arXiv subjects

Olivier Ploton

Publications and source records attributed to Olivier Ploton.

3 recordsLinked to original sources

arXiv2026

Heuristic approaches for solving a bilevel optimistic scheduling problem on parallel machines

This work addresses the uniform parallel machine scheduling problem within an optimistic bilevel optimization framework. The leader seeks to minimize the weighted number of tardy jobs, while the follower aims to minimize the total completion time across a set of uniform machines. The hierarchical decision-making process of the bilevel problem makes designing effective heuristics challenging. To tackle this, we exploit a property of the follower that enables the construction of optimal schedules. From this property, we derive an effective branching scheme that simultaneously accounts for both leader and follower decisions. This branching scheme allows us to design a Recovering Beam Search (RBS), which represents a significant contribution from a bilevel perspective. Then we propose a Multi-Start Local Search (MSLS) algorithm based on an innovative scheme that couples the RBS and a Local Search (LS). To the best of our knowledge, while hybridizing beam search with local search is known in other contexts, our approach of leveraging a bilevel-specific branching scheme to efficiently explore the search space is novel. Moreover, we propose an automated method for determining heuristic parameters via Bayesian optimization. This reduces computational resource requirements and yields better parameters than the usual empirical approach. Finally, computational experiments are presented for instances with up to 500 jobs and 10 machines.

math.OC↗

arXiv2026

Solution of a bilevel optimistic scheduling problem on parallel machines

We consider the uniform parallel machines scheduling problem in the context of optimistic bilevel optimization, where two speed options are considered. In this scenario, the leader aims to minimize the weighted number of tardy jobs, while the follower seeks to minimize the total completion time on a set of uniform machines. This problem has practical applications in Industry 4.0. We show that this problem is NP-hard in the strong sense by providing a reduction from the Numerical 3-Dimensional Matching problem and we provide a moderately exponential-time dynamic programming algorithm. The problem is solved by means of a concise MIP formulation and a branch-and-bound algorithm that embeds a column generation approach for the lower bound computation. Computational experiments are presented for instances with up to 80 jobs and 4 machines while larger problems are out of reach for the proposed approaches.

math.OC↗

arXiv2024

Moderate Exponential-time Quantum Dynamic Programming Across the Subsets for Scheduling Problems

Grover Search is currently one of the main quantum algorithms leading to hybrid quantum-classical methods that reduce the worst-case time complexity for some combinatorial optimization problems. Specifically, the combination of Quantum Minimum Finding (obtained from Grover Search) with dynamic programming has proved particularly efficient in improving the complexity of NP-hard problems currently solved by classical dynamic programming. For these problems, the classical dynamic programming complexity in $\mathcal{O}^*(c^n)$, where $\mathcal{O}^*$ denotes that polynomial factors are ignored, can be reduced by a hybrid algorithm to $\mathcal{O}^*(c_{quant}^n)$, with $c_{quant} < c$. In this paper, we provide a bounded-error hybrid algorithm that achieves such an improvement for a broad class of NP-hard single-machine scheduling problems for which we give a generic description. Moreover, we extend this algorithm to tackle the 3-machine flowshop problem. Our algorithm reduces the exponential-part complexity compared to the best-known classical algorithm, sometimes at the cost of an additional pseudo-polynomial factor.

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