134 research outputs found

    Generalizing Refinement Operators to Learn Prenex Conjunctive Normal Forms

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    Inductive Logic Programming considers almost exclusively universally quantied theories. To add expressiveness, prenex conjunctive normal forms (PCNF) with existential variables should also be considered. ILP mostly uses learning with refinement operators. To extend refinement operators to PCNF, we should first do so with substitutions. However, applying a classic substitution to a PCNF with existential variables, one often obtains a generalization rather than a specialization. In this article we define substitutions that specialize a given PCNF and a weakly complete downward refinement operator. Moreover, we analyze the complexities of this operator in different types of languages and search spaces. In this way we lay a foundation for learning systems on PCNF. Based on this operator, we have implemented a simple learning system PCL on some type of PCNF.learning;PCNF;completeness;refinement;substitutions

    Generalizing Refinement Operators to Learn Prenex Conjunctive Normal Forms

    Get PDF
    Inductive Logic Programming considers almost exclusively universally quantied theories. To add expressiveness, prenex conjunctive normal forms (PCNF) with existential variables should also be considered. ILP mostly uses learning with refinement operators. To extend refinement operators to PCNF, we should first do so with substitutions. However, applying a classic substitution to a PCNF with existential variables, one often obtains a generalization rather than a specialization. In this article we define substitutions that specialize a given PCNF and a weakly complete downward refinement operator. Moreover, we analyze the complexities of this operator in different types of languages and search spaces. In this way we lay a foundation for learning systems on PCNF. Based on this operator, we have implemented a simple learning system PCL on some type of PCNF

    Weighted Constraints in Fuzzy Optimization

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    Many practical optimization problems are characterized by someflexibility in the problem constraints, where this flexibility canbe exploited for additional trade-off between improving theobjective function and satisfying the constraints. Especially indecision making, this type of flexibility could lead to workablesolutions, where the goals and the constraints specified bydifferent parties involved in the decision making are traded offagainst one another and satisfied to various degrees. Fuzzy setshave proven to be a suitable representation for modeling this typeof soft constraints. Conventionally, the fuzzy optimizationproblem in such a setting is defined as the simultaneoussatisfaction of the constraints and the goals. No additionaldistinction is assumed to exist amongst the constraints and thegoals. This report proposes an extension of this model forsatisfying the problem constraints and the goals, where preferencefor different constraints and goals can be specified by thedecision-maker. The difference in the preference for theconstraints is represented by a set of associated weight factors,which influence the nature of trade-off between improving theoptimization objectives and satisfying various constraints.Simultaneous weighted satisfaction of various criteria is modeledby using the recently proposed weighted extensions of(Archimedean) fuzzy t-norms. The weighted satisfaction of theproblem constraints and goals are demonstrated by using a simplefuzzy linear programming problem. The framework, however, is moregeneral, and it can also be applied to fuzzy mathematicalprogramming problems and multi-objective fuzzy optimization.wiskundige programmering;fuzzy sets;optimalisatie

    Crew Rostering for the High Speed Train

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    At the time of writing we entered the final stage of implementing the crew rostering system Harmony CDR to facilitate the planning of catering crews on board of the Thalys, the High Speed Train connecting Paris, Cologne, Brussels, Amsterdam, and Geneva. Harmony CDR optimally supports the creation of crew rosters in two ways. Firstly, Harmony CDR contains a powerful algorithm to automatically generate a set of rosters, which is especially developed for this specific situation. As the user has some control over the objectives of the algorithm, several scenarios can be studied before a set of rosters is adopted. An important feature of the automatic roster generator is that it respects requirements, directives, and requests stemming from legal, union, and/or company regulations and/or from individual crew. Secondly, Harmony CDR provides user-interface data manipulation at various levels of detail. The user interface enables the planner to easily obtain many different views on the planning data and to manipulate the planning manually. So again, the planner gets optimal support from the system while he or she is still in control. Also, violating a requirement, directive, or request is detected and displayed, but can be accepted by the planner. In this paper we describe the crew rostering problem for the catering crews of the High Speed Train and the Harmony CDR solution in more detail.decision support systems;railways;crew rostering

