS for Method C with no overconfidence adjustment is 4.3 ± 0.7 K. For Method U with a large overconfidence adjustment, it is 4.0 ± 1.3 K. This study adds confidence to past findings that most constraints predict higher climate sensitivity than the CMIP mean.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1990

Direct handling of equality constraints in multilevel optimization

In recent years there have been several hierarchic multilevel optimization algorithms proposed and implemented in design studies. Equality constraints are often imposed between levels in these multilevel optimizations to maintain system and subsystem variable continuity. Equality constraints of this nature will be referred to as coupling equality constraints. In many implementation studies these coupling equality constraints have been handled indirectly. This indirect handling has been accomplished using the coupling equality constraints' explicit functional relations to eliminate design variables (generally at the subsystem level), with the resulting optimization taking place in a reduced design space. In one multilevel optimization study where the coupling equality constraints were handled directly, the researchers encountered numerical difficulties which prevented their multilevel optimization from reaching the same minimum found in conventional single level solutions. The researchers did not explain the exact nature of the numerical difficulties other than to associate them with the direct handling of the coupling equality constraints. The coupling equality constraints are handled directly, by employing the Generalized Reduced Gradient (GRG) method as the optimizer within a multilevel linear decomposition scheme based on the Sobieski hierarchic algorithm. Two engineering design examples are solved using this approach. The results show that the direct handling of coupling equality constraints in a multilevel optimization does not introduce any problems when the GRG method is employed as the internal optimizer. The optimums achieved are comparable to those achieved in single level solutions and in multilevel studies where the equality constraints have been handled indirectly.

Renaud, John E.↗
NASA NTRS1993

A global approach to kinematic path planning to robots with holonomic and nonholonomic constraints

Robots in applications may be subject to holonomic or nonholonomic constraints. Examples of holonomic constraints include a manipulator constrained through the contact with the environment, e.g., inserting a part, turning a crank, etc., and multiple manipulators constrained through a common payload. Examples of nonholonomic constraints include no-slip constraints on mobile robot wheels, local normal rotation constraints for soft finger and rolling contacts in grasping, and conservation of angular momentum of in-orbit space robots. The above examples all involve equality constraints; in applications, there are usually additional inequality constraints such as robot joint limits, self collision and environment collision avoidance constraints, steering angle constraints in mobile robots, etc. The problem of finding a kinematically feasible path that satisfies a given set of holonomic and nonholonomic constraints, of both equality and inequality types is addressed. The path planning problem is first posed as a finite time nonlinear control problem. This problem is subsequently transformed to a static root finding problem in an augmented space which can then be iteratively solved. The algorithm has shown promising results in planning feasible paths for redundant arms satisfying Cartesian path following and goal endpoint specifications, and mobile vehicles with multiple trailers. In contrast to local approaches, this algorithm is less prone to problems such as singularities and local minima.

Divelbiss, Adam↗
NASA NTRS1992

Reformulating Constraints for Compilability and Efficiency

KBSDE is a knowledge compiler that uses a classification-based approach to map solution constraints in a task specification onto particular search algorithm components that will be responsible for satisfying those constraints (e.g., local constraints are incorporated in generators; global constraints are incorporated in either testers or hillclimbing patchers). Associated with each type of search algorithm component is a subcompiler that specializes in mapping constraints into components of that type. Each of these subcompilers in turn uses a classification-based approach, matching a constraint passed to it against one of several schemas, and applying a compilation technique associated with that schema. While much progress has occurred in our research since we first laid out our classification-based approach [Ton91], we focus in this paper on our reformulation research. Two important reformulation issues that arise out of the choice of a schema-based approach are: (1) compilability-- Can a constraint that does not directly match any of a particular subcompiler's schemas be reformulated into one that does? and (2) Efficiency-- If the efficiency of the compiled search algorithm depends on the compiler's performance, and the compiler's performance depends on the form in which the constraint was expressed, can we find forms for constraints which compile better, or reformulate constraints whose forms can be recognized as ones that compile poorly? In this paper, we describe a set of techniques we are developing for partially addressing these issues.

Tong, Chris↗
NASA NTRS2006

Hard and Soft Constraints in Reliability-Based Design Optimization

This paper proposes a framework for the analysis and design optimization of models subject to parametric uncertainty where design requirements in the form of inequality constraints are present. Emphasis is given to uncertainty models prescribed by norm bounded perturbations from a nominal parameter value and by sets of componentwise bounded uncertain variables. These models, which often arise in engineering problems, allow for a sharp mathematical manipulation. Constraints can be implemented in the hard sense, i.e., constraints must be satisfied for all parameter realizations in the uncertainty model, and in the soft sense, i.e., constraints can be violated by some realizations of the uncertain parameter. In regard to hard constraints, this methodology allows (i) to determine if a hard constraint can be satisfied for a given uncertainty model and constraint structure, (ii) to generate conclusive, formally verifiable reliability assessments that allow for unprejudiced comparisons of competing design alternatives and (iii) to identify the critical combination of uncertain parameters leading to constraint violations. In regard to soft constraints, the methodology allows the designer (i) to use probabilistic uncertainty models, (ii) to calculate upper bounds to the probability of constraint violation, and (iii) to efficiently estimate failure probabilities via a hybrid method. This method integrates the upper bounds, for which closed form expressions are derived, along with conditional sampling. In addition, an l(sub infinity) formulation for the efficient manipulation of hyper-rectangular sets is also proposed.

