京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第19117号 / 情博第563号 / 新制||情||99(附属図書館) / 32068 / 京都大学大学院情報学研究科社会情報学専攻 / (主査)教授 石田 亨, 教授 吉川 正俊, 教授 河原 達也 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

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In this thesis we derive novel results on the complexity of idempotent Mal'tsev condition satisfaction problems. For a Mal'tsev condition M, the idempotent M- satisfaction problem is the decision problem defined via: INPUT: A finite idempotent algebra A. QUESTION: Does A satisfy M? In particular we are able to prove that this decision problem is in the complexity class NP whenever M satisfi es one of the following conditions: 1. M is a strong Mal'tsev condition which implies the existence of a near unanimity term. 2. M is a strong Mal'tsev condition of height < 1 (see Definition 5.1.1). As a porism of these two results, we are able to derive the stronger result that the complexity of the idempotent M-satisfaction problem is in NP whenever M is a strong Mal'tsev condition which implies the existence of an edge term. On top of this we also outline a polynomial-time algorithm for the idempotent M-satisfaction problem when M is a linear strong Mal'tsev condition which implies the existence of a near unanimity term. We also examine the related search problem in which the goal is to produce operation tables of term operations of the algebra A which witness that A satisfies the Mal'tsev condition M whenever such terms exist (and otherwise correctly decide that such terms do not exist). We outline polynomial-time algorithms for this search problem for various strong Mal'tsev conditions. We close the thesis with a short list of open problems as suggested directions for further research. / Thesis / Doctor of Philosophy (PhD)

The main theme shared by the two main parts of this thesis is EFFICIENT AUTOMATED REASONING.Part I is focussed on a general theory underpinning a number of efficient approximate algorithms for Constraint Satisfaction Problems (CSPs),the constraint propagation algorithms.In Chapter 3, we propose a Structured Generic Algorithm schema (SGI) for these algorithms. This iterates functions according to a certain strategy, i.e. by searching for a common fixpoint of the functions. A simple theory for SGI is developed by studying properties of functions and of the ways these influence the basic strategy. One of the primary objectives of our theorisation is thus the following: using SGI or some of its variations for DESCRIBINING and ANALISYING HOW the "pruning" and "propagation" process is carried through by constraint propagation algorithms.Hence, in Chapter 4, different domains of functions (e.g., domain orderings) are related to different classes of constraint propagation algorithms (e.g., arc consistency algorithms); thus each class of constraint propagation algorithms is associated with a "type" of function domains, and so separated from the others. Then we analys each such class: we distinguished functions on the same domains for their different ways of performing pruning (point or set based), and consequently differentiated between algorithms of the same class (e.g., AC-1 and AC-3 versus AC-4 or AC-5). Besides, we also show how properties of functions (e.g., commutativity or stationarity) are related to different strategies of propagation in constraint algorithms of the same class (see, for instance, AC-1 versus AC-3). In Chapter 5 we apply the SGI schema to the case of soft CSPs (a generalisation of CSPs with sort-of preferences), thereby clarifying some of the similarities and differences between the "classical" and soft constraint-propagation algorithms. Finally, in Chapter 6, we summarise and characterise all the functions used for constraint propagation; in fact, the other goal of our theorisation is abstracting WHICH functions, iterated as in SGI or its variations, perform the task of "pruning" or "propagation" of inconsistencies in constraint propagation algorithms.We focus on relations and relational structures in Part II of the thesis. More specifically, modal languages allow us to talk about various relational structures and their properties. Once the latter are formulated in a modal language, they can be passed to automated theorem provers and tested for satisfiability, with respect to certain modal logics. Our task, in this part, can be described as follows: determining the satisfiability of modal formulas in an efficient manner. In Chapter 8, we focus on one way of doing this: we refine the standard translation as the layered translation, and use existing theorem provers for first-order logic on the output of this refined translation. We provide ample experimental evidence on the improvements in performances that were obtained by means of the refinement.The refinement of the standard translation is based on the tree model property. This property is also used in the basic algorithm schema in Chapter 9 ---the original schema is due to~\cite{seb97}. The proposed algorithm proceeds layer by layer in the modal formula and in its candidate models, applying constraint propagation and satisfaction algorithms for finite CSPs at each layer. With Chapter 9, we wish to draw the attention of constraint programmers to modal logics, and of modal logicians to CSPs.Modal logics themselves express interesting problems in terms of relations and unary predicates, like temporal reasoning tasks. On the other hand, constraint algorithms manipulate relations in the form of constraints, and unary predicates in the form of domains or unary constraints, see Chapter 6. Thus the question of how efficiently those algorithms can be applied to modal reasoning problems seems quite natural and challenging.

