The Experts below are selected from a list of 198 Experts worldwide ranked by ideXlab platform
W Y Szeto - One of the best experts on this subject based on the ideXlab platform.
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bounding the inefficiency of the reliability based continuous network design problem under cost recovery
Networks and Spatial Economics, 2020Co-Authors: Anny B Wang, W Y SzetoAbstract:This study defines the price of anarchy for general reliability-based transport network design problems, which is an indicator of inefficiency that reveals how much the design objective value exceeds its theoretical minimum value due to the risk averse and selfish routing behavior of travelers. This study examines a new problem, which is a reliability-based continuous network design problem under cost recovery. In this problem, the variations of system travel time and path travel times, the risk attitudes of the system manager and travelers, congestion toll charges, capacity expansions, and cost recovery Constraint are explicitly considered. The design problem is formulated as a min-max problem with the reliability-based user Equilibrium Constraint. It is proved that the price of anarchy for this problem is bounded above, and the upper bound is independent of travel time functions, demands, and network topology. The upper bound is related to the travel time variations, the value of reliability, and the value of time.
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bike network design problem with a path size logit based Equilibrium Constraint formulation global optimization and matheuristic
Transportation Research Part E-logistics and Transportation Review, 2019Co-Authors: Haoxiang Liu, W Y Szeto, Jiancheng LongAbstract:Abstract This study focuses on the optimal network design problem of bike paths, which are on or adjacent to roadways but are physically separated from motorized traffic within the existing urban network. The problem seeks to maximize the total route utilities of cyclists and capture their actual route choice behavior using a path-size logit model. A mixed-integer nonlinear nonconvex model is developed for the problem and is reformulated and linearized into a mixed-integer linear program. The program is solved with a global optimization method and a matheuristic. Results are provided to illustrate the performance of these methods and the model properties.
M. Ortiz - One of the best experts on this subject based on the ideXlab platform.
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Symmetric Div-Quasiconvexity and the Relaxation of Static Problems
Archive for Rational Mechanics and Analysis, 2020Co-Authors: S. Conti, S. Müller, M. OrtizAbstract:We consider problems of static Equilibrium in which the primary unknown is the stress field and the solutions maximize a complementary energy subject to Equilibrium Constraints. A necessary and sufficient condition for the sequential lower-semicontinuity of such functionals is symmetric $$\mathrm{div}$$ div -quasiconvexity; a special case of Fonseca and Müller’s $$\mathcal {A}$$ A -quasiconvexity with $$\mathcal {A}= \mathrm{div}$$ A = div acting on $$\mathbb {R}^{n\times n}_\mathrm {sym}$$ R sym n × n . We specifically consider the example of the static problem of plastic limit analysis and seek to characterize its relaxation in the non-standard case of a non-convex elastic domain. We show that the symmetric $$\mathrm{div}$$ div -quasiconvex envelope of the elastic domain can be characterized explicitly for isotropic materials whose elastic domain depends on pressure p and Mises effective shear stress q . The envelope then follows from a rank-2 hull construction in the ( p , q )-plane. Remarkably, owing to the Equilibrium Constraint, the relaxed elastic domain can still be strongly non-convex, which shows that convexity of the elastic domain is not a requirement for existence in plasticity.
Michael Yu Wang - One of the best experts on this subject based on the ideXlab platform.
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Shape Equilibrium Constraint: a strategy for stress-constrained structural topology optimization
Structural and Multidisciplinary Optimization, 2013Co-Authors: Michael Yu WangAbstract:In topology optimization of a continuum, it is important to consider stress-related objective or Constraints, from both theoretical and application perspectives. It is known that the problem is challenging. Although remarkable achievements have been made with the SIMP (Solid Isotropic Material with Penalization) framework, a number of critical issues are yet to be fully resolved. In the paper, we present an approach of a shape Equilibrium Constraint strategy with the level-set/X-FEM framework. We formulate the topology optimization problem under (spatially-distributed) stress Constraints into a shape Equilibrium problem of active stress Constraint. This formulation allows us to effectively handle the stress Constraint, and the intrinsic non-differentiability introduced by local stress Constraints is removed. The optimization problem is made into one of continuous shape-sensitivity and it is solved by evolving a coherent interface of the shape Equilibrium concurrently with shape variation in the structural boundary during a level-set evolution process. Several numerical examples in two dimensions are provided as a benchmark test of the proposed shape Equilibrium Constraint strategy for minimum-weight and fully-stressed designs and for designs with stress Constraint satisfaction.
Li Li - One of the best experts on this subject based on the ideXlab platform.
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Shape Equilibrium Constraint: a strategy for stress-constrained structural topology optimization
Structural and Multidisciplinary Optimization, 2013Co-Authors: Li LiAbstract:In topology optimization of a continuum, it is important to consider stress-related objective or Constraints, from both theoretical and application perspectives. It is known that the problem is challenging. Although remarkable achievements have been made with the SIMP (Solid Isotropic Material with Penalization) framework, a number of critical issues are yet to be fully resolved. In the paper, we present an approach of a shape Equilibrium Constraint strategy with the level-set/X-FEM framework. We formulate the topology optimization problem under (spatially-distributed) stress Constraints into a shape Equilibrium problem of active stress Constraint. This formulation allows us to effectively handle the stress Constraint, and the intrinsic non-differentiability introduced by local stress Constraints is removed. The optimization problem is made into one of continuous shape-sensitivity and it is solved by evolving a coherent interface of the shape Equilibrium concurrently with shape variation in the structural boundary during a level-set evolution process. Several numerical examples in two dimensions are provided as a benchmark test of the proposed shape Equilibrium Constraint strategy for minimum-weight and fully-stressed designs and for designs with stress Constraint satisfaction.
Qun Chen - One of the best experts on this subject based on the ideXlab platform.
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An Algorithm for the Mixed Transportation Network Design Problem.
PLOS ONE, 2016Co-Authors: Xinyu Liu, Qun ChenAbstract:This paper proposes an optimization algorithm, the dimension-down iterative algorithm (DDIA), for solving a mixed transportation network design problem (MNDP), which is generally expressed as a mathematical programming with Equilibrium Constraint (MPEC). The upper level of the MNDP aims to optimize the network performance via both the expansion of the existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user Equilibrium (UE) problem. The idea of the proposed solution algorithm (DDIA) is to reduce the dimensions of the problem. A group of variables (discrete/continuous) is fixed to optimize another group of variables (continuous/discrete) alternately; then, the problem is transformed into solving a series of CNDPs (continuous network design problems) and DNDPs (discrete network design problems) repeatedly until the problem converges to the optimal solution. The advantage of the proposed algorithm is that its solution process is very simple and easy to apply. Numerical examples show that for the MNDP without budget Constraint, the optimal solution can be found within a few iterations with DDIA. For the MNDP with budget Constraint, however, the result depends on the selection of initial values, which leads to different optimal solutions (i.e., different local optimal solutions). Some thoughts are given on how to derive meaningful initial values, such as by considering the budgets of new and reconstruction projects separately.