Crespo, L.uis G.↗
NASA NTRS2011

Constraint Embedding Technique for Multibody System Dynamics

Multibody dynamics play a critical role in simulation testbeds for space missions. There has been a considerable interest in the development of efficient computational algorithms for solving the dynamics of multibody systems. Mass matrix factorization and inversion techniques and the O(N) class of forward dynamics algorithms developed using a spatial operator algebra stand out as important breakthrough on this front. Techniques such as these provide the efficient algorithms and methods for the application and implementation of such multibody dynamics models. However, these methods are limited only to tree-topology multibody systems. Closed-chain topology systems require different techniques that are not as efficient or as broad as those for tree-topology systems. The closed-chain forward dynamics approach consists of treating the closed-chain topology as a tree-topology system subject to additional closure constraints. The resulting forward dynamics solution consists of: (a) ignoring the closure constraints and using the O(N) algorithm to solve for the free unconstrained accelerations for the system; (b) using the tree-topology solution to compute a correction force to enforce the closure constraints; and (c) correcting the unconstrained accelerations with correction accelerations resulting from the correction forces. This constraint-embedding technique shows how to use direct embedding to eliminate local closure-loops in the system and effectively convert the system back to a tree-topology system. At this point, standard tree-topology techniques can be brought to bear on the problem. The approach uses a spatial operator algebra approach to formulating the equations of motion. The operators are block-partitioned around the local body subgroups to convert them into aggregate bodies. Mass matrix operator factorization and inversion techniques are applied to the reformulated tree-topology system. Thus in essence, the new technique allows conversion of a system with closure-constraints into an equivalent tree-topology system, and thus allows one to take advantage of the host of techniques available to the latter class of systems. This technology is highly suitable for the class of multibody systems where the closure-constraints are local, i.e., where they are confined to small groupings of bodies within the system. Important examples of such local closure-constraints are constraints associated with four-bar linkages, geared motors, differential suspensions, etc. One can eliminate these closure-constraints and convert the system into a tree-topology system by embedding the constraints directly into the system dynamics and effectively replacing the body groupings with virtual aggregate bodies. Once eliminated, one can apply the well-known results and algorithms for tree-topology systems to solve the dynamics of such closed-chain system.

Woo, Simon S.↗
NASA NTRS2003

A Variational Analysis of Divergence Profiles Based upon Column-Integrated Mass, Moisture and Energetic Constraints with Satellite-Derived Boundary Fluxes

A diagnostic study is made of the mean global divergent circulation based upon a constrained least action principle that minimizes column-integrated divergent kinetic energy subject to constraints on mass, moisture, available potential energy (ape) and total kinetic energy. The concept of gross moist stability was incorporated in the prescription of Lagrange weight function associated with the ape constraint in order to simulate the net effects of cumulus convective heating in the tropics. The variational analyses were validated satisfactorily with the original NCEP/NCAR-reanalysis divergence fields for the Septembers of 1987 and 1988. Further analyses show that in the tropical ascending regions, the analyzed divergences are dominated by the mass and ape constraints; the moisture constraint is implicitly satisfied while the kinetic energy constraint is highly dependent on the ape constraint. In the subtropical descending regions, the analyzed divergences are dominated by the mass, moisture and kinetic energy constraints; the ape constraint is implicitly satisfied. When the constraint integrals were blended with the satellite-derived boundary flux data from GPCP precipitation and ERBE/SRB radiation estimates, the newly analyzed divergences are significantly stronger than the reanalysis divergences in the areas where the estimates of precipitation rates are higher. With few exceptions, the increases in upper-layer divergences are coupled with nearly equal increases in lower-layer convergences.