This dissertation addresses a fundamental question of multi-agent coordination: what infor- mation should be sent to whom and when, with the limited resources available to each agent? Communication requirements for multi-agent systems can be rather high when an accurate picture of the environment and the state of other agents must be maintained. To reduce the impact of multi-agent coordination on networked systems, e.g., power and bandwidth, this dissertation introduces new concepts to enable Intelligent Knowledge Distribution (IKD), including Constrained-action POMDPs (CA-POMDP) and concurrent decentralized (CoDec) POMDPs for an agnostic plug-and-play capability for fully autonomous systems. Each agent runs a CoDec POMDP where all the decision making (motion planning, task allocation, asset monitoring, and communication) are separated into concurrent individual MDPs to reduce the combinatorial explosion of the action and state space while maintaining dependencies between the models. We also introduce the CA-POMDP with action-based constraints on partially observable Markov decision processes, rewards driven by the value of information, and probabilistic constraint satisfaction through discrete optimization and Markov chain Monte Carlo analysis. IKD is adapted real-time through machine learning of the actual environmental impacts on the behavior of the system, including collaboration strategies between autonomous agents, the true value of information between heterogeneous systems, observation probabilities and resource utilization. / Doctor of Philosophy / This dissertation addresses a fundamental question behind when multiple autonomous sys- tems, like drone swarms, in the field need to coordinate and share data: what information should be sent to whom and when, with the limited resources available to each agent? Intelligent Knowledge Distribution is a framework that answers these questions. Communication requirements for multi-agent systems can be rather high when an accurate picture of the environment and the state of other agents must be maintained. To reduce the impact of multi-agent coordination on networked systems, e.g., power and bandwidth, this dissertation introduces new concepts to enable Intelligent Knowledge Distribution (IKD), including Constrained-action POMDPs and concurrent decentralized (CoDec) POMDPs for an agnostic plug-and-play capability for fully autonomous systems. The IKD model was able to demonstrate its validity as a "plug-and-play" library that manages communications between agents that ensures the right information is being transmitted at the right time to the right agent to ensure mission success.

Constraint Satisfaction Probleme tauchen in vielen Gebieten der theoretischen Informatik auf. Häufig lassen sie sich auf natürliche Weise als Homomorphieprobleme für eine festgelassene Struktur Gamma formulieren: Die Berechnungsaufgabe besteht dann darin, für eine gegebene Struktur S mit der gleichen relationalen Signatur wie Gamma festzustellen, ob es einen Homomorphismus von S nach Gamma gibt. Dieses Problem wurde für enliche Strukturen Gamma intensiv untersucht. Viele der Constraint Satisfaction Probleme, die in der Literatur betrachtet werden, lassen sich jedoch nicht mit endlichen Schablonen Gamma formulieren. Diese Arbeit verallgemeinert Techniken zur Untersuchung der Berechnungskomplexität von Constraint Satisfaction Problemen mit endlichen Schablonen auf unendliche Schablonen. Insbesondere betrachten wir abzählbar kategorische Schablonen, die von zentraler Bedeutung in Modelltheorie sind. / Constraint satisfaction problems occur in many areas of computer science. Often they have a natural formulation as a homomorphism problem for a fixed relational structure Gamma: Given a structure S with the same relational signature as Gamma, is there a homomorphism from S to Gamma? This problem is known as the constraint satisfaction problem CSP(Gamma) for the template Gamma and is intensively studied for relational structures Gamma with a finite domain. However, many constraint satisfaction problems in the literature can not be formulated with a finite template. This thesis generalizes techniques to determine the complexity of constraint satisfaction with finite templates to constraint satisfaction with templates over an infinite domain. In particular, we study templates that are countably categorical. Such structures are a central and well-studied concept in model-theory.

