arXiv subjects

Madalina Erascu

Publications and source records attributed to Madalina Erascu.

6 recordsLinked to original sources

arXiv2026

When Algebraic Symmetry Breaking Meets Solvers: An Experimental Study

We present an experimental evaluation of automatically generated polynomial symmetry breaking constraints for integer linear programs. Starting from the method that we introduced at the International Symposium on Symbolic and Algebraic Computation (ISSAC) 2026, we compare solver native quadratic handling, solver-internal reformulation, and explicit linearization on near half-capacity bin-packing benchmarks. Experiments with several mathematical programming solvers and satisfiability modulo theory solvers show that the effectiveness of polynomial symmetry breaking is strongly solver-dependent. Compact quadratic breaker families can improve performance, whereas linearization, large breaker sets, or solver reformulations may offset these gains through increased model size or less favorable search behavior. These results suggest that automatically generated symmetry breakers should be evaluated in a solver-aware manner rather than treated as solver-independent additions to a model.

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arXiv2026

Automatic Generation of Polynomial Symmetry Breaking Constraints

Symmetry in integer programming causes redundant search and is often handled with symmetry breaking constraints that remove as many equivalent solutions as possible. We propose an algebraic method which allows to generate a random family of polynomial inequalities which can be used as symmetry breakers. The method requires as input an arbitrary base polynomial and a group of permutations which is specific to the integer program. The computations can be easily carried out in any major symbolic computation software. In order to test our approach, we describe a case study on near half-capacity 0-1 bin packing instances which exhibit substantial symmetries. We statically generate random quadratic breakers and add them to a baseline integer programming problem which we then solve with Gurobi. It turns out that simple symmetry breakers, especially combining few variables and permutations, most consistently reduce work time.

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arXiv2025

Neuro-Symbolic Constrained Optimization for Cloud Application Deployment via Graph Neural Networks and Satisfiability Modulo Theory

This paper proposes a novel hybrid neuro-symbolic framework for the optimal and scalable deployment of component-based applications in the Cloud. The challenge of efficiently mapping application components to virtual machines (VMs) across diverse VM Offers from Cloud Providers is formalized as a constrained optimization problem (COP), considering both general and application-specific constraints. Due to the NP-hard nature and scalability limitations of exact solvers, we introduce a machine learning-enhanced approach where graph neural networks (GNNs) are trained on small-scale deployment instances and their predictions are used as soft constraints within the Z3 SMT solver. The deployment problem is recast as a graph edge classification task over a heterogeneous graph, combining relational embeddings with constraint reasoning. Our framework is validated through several realistic case studies, each highlighting different constraint profiles. Experimental results confirm that incorporating GNN predictions improves solver scalability and often preserves or even improves cost-optimality. This work demonstrates the practical benefits of neuro-symbolic coupling for Cloud infrastructure planning and contributes a reusable methodology for general NP-hard problems.

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arXiv2023

SAGE -- A Tool for Optimal Deployments in Kubernetes Clusters

Cloud computing has brought a fundamental transformation in how organizations operate their applications, enabling them to achieve affordable high availability of services. Kubernetes has emerged as the preferred choice for container orchestration and service management across many Cloud computing platforms. The scheduler in Kubernetes plays a crucial role in determining the placement of newly deployed service containers. However, the default scheduler, while fast, often lacks optimization, leading to inefficient service placement or even deployment failures. This paper introduces SAGE, a tool for optimal solutions in Kubernetes clusters that can also assist the Kubernetes default scheduler and any other custom scheduler in application deployment. SAGE computes an optimal deployment plan based on the constraints of the application to be deployed and the available Cloud resources. We show the potential benefits of using SAGE by considering test cases with various characteristics. It turns out that SAGE surpasses other schedulers by comprehensively analyzing the application demand and cluster image. This ability allows it to better understand the needs of the pods, resulting in consistently optimal solutions across all scenarios. The accompanying material of this paper is publicly available at https://github.com/SAGE-Project/SAGE-Predeployer.

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arXiv2023

Benchmarking Optimization Solvers and Symmetry Breakers for the Automated Deployment of Component-based Applications in the Cloud (EXTENDED ABSTRACT)

Optimization solvers based on methods from constraint programming (OR-Tools, Chuffed, Gecode), optimization modulo theory (Z3), and mathematical programming (CPLEX) are successfully applied nowadays to solve many non-trivial examples. However, for solving the problem of automated deployment in the Cloud of component-based applications, their computational requirements are huge making automatic optimization practically impossible with the current general optimization techniques. To overcome the difficulty, we exploited the sweet spots of the underlying problem in order to identify search space reduction methods. We came up with 15 symmetry breaking strategies which we tested in a static symmetry breaking setting on the solvers enumerated above and on 4 classes of problems. As a result, all symmetry breaking strategies led to significant improvement of the computational time of all solvers, most notably, Z3 performed the best compared to the others. As an observation, the symmetry breaking strategies confirmed that, when applied in a static setting, they may interact badly with the underlying techniques implemented by the solvers.

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arXiv2020

Scalable Optimal Deployment in the Cloud of Component-based Applications using Optimization Modulo Theory, Mathematical Programming and Symmetry Breaking

The problem of Cloud resource provisioning for component-based applications consists in the allocation of virtual machines (VMs) offers from various Cloud Providers to a set of applications such that the constraints induced by the interactions between components and by the components hardware/software requirements are satisfied and the performance objectives are optimized (e.g. costs are minimized). It can be formulated as a constraint optimization problem, hence, in principle the optimization can be carried out automatically. In the case the set of VM offers is large (several hundreds), the computational requirement is huge, making the automatic optimization practically impossible with the current general optimization modulo theory (OMT) and mathematical programming (MP) tools. We overcame the difficulty by methodologically analyzing the particularities of the problem with the aim of identifying search space reduction methods. These are methods exploiting:(1) the symmetries of the general Cloud deployment problem, (2) the graph representation associated to the structural constraints specific to each particular application, and (3) their combination. An extensive experimental analysis has been conducted on four classes of real-world problems, using six symmetry breaking strategies and two types of optimization solvers. As a result, the combination of a variable reduction strategy with a column-wise symmetry breaker leads to a scalable deployment solution, when OMT is used to solve the resulting optimization problem.

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