Sequential decision-making under uncertainty often uses an approach in which a plan is built over a given horizon ahead using a deterministic model, the first decisions in this plan are applied, new information is acquired, the plan is adapted or rebuilt from scratch over a sliding horizon, and so on. This paper introduces a generic local search library that can be used in this context to quickly build and rebuild good quality plans. This library is built upon the notion of invariant used in constraint-based local search. Invariants allow temporal constraints, resource constraints, and criteria to be very quickly evaluated from a variable assignment and re-evaluated from a small change in this assignment. The paper also shows how the library can be used to reason on dynamic problem instances using a unique static problem model, without dynamic memory allocation. The approach is illustrated on a problem of data download under uncertainty about the volume of data, coming from the space domain.

Sequence optimization is an important problem in many production automation scenarios involving industrial robots. Mostly, this is done by reducing it to Traveling Salesman Problem (TSP). However, in many industrial scenarios optimization potential is not only hidden in optimizing a sequence of operations but also in optimizing the individual operations themselves. From a formal point of view, this leads to the Traveling Salesman Problem with Neighborhoods (TSPN). TSPN is a generalization of TSP where areas should be visited instead of points. In this paper we propose a new method for solving TSPN efficiently. We compare the new method to the related approaches using existing test benchmarks from the literature. According to the evaluation on instances with known optimal values, our method is able to obtain a solution close to the optimum.

We address a dynamic repair shop scheduling problem in the context of military aircraft fleet management where the goal is to maintain a full complement of aircraft over the long-term. A number of flights, each with a requirement for a specific number and type of aircraft, are already scheduled over a long horizon. We need to assign aircraft to flights and schedule repair activities while considering the flights requirements, repair capacity, and aircraft failures. The number of aircraft awaiting repair dynamically changes over time due to failures and it is therefore necessary to rebuild the repair schedule online. To solve the problem, we view the dynamic repair shop as successive static repair scheduling sub-problems over shorter time periods. We propose a complete approach based on the logic-based Benders decomposition to solve the static sub-problems, and design different rescheduling policies to schedule the dynamic repair shop. Computational experiments demonstrate that the Benders model is able to find and prove optimal solutions on average four times faster than a mixed integer programming model. The rescheduling approach having both aspects of scheduling over a longer horizon and quickly adjusting the schedule increases aircraft available in the long term by 10% compared to the approaches having either one of the aspects alone.

Comparative preference statements are the basic ingredients of conditional logics for representing users’ preferences in a compact way. These statements may be strict or not and obey different semantics. Algorithms have been developed in the literature to compute a preference relation over outcomes given a set of comparative preference statements and one or several semantics. These algorithms are based on insights from non-monotonic reasoning (more specifically, minimal and maximal specificity principles) enforcing the preference relations to be a complete preorder. The main limitation of these logics however relies in preference queries when comparing two outcomes. Indeed given two outcomes having the same preference w.r.t. the preference relation, there is no indication whether this equality results from an equality between two preference statements or the outcomes are in fact incomparable and equality has been enforced by specificity principles. On the other hand, comparative preference statements and their associated semantics can be translated into qualitative constraint satisfaction problems in which one can have a precise ordering over two outcomes. In this paper we investigate this bridge and provide a compilation of conditional logics-based preference queries in qualitative constraint problems.

The state-of-the-art Data-Peeler algorithm extracts closed patterns in n-ary relations. Because it refines both a lower and an upper bound of the pattern space, Data-Peeler can, in some circumstances, guarantee that a region of that space does not contain any closed n-set satisfying some relevance constraint. Whenever it happens, such region is not explored and some time is saved. This paper shows that some constraints, which Data-Peeler can efficiently enforce, define useful patterns in the context of a relation with groups of elements in arbitrary dimensions. For instance, it can list the so-called straddling biclusters, which cover at least some given portions of every group. It can discover, as well, closed n-sets that discriminate a group from the others. The experimental section focuses on the latter case. It shows that Data-Peeler is highly competitive despite its general enumeration principles and its expressive class of constraints that open up new applicative perspectives.

