Perprof-py: A Python Package for Performance Profile of Mathematical
                        Optimization Software

Siqueira, Abel Soares; Silva, Raniere; Santos, Luiz-Rafael

doi:10.5334/jors.81

Cited by 10 publications

(1 citation statement)

References 13 publications

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“…We analyze the time consumption in the SIMP method using the Python performance profiling tool Line profiler [31], as shown in Table 1. The higher computation effort is associated with the modules of FEA calculation and advanced filter techniques, especially when a refined mesh strategy is applied for describing the structural geometry with high resolution.…”

Section: Methodsmentioning

confidence: 99%

Compliance Prediction for Structural Topology Optimization on the Basis of Moment Invariants and a Generalized Regression Neural Network

Zhao,

Chen,

Dong

2023

Entropy

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Topology optimization techniques are essential for manufacturing industries, such as designing fiber-reinforced polymer composites (FRPCs) and structures with outstanding strength-to-weight ratios and light weights. In the SIMP approach, artificial intelligence algorithms are commonly utilized to enhance traditional FEM-based compliance minimization procedures. Based on an effective generalized regression neural network (GRNN), a new deep learning algorithm of compliance prediction for structural topology optimization is proposed. The algorithm learns the structural information using a fourth-order moment invariant analysis of the structural topology obtained from FEA at different iterations of classical topology optimization. A cantilever and a simply supported beam problem are used as ground-truth datasets, and the moment invariants are used as independent variables for input features. By comparing it with the well-known convolutional neural network (CNN) and deep neural network (DNN) models, the proposed GRNN model achieves a high prediction accuracy (R2 > 0.97) and drastically shortens the training and prediction cost. Furthermore, the GRNN algorithm exhibits excellent generalization ability on the prediction performance of the optimized topology with rotations and varied material volume fractions. This algorithm is promising for the replacement of the FEA calculation in the SIMP method, and can be applied to real-time optimization for advanced FRPC structure design.

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Section: Methodsmentioning

confidence: 99%

Compliance Prediction for Structural Topology Optimization on the Basis of Moment Invariants and a Generalized Regression Neural Network

Zhao,

Chen,

Dong

2023

Entropy

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Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: Part I

Beach,

Burlacu,

Bärmann

et al. 2024

Comput Optim Appl

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We study mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non-convex continuous variable products. In this paper, we consider MIP relaxations based on separable reformulation. The main focus is the introduction of the enhanced separable MIP relaxation for non-convex quadratic products of the form $$z=xy$$ z = x y , called hybrid separable (HybS). Additionally, we introduce a logarithmic MIP relaxation for univariate quadratic terms, called sawtooth relaxation, based on Beach (Beach in J Glob Optim 84:869–912, 2022). We combine the latter with HybS and existing separable reformulations to derive MIP relaxations of MIQCQPs. We provide a comprehensive theoretical analysis of these techniques, underlining the theoretical advantages of HybS compared to its predecessors. We perform a broad computational study to demonstrate the effectiveness of the enhanced MIP relaxation in terms of producing tight dual bounds for MIQCQPs. In Part II, we study MIP relaxations that extend the MIP relaxation normalized multiparametric disaggregation technique (NMDT) (Castro in J Glob Optim 64:765–784, 2015) and present a computational study which also includes the MIP relaxations from this work and compares them with a state-of-the-art of MIQCQP solvers.

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Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: part II

Beach,

Burlacu,

Bärmann

et al. 2024

Comput Optim Appl

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This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products where both variables are bounded and extend the well-known MIP relaxation normalized multiparametric disaggregation technique(NMDT), applying a sophisticated discretization to both variables. We refer to this approach as doubly discretized normalized multiparametric disaggregation technique (D-NMDT). In a comprehensive theoretical analysis, we underline the theoretical advantages of the enhanced method D-NMDT compared to NMDT. Furthermore, we perform a broad computational study to demonstrate its effectiveness in terms of producing tight dual bounds for MIQCQPs. Finally, we compare D-NMDT to the separable MIP relaxations from Part I and a state-of-the-art MIQCQP solver.

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Perprof-py: A Python Package for Performance Profile of Mathematical Optimization Software

Cited by 10 publications

References 13 publications

Compliance Prediction for Structural Topology Optimization on the Basis of Moment Invariants and a Generalized Regression Neural Network

Compliance Prediction for Structural Topology Optimization on the Basis of Moment Invariants and a Generalized Regression Neural Network

Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: Part I

Enhancements of discretization approaches for non-convex mixed-integer quadratically constrained quadratic programming: part II

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