    Symbolic reactive synthesis

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    In this thesis, we develop symbolic algorithms for the synthesis of reactive systems. Synthesis, that is the task of deriving correct-by-construction implementations from formal specifications, has the potential to eliminate the need for the manual—and error-prone—programming task. The synthesis problem can be formulated as an infinite two-player game, where the system player has the objective to satisfy the specification against all possible actions of the environment player. The standard synthesis algorithms represent the underlying synthesis game explicitly and, thus, they scale poorly with respect to the size of the specification. We provide an algorithmic framework to solve the synthesis problem symbolically. In contrast to the standard approaches, we use a succinct representation of the synthesis game which leads to improved scalability in terms of the symbolically represented parameters. Our algorithm reduces the synthesis game to the satisfiability problem of quantified Boolean formulas (QBF) and dependency quantified Boolean formulas (DQBF). In the encodings, we use propositional quantification to succinctly represent different parts of the implementation, such as the state space and the transition function. We develop highly optimized satisfiability algorithms for QBF and DQBF. Based on a counterexample-guided abstraction refinement (CEGAR) loop, our algorithms avoid an exponential blow-up by using the structure of the underlying symbolic encodings. Further, we extend the solving algorithms to extract certificates in the form of Boolean functions, from which we construct implementations for the synthesis problem. Our empirical evaluation shows that our symbolic approach significantly outperforms previous explicit synthesis algorithms with respect to scalability and solution quality.In dieser Dissertation werden symbolische Algorithmen fĂŒr die Synthese von reaktiven Systemen entwickelt. Synthese, d.h. die Aufgabe, aus formalen Spezifikationen korrekte Implementierungen abzuleiten, hat das Potenzial, die manuelle und fehleranfĂ€llige Programmierung ĂŒberflĂŒssig zu machen. Das Syntheseproblem kann als unendliches Zweispielerspiel verstanden werden, bei dem der Systemspieler das Ziel hat, die Spezifikation gegen alle möglichen Handlungen des Umgebungsspielers zu erfĂŒllen. Die Standardsynthesealgorithmen stellen das zugrunde liegende Synthesespiel explizit dar und skalieren daher schlecht in Bezug auf die GrĂ¶ĂŸe der Spezifikation. Diese Arbeit prĂ€sentiert einen algorithmischen Ansatz, der das Syntheseproblem symbolisch löst. Im Gegensatz zu den StandardansĂ€tzen wird eine kompakte Darstellung des Synthesespiels verwendet, die zu einer verbesserten Skalierbarkeit der symbolisch dargestellten Parameter fĂŒhrt. Der Algorithmus reduziert das Synthesespiel auf das ErfĂŒllbarkeitsproblem von quantifizierten booleschen Formeln (QBF) und abhĂ€ngigkeitsquantifizierten booleschen Formeln (DQBF). In den Kodierungen verwenden wir propositionale Quantifizierung, um verschiedene Teile der Implementierung, wie den Zustandsraum und die Übergangsfunktion, kompakt darzustellen. Wir entwickeln hochoptimierte ErfĂŒllbarkeitsalgorithmen fĂŒr QBF und DQBF. Basierend auf einer gegenbeispielgefĂŒhrten Abstraktionsverfeinerungsschleife (CEGAR) vermeiden diese Algorithmen ein exponentielles Blow-up, indem sie die Struktur der zugrunde liegenden symbolischen Kodierungen verwenden. Weiterhin werden die Lösungsalgorithmen um Zertifikate in Form von booleschen Funktionen erweitert, aus denen Implementierungen fĂŒr das Syntheseproblem abgeleitet werden. Unsere empirische Auswertung zeigt, dass unser symbolischer Ansatz die bisherigen expliziten Synthesealgorithmen in Bezug auf Skalierbarkeit und LösungsqualitĂ€t deutlich ĂŒbertrifft