Lu, Huei-Lin↗
NASA NTRS2011

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗
NASA NTRS2013

Powered Descent Guidance with General Thrust-Pointing Constraints

The Powered Descent Guidance (PDG) algorithm and software for generating Mars pinpoint or precision landing guidance profiles has been enhanced to incorporate thrust-pointing constraints. Pointing constraints would typically be needed for onboard sensor and navigation systems that have specific field-of-view requirements to generate valid ground proximity and terrain-relative state measurements. The original PDG algorithm was designed to enforce both control and state constraints, including maximum and minimum thrust bounds, avoidance of the ground or descent within a glide slope cone, and maximum speed limits. The thrust-bound and thrust-pointing constraints within PDG are non-convex, which in general requires nonlinear optimization methods to generate solutions. The short duration of Mars powered descent requires guaranteed PDG convergence to a solution within a finite time; however, nonlinear optimization methods have no guarantees of convergence to the global optimal or convergence within finite computation time. A lossless convexification developed for the original PDG algorithm relaxed the non-convex thrust bound constraints. This relaxation was theoretically proven to provide valid and optimal solutions for the original, non-convex problem within a convex framework. As with the thrust bound constraint, a relaxation of the thrust-pointing constraint also provides a lossless convexification that ensures the enhanced relaxed PDG algorithm remains convex and retains validity for the original nonconvex problem. The enhanced PDG algorithm provides guidance profiles for pinpoint and precision landing that minimize fuel usage, minimize landing error to the target, and ensure satisfaction of all position and control constraints, including thrust bounds and now thrust-pointing constraints.

Carson, John M., III↗
NASA NTRS1987

Trimodal interpretation of constraints for planning

Constraints are used in the CAMPS knowledge based planning system to represent those propositions that must be true for a plan to be acceptable. CAMPS introduces the make-mode for interpreting a constraint. Given an unsatisfied constraint, make evaluation mode suggests planning actions which, if taken, would result in a modified plan in which the constraint in question may be satisfied. These suggested planning actions, termed delta-tuples, are the raw material of intelligent plan repair. They are used both in debugging an almost-right plan and in replanning due to changing situations. Given a defective plan in which some set of constraints are violated, a problem solving strategy selects one or more constraints as a focus of attention. These selected constraints are evaluated in the make-mode to produce delta-tuples. The problem solving strategy then reviews the delta-tuples according to its application and problem-specific criteria to find the most acceptable change in terms of success likelihood and plan disruption. Finally, the problem solving strategy makes the suggested alteration to the plan and then rechecks constraints to find any unexpected consequences.

Krieger, David↗
NASA NTRS1990

Constraint-based evaluation of sequential procedures

Constraining the operation of an agent requires knowledge of the restrictions to physical and temporal capabilities of that agent, as well as an inherent understanding of the desires being processed by that agent. Usually a set of constraints are available that must be adhered to in order to foster safe operations. In the worst case, violation of a constraint may be cause to terminate operation. If the agent is carrying out a plan, then a method for predicting the agent's desires, and therefore possible constraint violations, is required. The conceptualization of constraint-based reasoning used herein assumes that a system knows how to select a constraint for application as well as how to apply that constraint once it is selected. The application of constraint-based reasoning for evaluating certain kinds of plans known as sequential procedures is discussed. By decomposing these plans, it is possible to apply context dependent constraints in production system fashion without incorporating knowledge of the original planning process.

Barry, Matthew R.↗
NASA NTRS1994

Propagating orientation constraints for the Hubble Space Telescope

An observing program on the Hubble Space Telescope (HST) is described in terms of exposures that are obtained by one or more of the instruments onboard the HST. Many requested exposures might specify orientation requirements and accompanying ranges. Orientation refers to the amount of roll (in degrees) about the line of sight. The range give the permissible tolerance (also in degrees). These requirements may be (1) absolute (in relation to the celestial coordinate system), (2) relative to the nominal roll angle for HST during that exposure, or (3) relative (in relation to other exposures in the observing program). The TRANSformation expert system converts proposals for astronomical observations with HST into detailed observing plans. Part of the conversion involves grouping exposures into higher level structures based on exposure characteristics. Exposures constrained to be at different orientations cannot be grouped together. Because relative orientation requirements cause implicit constraints, orientation constraints have to be propagated. TRANS must also identify any inconsistencies that may exist so they can be corrected. We have designed and implemented an orientation constraint propagator as part of TRANS. The propagator is based on an informal algebra that facilitates the setting up and propagation of the orientation constraints. The constraint propagator generates constraints between directly related exposures, and propagates derived constraints between exposures that are related indirectly. It provides facilities for path-consistency checking, identification of unsatisfiable constraints, and querying of orientation relationships. The system has been successfully operational as part of TRANS for over seven months. The solution has particular significance to space applications in which satellite/telescope pointing and attitude are constrained and relationships exist between multiple configurations.