Cette thèse se situe dans le contexte de la programmation par contraintes (CP). Plus précisément, nous nous sommes intéressés au problème de satisfaction de contraintes pondérées (WCSP). De nombreuses approches ont été proposées pour traiter ce problème d’optimisation. Les méthodes les plus efficaces utilisent des cohérences locales souples sophistiquées comme par exemple la cohérence d’arc directionnelle complète FDAC∗, la cohérence d’arc directionnelle existentielle EDAC∗, etc. Établies grâce à des opérations de transferts de coût préservant l’équivalence des réseaux, l’utilisation de ces cohérences permet généralement d’accélérer la résolution en réduisant l’espace de recherche via la suppression de valeurs et le calcul de bornes inférieures utiles en pratique. Cependant, l’utilisation de ces méthodes pose un problème lorsque l’arité des contraintes augmente de manière significative. L’efficacité des techniques du cadre du problème de satisfaction de contraintes (CSP) étant avérée, nous pensons que l’intégration de techniques CSP peut être très utile à la résolution d’instances WCSP. Dans cette thèse, nous proposons tout d’abord un algorithme de filtrage établissant la cohérence d’arc souple généralisée GAC∗ sur des contraintes tables souples de grande arité. Cette approche combine la technique de réduction tabulaire simple (STR), issue du cadre CSP, et le principe de transfert de coûts. Notre approche qui est polynomiale calcule efficacement pour chaque valeur les coûts minimaux dans les tuples explicites et implicites des contraintes tables souples. Ces coûts minimaux sont ensuite utilisés pour transférer les coûts afin d’établir GAC∗. Dans un second temps, nous proposons une approche alternative aux méthodes de résolution habituelles du problème WCSP. Elle consiste à résoudre une instance WCSP en résolvant une séquence d’instances CSP classiques obtenues depuis cette instance WCSP. À partir d’une instance CSP dans laquelle toutes les contraintes de l’instanceWCSP d’origine sont durcies au maximum, les instances CSP suivantes correspondent à un relâchement progressif de contraintes de l’instance WCSP déterminées par l’extraction de noyaux insatisfaisables minimaux (MUC) depuis les réseaux insatisfaisables de la séquence. Nos résultats expérimentaux montrent que notre première approche est compétitive avec l’état de l’art, tandis que la deuxième représente une approche alternative aux méthodes de résolutionhabituelles d’instances WCSP. / This thesis is in the context of constraint programming (CP). Specifically, we are interested in the Weighted Constraint Satisfaction Problem (WCSP). Many approaches have been proposed to handle this optimization problem. The most effective methods use sophisticated soft local consistencies such as, for example, full directional arc consistency FDAC∗, existential directional arc consistency EDAC∗, etc. Established by equivalence preserving transformations (cost transfer operations), the use of these consistencies generally allows both to accelerate the resolution by reducing the search space through the elimination of values and to compute lower bounds useful in practice. However, these methods reach theirlimits when the arity of constraints increases significantly. The techniques of the Constraint Satisfaction Problem framework (CSP) having proved efficienty, we believe that the integration of CSP techniques can be very useful for solving WCSP instances. In this thesis, we first propose a filtering algorithm to enforce a soft version of generalized arc consistency (GAC∗) on soft table constraints of large arity. This approach combines the techniques of simple tabular reduction (STR), from the CSP framework, with the techniques of cost transfer. Our approach, proved polynomial, efficiently calculates for each value the minimum cost of the explicit and implicit tuples from soft table constraints. The minimum costs are thenused to transfer costs to establish GAC∗. In a second step, we propose an alternative approach to the usual techniques to solve WCSP. The principle is to solve a WCSP instance by solving a sequence of classical CSP instances obtained from this WCSP instance. From a CSP instance containing all the constraints hardened to the maximum from the WCSP instance, the next CSP instances correspond to a progressive relaxation of constraints defined by extraction of minimal unsatisfiable cores (MUC) from unsatisfiable networks of the sequence. Our experimental results show that our first approach is competitive with the state-of-the-art, whereas the second one represents an alternative approach to the usual methods to solve WCSP instances.

