arXiv subjects

Pascale Bendotti

Publications and source records attributed to Pascale Bendotti.

7 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.

math.OC↗

arXiv2026

A Quantum Photonic Approach to Graph Coloring

Gaussian Boson Sampling (GBS) is a quantum computational model that leverages linear optics to solve sampling problems believed to be classically intractable. Recent experimental breakthroughs have demonstrated quantum advantage using GBS, motivating its application to real-world combinatorial optimization problems. In this work, we reformulate the graph coloring problem as an integer programming problem using the independent set formulation. This enables the use of GBS to identify cliques in the complement graph, which correspond to independent sets in the original graph. Our method is benchmarked against classical heuristics and exact algorithms on two sets of instances: Erd\H{o}s-R\'enyi random graphs and graphs derived from a smart-charging use case. The results demonstrate that GBS can provide competitive solutions, highlighting its potential as a quantum-enhanced heuristic for graph-based optimization.

quant-ph↗

arXiv2024

Implementing transferable annealing protocols for combinatorial optimisation on neutral atom quantum processors: a case study on smart-charging of electric vehicles

In the quantum optimization paradigm, variational quantum algorithms face challenges with hardware-specific and instance-dependent parameter tuning, which can lead to computational inefficiencies. The promising potential of parameter transferability across problem instances with similar local structures has been demonstrated in the context of the quantum approximate optimization algorithm. In this paper we build on these advancements by extending the concept to annealing-based protocols, employing Bayesian optimization to design robust quasi adiabatic schedules. Our study reveals that, for maximum independent set problems on graph families with shared geometries, optimal parameters naturally concentrate, enabling efficient transferability between similar instances and from smaller to larger ones. Experimental results on the Orion Alpha platform validate the effectiveness of our approach, scaling to problems with up to $100$ qubits. We apply this method to address a smart-charging optimization problem on a real dataset. These findings highlight a scalable, resource-efficient path for hybrid optimization strategies applicable in real-world scenarios.

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arXiv2024

Resource Leveling: Complexity of a UET two-processor scheduling variant and related problems

This paper mainly focuses on a resource leveling variant of a two-processor scheduling problem. The latter problem is to schedule a set of dependent UET jobs on two identical processors with minimum makespan. It is known to be polynomial-time solvable. In the variant we consider, the resource constraint on processors is relaxed and the objective is no longer to minimize makespan. Instead, a deadline is imposed on the makespan and the objective is to minimize the total resource use exceeding a threshold resource level of two. This resource leveling criterion is known as the total overload cost. Sophisticated matching arguments allow us to provide a polynomial algorithm computing the optimal solution as a function of the makespan deadline. It extends a solving method from the literature for the two-processor scheduling problem. Moreover, the complexity of related resource leveling problems sharing the same objective is studied. These results lead to polynomial or pseudo-polynomial algorithms or NP-hardness proofs, allowing for an interesting comparison with classical machine scheduling problems.

cs.CC↗

arXiv2021

Dominance-based linear formulation for the Anchor-Robust Project Scheduling Problem

In project scheduling under processing times uncertainty, the Anchor-Robust Project Scheduling Problem is to find a baseline schedule of bounded makespan and a max-weight subset of jobs whose starting times are guaranteed. The problem was proven NP-hard even for budgeted uncertainty. In the present work we design mixed-integer programming (MIP) formulations that are valid for a variety of uncertainty sets encompassing budgeted uncertainty. A new dominance among solutions is proposed, resulting into an MIP formulation. We further study the combinatorial structure of the problem. Non-trivial polynomial cases under budgeted uncertainty are exhibited, where the dominance-based formulation yields a polyhedral characterization of integer solutions. In more general cases, the dominance-based formulation is shown to be tighter than all previously known formulations. In numerical experiments we investigate how the formulation performs on instances around the polynomial cases, for both budgeted uncertainty sets and more elaborate uncertainty sets involving several budgets.

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arXiv2020

Exact and heuristic methods for Anchor-Robust and Adjustable-Robust RCPSP

The concept of anchored solutions is proposed as a new robust optimization approach to the Resource-Constrained Project Scheduling Problem (RCPSP) under processing times uncertainty. The Anchor-Robust RCPSP is defined, to compute a baseline schedule with bounded makespan, sequencing decisions, and a max-size subset of jobs with guaranteed starting times, called anchored set. It is shown that the Adjustable-Robust RCPSP from the literature fits within the framework of anchored solutions. The Anchor-Robust RCPSP and the Adjustable-Robust RCPSP can benefit from each other to find both a worst-case makespan and a baseline schedule with an anchored set. A dedicated graph model for anchored solutions is proposed for budgeted uncertainty. Compact MIP reformulations are derived for both the Adjustable-Robust RCPSP and the Anchor-Robust RCPSP. Dedicated heuristics are designed based on the graph model. For both problems, the efficiency of the proposed MIP reformulations and heuristic approaches is assessed through numerical experiments on benchmark instances.

math.OC↗

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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