Bose, Ashim↗
NASA NTRS2005

PlanWorks: A Debugging Environment for Constraint Based Planning Systems

Numerous planning and scheduling systems employ underlying constraint reasoning systems. Debugging such systems involves the search for errors in model rules, constraint reasoning algorithms, search heuristics, and the problem instance (initial state and goals). In order to effectively find such problems, users must see why each state or action is in a plan by tracking causal chains back to part of the initial problem instance. They must be able to visualize complex relationships among many different entities and distinguish between those entities easily. For example, a variable can be in the scope of several constraints, as well as part of a state or activity in a plan; the activity can arise as a consequence of another activity and a model rule. Finally, they must be able to track each logical inference made during planning. We have developed PlanWorks, a comprehensive system for debugging constraint-based planning and scheduling systems. PlanWorks assumes a strong transaction model of the entire planning process, including adding and removing parts of the constraint network, variable assignment, and constraint propagation. A planner logs all transactions to a relational database that is tailored to support queries for of specialized views to display different forms of data (e.g. constraints, activities, resources, and causal links). PlanWorks was specifically developed for the Extensible Universal Remote Operations Planning Architecture (EUROPA(sub 2)) developed at NASA, but the underlying principles behind PlanWorks make it useful for many constraint-based planning systems. The paper is organized as follows. We first describe some fundamentals of EUROPA(sub 2). We then describe PlanWorks' principal components. We then discuss each component in detail, and then describe inter-component navigation features. We close with a discussion of how PlanWorks is used to find model flaws.

Daley, Patrick↗
NASA NTRS2008

Using LDPC Code Constraints to Aid Recovery of Symbol Timing

A method of utilizing information available in the constraints imposed by a low-density parity-check (LDPC) code has been proposed as a means of aiding the recovery of symbol timing in the reception of a binary-phase-shift-keying (BPSK) signal representing such a code in the presence of noise, timing error, and/or Doppler shift between the transmitter and the receiver. This method and the receiver architecture in which it would be implemented belong to a class of timing-recovery methods and corresponding receiver architectures characterized as pilotless in that they do not require transmission and reception of pilot signals. Acquisition and tracking of a signal of the type described above have traditionally been performed upstream of, and independently of, decoding and have typically involved utilization of a phase-locked loop (PLL). However, the LDPC decoding process, which is iterative, provides information that can be fed back to the timing-recovery receiver circuits to improve performance significantly over that attainable in the absence of such feedback. Prior methods of coupling LDPC decoding with timing recovery had focused on the use of output code words produced as the iterations progress. In contrast, in the present method, one exploits the information available from the metrics computed for the constraint nodes of an LDPC code during the decoding process. In addition, the method involves the use of a waveform model that captures, better than do the waveform models of the prior methods, distortions introduced by receiver timing errors and transmitter/ receiver motions. An LDPC code is commonly represented by use of a bipartite graph containing two sets of nodes. In the graph corresponding to an (n,k) code, the n variable nodes correspond to the code word symbols and the n-k constraint nodes represent the constraints that the code places on the variable nodes in order for them to form a valid code word. The decoding procedure involves iterative computation of values associated with these nodes. A constraint node represents a parity-check equation using a set of variable nodes as inputs. A valid decoded code word is obtained if all parity-check equations are satisfied. After each iteration, the metrics associated with each constraint node can be evaluated to determine the status of the associated parity check. Heretofore, normally, these metrics would be utilized only within the LDPC decoding process to assess whether or not variable nodes had converged to a codeword. In the present method, it is recognized that these metrics can be used to determine accuracy of the timing estimates used in acquiring the sampled data that constitute the input to the LDPC decoder. In fact, the number of constraints that are satisfied exhibits a peak near the optimal timing estimate. Coarse timing estimation (or first-stage estimation as described below) is found via a parametric search for this peak. The present method calls for a two-stage receiver architecture illustrated in the figure. The first stage would correct large time delays and frequency offsets; the second stage would track random walks and correct residual time and frequency offsets. In the first stage, constraint-node feedback from the LDPC decoder would be employed in a search algorithm in which the searches would be performed in successively narrower windows to find the correct time delay and/or frequency offset. The second stage would include a conventional first-order PLL with a decision-aided timing-error detector that would utilize, as its decision aid, decoded symbols from the LDPC decoder. The method has been tested by means of computational simulations in cases involving various timing and frequency errors. The results of the simulations ined in the ideal case of perfect timing in the receiver.

Jones, Christopher↗
NASA NTRS2009

A Comparative Study of Randomized Constraint Solvers for Random-Symbolic Testing

The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a random solver, three hybrid solvers (i.e., mix of random and symbolic), and two heuristic search solvers. We evaluate the solvers on two benchmarks: one consisting of manually generated constraints and another generated with a concolic execution of 8 subjects. In addition to fully decidable constraints, the benchmarks include constraints with non-linear integer arithmetic, integer modulo and division, bitwise arithmetic, and floating-point arithmetic. As expected symbolic solving (in particular, CVC3) subsumes the other solvers for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the solvers are complementary.

Takaki, Mitsuo↗