The object of the thesis is the computational complexity of certain combinatorial optimisation problems called \emph{valued constraint satisfaction problems}, or \emph{VCSPs} for short. The requirements and optimisation criteria of these problems are expressed by sums of \emph{(valued) constraints} (also called \emph{cost functions}). More precisely, the input of a VCSP consists of a finite set of variables, a finite set of cost functions that depend on these variables, and a cost $u$; the task is to find values for the variables such that the sum of the cost functions is at most $u$. By restricting the set of possible cost functions in the input, a great variety of computational optimisation problems can be modelled as VCSPs. Recently, the computational complexity of all VCSPs for finite sets of cost functions over a finite domain has been classified. Many natural optimisation problems, however, cannot be formulated as VCSPs over a finite domain. We initiate the systematic investigation of infinite-domain VCSPs by studying the complexity of VCSPs for piecewise linear (PL) and piecewise linear homogeneous (PLH) cost functions. The VCSP for a finite set of PLH cost functions can be solved in polynomial time if the cost functions are improved by fully symmetric fractional operations of all arities. We show this by (polynomial-time many-one) reducing the problem to a finite-domain VCSP which can be solved using a linear programming relaxation. We apply this result to show the polynomial-time tractability of VCSPs for {\it submodular} PLH cost functions, for {\it convex} PLH cost functions, and for {\it componentwise increasing} PLH cost functions; in fact, we show that submodular PLH functions and componentwise increasing PLH functions form maximally tractable classes of PLH cost functions. We define the notion of {\it expressive power} for sets of cost functions over arbitrary domains, and discuss the relation between the expressive power and the set of fractional operations improving the same set of cost functions over an arbitrary countable domain. Finally, we provide a polynomial-time algorithm solving the restriction of the VCSP for {\it all} PL cost functions to a fixed number of variables.

Nowadays, assembly robots are increasingly used in the manufacturing industry to replace or collaborate with human labors. This is the goal of the dual arm assembly robot developed by ABB. With the rapid upgrading in consumer electronics products, the lifetime of an assembly line could be only a few months. However, even for experienced programmers, to manually construct a good enough assembly sequence is time consuming, and the quality of the generated assembly sequence is not guaranteed. Moreover, a good robot assembly sequence is important to the throughput of an assembly line. For dual arm robots, it is also important to obtain a balance between the two arms, as well as handling scheduling conflicts and avoiding collisions in a crowded environment. In this master thesis, a program is produced to automatically generate the optimal assembly sequence for a class of real-world assembly cases. The solution also takes the layout of the assembly cell into account, thus constructing the best combination of cell layout, workload balancing, task sequence and task scheduling. The program is implemented using Google OR-Tools – an open-source support library for combinatorial optimization. A customized search strategy is proposed and a comparison between this strategy and the built-in search strategy of Google OR-Tools is done. The result shows that the used approach is effective for the problem study case. It takes about 4 minutes to find the optimal solution and 32 minutes to prove its optimality. In addition, the result also shows that the customized search strategy works consistently with good performance for different problem cases. Moreover, the customized strategy is more efficient than built-in search strategy in many cases. / Numera används monteringsrobotar alltmer inom tillverkningsindustrin för att ersätta eller samarbeta med människor. Detta är måluppgiften för den tvåarmiga monteringsroboten, YuMi, som utvecklats av ABB. Med den korta produktlivslängden för hemelektronikprodukter kan livslängden för en monteringslinje vara ett fåtal månader. Även för erfarna robotprogrammerare är det svårt och tidsödande att manuellt konstruera en tillräckligt bra monteringsordning, och dessutom kan resultatets kvalitet inte garanteras. En bra monteringsordning är nödvändig för genomströmningen i en monteringslinje. För tvåarmiga robotar, är det också viktigt att få en balans mellan de två armarna, samt hantering av schemakrockar och undvika kollisioner i en trång miljö. I detta examensarbete har ett program skrivits, som automatiskt genererar optimala lösningar för en klass av verkliga monteringsfall. Lösningen tar hänsyn till utformningen av monteringscellen och arrangerar cellen på bästa sätt, balanserar arbetsbelastningen, ordnar och tidsbestämmer uppgifter. Programmet använder sig av Google OR-Tools – ett öppet kodbibliotek för kombinatorisk optimering. Dessutom föreslås en skräddarsydd sökstrategi, som jämförs med Google OR-Tools inbyggda sökstrategi. Resultatet visar att den använda metoden är effektiv för problemtypen. Det tar ungefär 4 minuter att hitta den optimala lösningen och 32 minuter för att bevisa optimalitet. Dessutom visar resultatet att den anpassade sökstrategin konsekvent har en bra prestanda för olika problemfall. Dessutom är den anpassade strategin effektivare än den inbyggda sökstrategin i många fall.