arXiv subjects

Cécile Rottner

Publications and source records attributed to Cécile Rottner.

2 recordsLinked to original sources

arXiv2026

BORWin: Exact algorithm based on a Bi-Objective Relaxation for Window-constrained problems

A mixed integer maximization problem involving several additional constraints defined with both a lower and an upper bound is considered. It is assumed that one of such constraints is more restrictive than the others. As it can be seen as a resource window constraint, it defines the so-called window-constrained problem. From a bi-objective perspective, a 2-phase algorithm, called BORWin, is devised. It stands for Bi-Objective Relaxation for Window-constrained problems. The first phase is generic for any window-constrained problem and provides a family of upper bounds based on a bi-objective relaxation of the additional constraints. It is shown that the latter bounds strongly relate to the Lagrangian dual bounds. The second phase is derived for a variant involving a graph structure, namely the window-constrained longest-path problem on an acyclic graph. The aim is to take advantage of the upper bounds to devise an efficient label extension algorithm. It is shown that complementary upper bounds could be derived to further improve performance in some special cases. A typical example is when the additional constraints have special knapsack structures. This is the case for the Hydro-Unit Commitment problem with a single plant (1-HUC). From numerical experiments for the 1-HUC, BOR-Win appears to be very efficient compared to state-of-the-art approaches.

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arXiv2018

Orbitopal fixing for the full (sub)-orbitope and application to the Unit Commitment Problem

This paper focuses on integer linear programs where solutions are binary matrices, and the corresponding symmetry group is the set of all column permutations. Orbitopal fixing, as introduced by Kaibel et al., is a technique designed to break symmetries in the special case of partitioning (resp. packing) formulations involving matrices with exactly (resp. at most) one 1-entry in each row.The main result of this paper is to extend orbitopal fixing to the full orbitope, defined as the convex hull of binary matrices with lexicographically nonincreasing columns.We determine all the variables whose values are fixed in the intersection of an hypercube face with the full orbitope.Sub-symmetries arising in a given subset of matrices are also considered, thus leading to define the full sub-orbitope in the case of the sub-symmetric group.We propose a linear time orbitopal fixing algorithm handling both symmetries and sub-symmetries.We introduce a dynamic variant of this algorithm where the lexicographical order follows the branching decisions occurring alongthe B&B search. Experimental results for the Unit Commitment Problem are presented. A comparison with state-of-the-art techniques is considered to show the effectiveness of the proposed variants of the algorithm.

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