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Constraint-Based Reasoning: Overviews


Agile Earth observation satellite scheduling over 20 years: formulations, methods and future directions

arXiv.org Artificial Intelligence

Agile satellites with advanced attitude maneuvering capability are the new generation of Earth observation satellites (EOSs). The continuous improvement in satellite technology and decrease in launch cost have boosted the development of agile EOSs (AEOSs). To efficiently employ the increasing orbiting AEOSs, the AEOS scheduling problem (AEOSSP) aiming to maximize the entire observation profit while satisfying all complex operational constraints, has received much attention over the past 20 years. The objectives of this paper are thus to summarize current research on AEOSSP, identify main accomplishments and highlight potential future research directions. To this end, general definitions of AEOSSP with operational constraints are described initially, followed by its three typical variations including different definitions of observation profit, multi-objective function and autonomous model. A detailed literature review from 1997 up to 2019 is then presented in line with four different solution methods, i.e., exact method, heuristic, metaheuristic and machine learning. Finally, we discuss a number of topics worth pursuing in the future.


Graph Neural Networks Meet Neural-Symbolic Computing: A Survey and Perspective

arXiv.org Artificial Intelligence

Neural-symbolic computing has now become the subject of interest of both academic and industry research laboratories. Graph Neural Networks (GNN) have been widely used in relational and symbolic domains, with widespread application of GNNs in combinatorial optimization, constraint satisfaction, relational reasoning and other scientific domains. The need for improved explainability, interpretability and trust of AI systems in general demands principled methodologies, as suggested by neural-symbolic computing. In this paper, we review the state-of-the-art on the use of GNNs as a model of neural-symbolic computing. This includes the application of GNNs in several domains as well as its relationship to current developments in neural-symbolic computing.


A Survey on String Constraint Solving

arXiv.org Artificial Intelligence

They are a fundamental datatype in all the modern programming languages, and operations on strings frequently occur in disparate fields such as software analysis, model checking, database applications, web security, bioinformatics and so on[3, 11, 19, 21, 27, 28, 49, 60, 67]. Reasoning over strings requires solving arbitrarily complex string constraints, i.e., relations defined on a number of string variables. Typical examples of string constraints are string length, (dis-)equality, concatenation, substring, regular expression matching. With the term "string constraint solving" (in short, string solving or SCS) we refer to the process of modelling, processing, and solving combinatorial problems involving string constraints. We may see SCS as a declarative paradigm which falls at the intersection between constraint solving and combinatorics on words: the user states a problem with string variables and constraints, and a suitable string solver seeks a solution for that problem. Although works on the combinatorics of words were already published in the 1940s [110], the dawn of SCS dates back to the late 1980s in correspondence with the rise of Constraint Programming (CP) [114] and Constraint Logic Programming(CLP)[73] paradigms. Pioneers in this field were for example Trilogy[142], a language providing strings, integer and real constraints, and CLP(Σ) [144], an instance of the CLP scheme representing strings as regular sets. The latter in particular was the first known attempt to use string constraints like regular membership to denote regular sets.


A Constraint Driven Solution Model for Discrete Domains with a Case Study of Exam Timetabling Problems

arXiv.org Artificial Intelligence

Many science and engineering applications require finding solutions to planning and optimization problems by satisfying a set of constraints. These constraint problems (CPs) are typically NP-complete and can be formalized as constraint satisfaction problems (CSPs) or constraint optimization problems (COPs). Evolutionary algorithms (EAs) are good solvers for optimization problems ubiquitous in various problem domains, however traditional operators for EAs are 'blind' to constraints or generally use problem dependent objective functions; as they do not exploit information from the constraints in search for solutions. A variation of EA, Intelligent constraint handling evolutionary algorithm (ICHEA), has been demonstrated to be a versatile constraints-guided EA for continuous constrained problems in our earlier works in (Sharma and Sharma, 2012) where it extracts information from constraints and exploits it in the evolutionary search to make the search more efficient. In this paper ICHEA has been demonstrated to solve benchmark exam timetabling problems, a classic COP. The presented approach demonstrates competitive results with other state-of-the-art approaches in EAs in terms of quality of solutions. ICHEA first uses its inter-marriage crossover operator to satisfy all the given constraints incrementally and then uses combination of traditional and enhanced operators to optimize the solution. Generally CPs solved by EAs are problem dependent penalty based fitness functions. We also proposed a generic preference based solution model that does not require a problem dependent fitness function, however currently it only works for mutually exclusive constraints.


