Antoine Jouglet

A new constraint programming approach for the orthogonal packing problem

The two-dimensional orthogonal packing problem (2OPP) consists in determining if a set of rectangles can be packed in a larger rectangle of fixed size. We propose an exact method for 2OPP, based on a new constraint-based scheduling model. We provide a generalization of energetic reasoning techniques for the problem under investigation. Feasibility tests requiring the solution of subset-sum problems are described. Computational results confirm the efficiency of our method compared to others in the literature.

Optimal Object Association in the Dempster–Shafer Framework

Object association is a crucial step in target tracking and data fusion applications. This task can be formalized as the search for a relation between two sets (e.g., a sets of tracks and a set of observations) in such a way that each object in one set is matched with at most one object in the other set. In this paper, this problem is tackled using the formalism of belief functions. Evidence about the possible association of each object pair, usually obtained by comparing the values of some attributes, is modeled by a Dempster-Shafer mass function defined in the frame of all possible relations. These mass functions are combined using Dempsters rule, and the relation with maximal plausibility is found by solving an integer linear programming problem. This problem is shown to be equivalent to a linear assignment problem, which can be solved in polynomial time using, for example, the Hungarian algorithm. This method is demonstrated using simulated and real data. The 3-D extension of this problem (with three object sets) is also formalized and is shown to be NP-Hard.

A Branch-and-Bound procedure to minimize total tardiness on one machine with arbitrary release dates

In this paper, we present a Branch-and-Bound procedure to minimize total tardiness on one machine with arbitrary release dates. We introduce new lower bounds and we generalize some well-known dominance properties. Our procedure handles instances as large as 500 jobs although some 60 jobs instances remain open. Computational results show that the proposed approach outperforms the best known procedures.

Dominance rules for the parallel machine total weighted tardiness scheduling problem with release dates

We address the parallel machine total weighted tardiness scheduling problem with release dates. We describe dominance rules and filtering methods for this problem. Most of them are adaptations of dominance rules based on solution methods for the single-machine problem. We show how it is possible to deduce whether or not certain jobs can be processed by a particular machine in a particular context and we describe techniques that use this information to improve the dominance rules. On the basis of these techniques we describe an enumeration procedure and we provide experimental results to determine the effectiveness of the dominance rules.

A new lower bound for the non-oriented two-dimensional bin-packing problem

We propose a new scheme for computing lower bounds for the non-oriented bin-packing problem when the bin is a square. It leads to bounds that theoretically dominate previous results. Computational experiments show that the bounds are tight. We also discuss the case where the bin is not a square.

Dominance-based heuristics for one-machine total cost scheduling problems

We study the one-machine scheduling problem with release dates and we look at several objective functions including total (weighted) tardiness and total (weighted) completion time. We describe dominance rules for these criteria, as well as techniques for using these dominance rules to build heuristic solutions. We use them to improve certain well-known greedy heuristic algorithms from the literature. Finally, we introduce a Tabu Search method with a neighborhood based on our dominance rules. Experiments show the effectiveness of our techniques in obtaining very good solutions for all studied criteria.

A New Graph-Theoretical Model for the Guillotine-Cutting Problem

We consider the problem of determining whether a given set of rectangular items can be cut from a larger rectangle using so-called guillotine cuts only. We introduce a new class of arc-colored directed graphs called guillotine graphs and show that each guillotine graph can be associated with a specific class of pattern solutions that we call a guillotine-cutting class. The properties of guillotine graphs are examined, and some effective algorithms for dealing with guillotine graphs are proposed. As an application, we then describe a constraint programming method based on guillotine graphs, and we propose effective filtering techniques that use the graph model properties in order to reduce the search space efficiently. Computational experiments are reported on benchmarks from the literature: our algorithm outperforms previous methods when solving the most difficult instances exactly.

Single-machine scheduling with no idle time and release dates to minimize a regular criterion

We address the one-machine scheduling problem with release dates, in which the machine is subject to the non-idling constraint, i.e. no intermediate idle time is permitted between the jobs processed by the machine. The objective is to minimize a regular objective function. We describe a constraint programming approach for solving this type of problem exactly. Some necessary and/or sufficient conditions for obtaining non-idling semi-active, active and optimal schedules are described. We propose some propagation rules based on these properties. As an application, we apply the proposed method to the total (weighted) completion time problem, and we provide some experimental results to illustrate its effectiveness.

A new graph-theoretical model for k-dimensional guillotine-cutting problems

We consider the problem of determining if a given set of rectangular items can be cut in a large rectangle, using guillotine cuts only. We introduce a new class of arc-colored and oriented graphs, named guillotine graphs, which model guillotine patterns. Then we show that an uncolored and non-oriented multigraph is sufficient to obtain any guillotine pattern. We propose linear algorithms for recognizing these graphs, and computing the corresponding patterns. Finally we explain how the model can be used in a constraint programming approach.

On Minimizing Total Tardiness in a Serial Batching Problem

We study the problem of scheduling jobs on a serial batching machine to minimize total tardiness. Jobs of the same batch start and are completed simultaneously and the length of a batch equals the sum of the processing times of its jobs. When a new batch starts, a constant setup time s occurs. This problem 1| s-batch | ∑ T i is known to be NP-Hard in the ordinary sense. In this paper we show that it is solvable in pseudopolynomial time by dynamic programming.