A conditional CSP is a well known formalism for managing constraints in a dynamic environment where the possible changes are known a priori and can be enumerated beforehand. In this paper we argue that mixing preferences with Conditional CSPs brings more intuitive meaning to many real world applications. For example, in a product configuration problem the user preferences often co-exist with the configuration requirements in a dynamic environment. We propose here an extension of the Conditional CSP formalism in order to consider qualitative preferences. We use CP-nets as a representation for these preferences and define new concepts for preserving their semantics in dynamic settings.

In this paper, we propose an extension of our Mining for SAT framework to Constraint satisfaction Problem (CSP). We consider n-ary extensional constraints (table constraints). Our approach aims to reduce the size of the CSP by exploiting the structure of the constraints graph and of its associated microstructure. More precisely, we apply itemset mining techniques to search for closed frequent itemsets on these two representation. Using Tseitin extension, we rewrite the whole CSP to another compressed CSP equivalent with respect to satisfiability. Our approach contrast with previous proposed approach by Katsirelos and Walsh, as we do not change the structure of the constraints.

We aim at providing a foundation of a theory of "good" SAT representations F of boolean functions f. We argue that the hierarchy UC_k of unit-refutation complete clause-sets of level k, introduced by the authors, provides the most basic target classes, that is, F in UC_k is to be achieved for k as small as feasible. If F does not contain new variables, i.e., F is equivalent (as a CNF) to f, then F in UC_1 is similar to "achieving (generalised) arc consistency" known from the literature (it is somewhat weaker, but theoretically much nicer to handle). We show that for polysize representations of boolean functions in this sense, the hierarchy UC_k is strict. The boolean functions for these separations are "doped" minimally unsatisfiable clause-sets of deficiency 1; these functions have been introduced in [Sloan, Soerenyi, Turan, 2007], and we generalise their construction and show a correspondence to a strengthened notion of irredundant sub-clause-sets. Turning from lower bounds to upper bounds, we believe that many common CNF representations fit into the UC_k scheme, and we give some basic tools to construct representations in UC_1 with new variables, based on the Tseitin translation. Note that regarding new variables the UC_1-representations are stronger than mere "arc consistency", since the new variables are not excluded from consideration.

Generalized traveling salesman problem (GTSP) is an extension of classical traveling salesman problem (TSP), which is a combinatorial optimization problem and an NP-hard problem. In this paper, an efficient discrete state transition algorithm (DSTA) for GTSP is proposed, where a new local search operator named \textit{K-circle}, directed by neighborhood information in space, has been introduced to DSTA to shrink search space and strengthen search ability. A novel robust update mechanism, restore in probability and risk in probability (Double R-Probability), is used in our work to escape from local minima. The proposed algorithm is tested on a set of GTSP instances. Compared with other heuristics, experimental results have demonstrated the effectiveness and strong adaptability of DSTA and also show that DSTA has better search ability than its competitors.

In this Part II, we apply the general theory developed in Part I to a detailed analysis of the Constraint Satisfaction Problem (CSP). We show how specific types of resolution rules can be defined. In particular, we introduce the general notions of a chain and a braid. As in Part I, these notions are illustrated in detail with the Sudoku example - a problem known to be NP-complete and which is therefore typical of a broad class of hard problems. For Sudoku, we also show how far one can go in 'approximating' a CSP with a resolution theory and we give an empirical statistical analysis of how the various puzzles, corresponding to different sets of entries, can be classified along a natural scale of complexity. For any CSP, we also prove the confluence property of some Resolution Theories based on braids and we show how it can be used to define different resolution strategies. Finally, we prove that, in any CSP, braids have the same solving capacity as Trial-and-Error (T&E) with no guessing and we comment this result in the Sudoku case.