Dimitris Magos

Hyperarc Consistency for the Stable Admissions Problem

This paper presents an algorithm achieving hyperarc consistency for the stable admissions problem and discusses computational results.The multiplication of very high resolution (spatial or spectral) remote sensing images appears to be an opportunity to identify objects in urban and periurban areas. The classification methods applied in the object-oriented image analysis approach could be based on the use of domain knowledge. A major issue in these approaches is domain knowledge formalization and exploitation. In this paper, we propose a recognition method based on an ontology which has been developed by experts of the domain. In order to give objects a semantic meaning, we have developed a matching process between an object and the concepts of the ontology. Experiments are made on a Quickbird image. The quality of the results shows the effectiveness of the proposed method.

On the system of two all_different predicates

Numerous real-life problems require certain variables to be assigned different values. This requirement is encapsulated in constraints of difference. If x1, x2 denote two problem variables, the (nonlinear) constraint of difference is x1 6= x2. Given that variables x1,..., xn must all be pairwise different, a constraint of the type all_different(x1, ..., xn) can be used to formulate in a compact manner the n(n−1) 2 binary constraints of difference. Such an n-ary constraint is also called a predicate because it imposes a logical condition on its variable set. Constraint Programming (CP) makes use of such elaborate predicates in order to provide a natural modelling framework ([2]). Such models are solved by CP techniques designed to produce feasible solutions. Alternatively, Integer Programming (IP) methods can be employed in cases where a logic predicate can be represented by linear inequalities involving integer variables ([1]). Apparently, such representations are important not only because they enrich the arsenal of resolution techniques but also because they motivate the integration of CP and IP in a unified modelling and algorithmic framework (see [3]). An efficient representation of a predicate must be tight, i.e. it must include facet-defining inequalities of the convex hull of integer solutions satisfying the predicate. Such representations have been proposed for the all_different predicate ([8]), for cardinality rules ([6]) and for the sum constraint ([7]). A next step would be to derive such representations for sets of more that one predicates. The current paper works towards this direction by studying a system of two all_different constraints which may share a number of variables. In particular, we examine the polytope defined by the convex hull of integer vectors satisfying the system of the two all_different predicates. The dimension of this polytope is established and subsequently two classes of facet-defining inequalities are exhibited. These classes are of exponential size, a fact that ∗Corresponding address: D. MAGOS, 30 Theodorou Geometrou Str., Athens 11743, Greece. Email:dmagos@teiath.gr

A polyhedral approach to the alldifferent system

This paper examines the facial structure of the convex hull of integer vectors satisfying a system of alldifferent predicates, also called an alldifferent system. The underlying analysis is based on a property, called inclusion, pertinent to such a system. For the alldifferent systems for which this property holds, we present two families of facet-defining inequalities, establish that they completely describe the convex hull and show that they can be separated in polynomial time. Consequently, the inclusion property characterises a group of alldifferent systems for which the linear optimization problem (i.e. the problem of optimizing a linear function over that system) can be solved in polynomial time. Furthermore, we establish that, for systems with three predicates, the inclusion property is also a necessary condition for the convex hull to be described by those two families of inequalities. For the alldifferent systems that do not possess that property, we establish another family of facet-defining inequalities and an accompanied polynomial-time separation algorithm. All the separation algorithms are incorporated within a cutting-plane scheme and computational experience on a set of randomly generated instances is reported. In concluding, we show that the pertinence of the inclusion property can be decided in polynomial time.

Integrating Constraint and Integer Programming for the Orthogonal Latin Squares Problem

We consider the problem of Mutually Orthogonal Latin Squares and propose two algorithms which integrate Integer Programming (IP) and Constraint Programming (CP). Their behaviour is examined and compared to traditional CP and IP algorithms. The results assess the quality of inference achieved by the CP and IP, mainly in terms of early identification of infeasible subproblems. It is clearly illustrated that the integration of CP and IP is beneficial and that one hybrid algorithm exhibits the best performance as the problem size grows. An approach for reducing the search by excluding isomorphic cases is also presented.

On the Facial Structure of the Alldifferent System

We study the facial structure of the alldifferent system, i.e., the polytope (namely,

Searching for mutually orthogonal latin squares via integer and constraint programming

P_{I}

A new class of facets for the Latin square polytope

) defined as the convex hull of integer vectors satisfying such a system. We derive classes of facets for

An LP-based proof for the non-existence of a pair of orthogonal Latin squares of order 6

P_{I}

LP relaxations of multiple all_different predicates

by examining induced subgraphs of the associated constraint graph. Some of these graphic structures (for example, odd holes, webs, etc.) are well known to induce facets of the set packing polytope, namely,

On the orthogonal Latin squares polytope

P_{S}