Lagrangean-based decomposition algorithms for multicommodity network design problems with penalized constraints

This paper discusses problems in the context of multicommodity network design where the additional constraints (such as capacity), rather than being imposed in a strict manner, are allowed to be violated at the expense of additional penalty costs. Such penalized cost structures allow these constraints to be treated as utilization targets and provide a better modelling framework in terms of strategic or tactical level planning of network design, especially in freight transportation systems. However, due to penalized costs, these problems are generally in the form of a nonlinear integer multicommodity network problem. This paper presents two algorithms based on Lagrangean relaxation and decomposition for the solution of such problems. The first is through relaxing flow constraints that results in an arc decomposition, and the second relies upon dualizing the capacity constraints that result in a flow decomposition. It is shown that nonlinearities in the decomposed substructures can be handled in a very efficient manner. Arc decomposition is shown, through computational experiments, to have better convergence properties. Through the proposed algorithms, reasonably good solutions can be obtained for these problems where publicly available state-of-the-art nonlinear optimization codes fail to identify feasible solutions

Decomposition algorithms for a class of nonlinear multicommodity network design problems

This paper discusses problems in the context of multicommodity network design where the additional constraints (such as capacity), rather than being imposed in a strict manner, are allowed to be violated at the expense of additional penalty costs. Such penalized cost structures allow these constraints to be treated as utilization targets and provide a better modelling framework in terms of strategic or tactical level planning of network design, especially in freight transportation systems. However, due to penalized costs, these problems are generally in the form of a nonlinear integer multicommodity network problem. This paper presents two algorithms based on Lagrangean relaxation and decomposition for the solution of such problems. The first is through relaxing flow constraints that results in an arc decomposition, and the second relies upon dualizing the capacity constraints that result in a flow decomposition. It is shown that nonlinearities in the decomposed substructures can be handled in a very efficient manner. Arc decomposition is shown, through computational experiments, to have better convergence properties. Through the proposed algorithms, reasonably good solutions can be obtained for these problems where publicly available state-of-the-art nonlinear optimization codes fail to identify feasible solutions

Elastic-viscoplastic notch correction methods

International audienceNeuber's type methods are dedicated to obtain fast estimation of elastic-plastic state at stress concentrations from elastic results. To deal with complex loadings, empirical rules are necessary and do not always give satisfying results. In this context, we propose a new approach based on homogenization techniques. The plastic zone is viewed as an inclusion in an infinite elastic matrix which results in relationships between the elastic solution of the problem and estimated stress-strain state at the notch tip. Three versions of the notch correction method are successively introduced, a linear one which directly uses Eshelby's solution to compute stresses and strains at the notch, a non-linear method that takes into account plastic accommodation through a ββ-rule correction and, finally, the extended method that is based on the transformation field analysis methods. All the notch correction methods need calibration of localization tensors. The corresponding procedures are proposed and analyzed. The methods are compared on different simulation cases of notched specimens and the predictive capabilities of the extended method in situations where plasticity is not confined at the notch are demonstrated. Finally, the case of a complex multiperforated specimen is addressed