Correcting Knowledge Base Assertions

arXiv.org Artificial Intelligence

The usefulness and usability of knowledge bases (KBs) is often limited by quality issues. One common issue is the presence of erroneous assertions, often caused by lexical or semantic confusion. We study the problem of correcting such assertions, and present a general correction framework which combines lexical matching, semantic embedding, soft constraint mining and semantic consistency checking. The framework is evaluated using DBpedia and an enterprise medical KB.


A Survey on the Use of Preferences for Virtual Machine Placement in Cloud Data Centers

arXiv.org Artificial Intelligence

With the rapid development of virtualization techniques, cloud data centers allow for cost effective, flexible, and customizable deployments of applications on virtualized infrastructure. Virtual machine (VM) placement aims to assign each virtual machine to a server in the cloud environment. VM Placement is of paramount importance to the design of cloud data centers. Typically, VM placement involves complex relations and multiple design factors as well as local policies that govern the assignment decisions. It also involves different constituents including cloud administrators and customers that might have disparate preferences while opting for a placement solution. Thus, it is often valuable to not only return an optimized solution to the VM placement problem but also a solution that reflects the given preferences of the constituents. In this paper, we provide a detailed review on the role of preferences in the recent literature on VM placement. We further discuss key challenges and identify possible research opportunities to better incorporate preferences within the context of VM placement.


Semiring Programming: A Declarative Framework for Generalized Sum Product Problems

arXiv.org Artificial Intelligence

To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration amongst these, contemporary representation methodologies offer little support for this. In an attempt to alleviate this situation, we introduce a new declarative programming framework that provides abstractions of well-known problems such as SAT, Bayesian inference, generative models, and convex optimization. The semantics of programs is defined in terms of first-order structures with semiring labels, which allows us to freely combine and integrate problems from different AI disciplines.


Phase Transition Behavior of Cardinality and XOR Constraints

arXiv.org Artificial Intelligence

The runtime performance of modern SAT solvers is deeply connected to the phase transition behavior of CNF formulas. While CNF solving has witnessed significant runtime improvement over the past two decades, the same does not hold for several other classes such as the conjunction of cardinality and XOR constraints, denoted as CARD-XOR formulas. The problem of determining the satisfiability of CARD-XOR formulas is a fundamental problem with a wide variety of applications ranging from discrete integration in the field of artificial intelligence to maximum likelihood decoding in coding theory. The runtime behavior of random CARD-XOR formulas is unexplored in prior work. In this paper, we present the first rigorous empirical study to characterize the runtime behavior of 1-CARD-XOR formulas. We show empirical evidence of a surprising phase-transition that follows a non-linear tradeoff between CARD and XOR constraints.


Compiling Stochastic Constraint Programs to And-Or Decision Diagrams

arXiv.org Artificial Intelligence

Factored stochastic constraint programming (FSCP) is a formalism to represent multi-stage decision making problems under uncertainty. FSCP models support factorized probabilistic models and involve constraints over decision and random variables. These models have many applications in real-world problems. However, solving these problems requires evaluating the best course of action for each possible outcome of the random variables and hence is computationally challenging. FSCP problems often involve repeated subproblems which ideally should be solved once. In this paper we show how identifying and exploiting these identical subproblems can simplify solving them and leads to a compact representation of the solution. We compile an And-Or search tree to a compact decision diagram. Preliminary experiments show that our proposed method significantly improves the search efficiency by reducing the size of the problem and outperforms the existing methods.


Allen's Interval Algebra Makes the Difference

arXiv.org Artificial Intelligence

Allen's Interval Algebra constitutes a framework for reaso n-ing about temporal information in a qualitative manner. In p articular, it uses intervals, i.e., pairs of endpoints, on the timeline to represent entities corresponding to actions, events, or tasks, and bi nary relations such as precedes and overlaps to encode the possible configurations between those entities. Allen's calculus has found its way in m any academic and industrial applications that involve, most commo nly, planning and scheduling, temporal databases, and healthcare. I n this paper, we present a novel encoding of Interval Algebra using answer -set programming (ASP) extended by difference constraints, i.e., th e fragment abbreviated as ASP(DL), and demonstrate its performance vi a a preliminary experimental evaluation. Although our ASP encoding i s presented in the case of Allen's calculus for the sake of clarity, we sug gest that analogous encodings can be devised for other point-based ca lculi, too.