    One and Two Way Packaging in the Dairy Sector

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    Choosing packaging material for dairy products and soft drinks is an interesting issue at the moment. Discussions arise on the costs impacts and environmental impacts of both one way packaging and reusable packaging. The aim of this article is to develop an evaluation tool providing costs and environmental impacts of the PC-bottle and the GT-packs in the dairy sector, considering forward and return flows. The evaluation tool enables the user to analyse the costs and environmental impacts of a supply chain with and without return flows using scenario analyses with respect to the use of various carrier types and the number of return loops. It appears that costs differences between PC-bottles and GT-pack are quite small. The PC bottle has a better environmental profile than the GT-pack. Scenario analysis on the carriers results in the advice to use preferably roll-in-containers with direct delivery, secondly roll-in-containers with delivery via distribution centers, thirdly in case of direct delivery either cartons or crates and cartons in case of delivery via distribution centers.pricing;supply chain management;reverse logistics;environment;life cycle assessment

    Probabilistic and Statistical Fuzzy Set Foundations of Competitive Exception Learning

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    Recently, a Competitive Exception Learning Algorithm (CELA) was introduced [1, 2]. This algorithm establishes an optimal mapping from a (continuous) M-dimensional input sample space to an N-dime

    Weighted Constraints in Fuzzy Optimization

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    Many practical optimization problems are characterized by some flexibility in the problem constraints, where this flexibility can be exploited for additional trade-off between improving the objective function and satisfying the constraints. Especially in decision making, this type of flexibility could lead to workable solutions, where the goals and the constraints specified by different parties involved in the decision making are traded off against one another and satisfied to various degrees. Fuzzy sets have proven to be a suitable representation for modeling this type of soft constraints. Conventionally, the fuzzy optimization problem in such a setting is defined as the simultaneous satisfaction of the constraints and the goals. No additional distinction is assumed to exist amongst the constraints and the goals. This report proposes an extension of this model for satisfying the problem constraints and the goals, where preference for different constraints and goals can be specified by the decision-maker. The difference in the preference for the constraints is represented by a set of associated weight factors, which influence the nature of trade-off between improving the optimization objectives and satisfying various constraints. Simultaneous weighted satisfaction of various criteria is modeled by using the recently proposed weighted extensions of (Archimed

    Crew Rostering for the High Speed Train

    Get PDF
    At the time of writing we entered the final stage of implementing the crew rostering system Harmony CDR to facilitate the planning of catering crews on board of the Thalys, the High Speed Train connecting Paris, Cologne, Brussels, Amsterdam, and Geneva. Harmony CDR optimally supports the creation of crew rosters in two ways. Firstly, Harmony CDR contains a powerful algorithm to automatically generate a set of rosters, which is especially developed for this specific situation. As the user has some control over the objectives of the algorithm, several scenarios can be studied before a set of rosters is adopted. An important feature of the automatic roster generator is that it respects requirements, directives, and requests stemming from legal, union, and/or company regulations and/or from individual crew. Secondly, Harmony CDR provides user-interface data manipulation at various levels of detail. The user interface enables the planner to easily obtain many different views on the planning data and to manipulate the planning manually. So again, the planner gets optimal support from the system while he or she is still in control. Also, violating a requirement, directive, or request is detected and displayed, but can be accepted by the planner. In this paper we describe the crew rostering problem for the catering crews of the High Speed Train and the Harmony CDR solution in more detail

    Mining frequent intemsets in memory-resident databases

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    Due to the present-day memory sizes, a memory-resident database has become a practical option. Consequently, new methods designed to mining in such databases are desirable. In the case of disk-resident databases, breadth-first search methods are commonly used. We propose a new algorithm, based upon depth-first search in a set-enumeration tree. For memory-resident databases, this method turns out to be superior to breadth-first search
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