The Experts below are selected from a list of 26940 Experts worldwide ranked by ideXlab platform
Tianyou Chai - One of the best experts on this subject based on the ideXlab platform.
-
an effective subgradient method for scheduling a steelmaking continuous casting process
IEEE Transactions on Automation Science and Engineering, 2015Co-Authors: Kun Mao, Quanke Pan, Tianyou Chai, Peter B LuhAbstract:The steelmaking-continuous-casting (SCC) process, which includes steelmaking, refining and continuous casting, is one of the major bottlenecks of iron and steel production. Efficient and effective scheduling of this process is essential to improve the productivity and reduce the production costs of the entire production system. We present a time-index formulation for this scheduling Problem and a Lagrangian relaxation (LR) approach based on the relaxation of the machine capacity constraints. The Relaxed Problem is solved using an efficient polynomial dynamic programming algorithm. The corresponding Lagrangian dual (LD) Problem is solved using a deflected conditional subgradient level method. Unlike the conventional subgradient algorithms for the LD Problem, our method guarantees convergence using the Brannlund's level control strategy to replace the strict convergence condition that the optimum of the dual Problem is known a priori. Furthermore, our method enhances the efficiency by introducing a deflected conditional subgradient to weaken the zigzagging phenomena that slows the convergence of conventional subgradient algorithms. The computational results demonstrate that the approaches can quickly obtain high-quality solutions and are notably promising for the SCC scheduling.
-
an effective lagrangian relaxation approach for rescheduling a steelmaking continuous casting process
Control Engineering Practice, 2014Co-Authors: Kun Mao, Quanke Pan, Xinfu Pang, Tianyou ChaiAbstract:Abstract This paper studies a steelmaking-continuous casting (SCC) rescheduling Problem with machine breakdown and processing time variations. Two objectives are considered in this study: the efficiency objective and the stability objective. The former refers to the total weighted completion time and total sojourn time, whereas the latter refers to the number of operations processed on different machines in the initial and revised schedules. We develop a time-index formulation and an effective Lagrangian relaxation (LR) approach with machine capacity relaxation to address the rescheduling Problem. The LR approach decomposes the Relaxed Problem into batch-level subProblems with variable processing times. A polynomial two-stage dynamic programming algorithm is proposed to solve the batch-level subProblems. An efficient subgradient algorithm with global convergence is presented to solve the corresponding Lagrangian dual (LD) Problem. Computational experiments based on practical production data show that the proposed approach not only produces a high quality schedule within an acceptable time but also performs much better than a practical SCC rescheduling method from a large iron and steel enterprise in China.
-
a novel lagrangian relaxation approach for a hybrid flowshop scheduling Problem in the steelmaking continuous casting process
European Journal of Operational Research, 2014Co-Authors: Kun Mao, Quanke Pan, Xinfu Pang, Tianyou ChaiAbstract:Abstract One of the largest bottlenecks in iron and steel production is the steelmaking-continuous casting (SCC) process, which consists of steel-making, refining and continuous casting. The SCC scheduling is a complex hybrid flowshop (HFS) scheduling Problem with the following features: job grouping and precedence constraints, no idle time within the same group of jobs and setup time constraints on the casters. This paper first models the scheduling Problem as a mixed-integer programming (MIP) Problem with the objective of minimizing the total weighted earliness/tardiness penalties and job waiting. Next, a Lagrangian relaxation (LR) approach relaxing the machine capacity constraints is presented to solve the MIP Problem, which decomposes the Relaxed Problem into two tractable subProblems by separating the continuous variables from the integer ones. Additionally, two methods, i.e. , the boundedness detection method and time horizon method, are explored to handle the unboundedness of the decomposed subProblems in iterations. Furthermore, an improved subgradient level algorithm with global convergence is developed to solve the Lagrangian dual (LD) Problem. The computational results and comparisons demonstrate that the proposed LR approach outperforms the conventional LR approaches in terms of solution quality, with a significantly shorter running time being observed.
Tony Q.s. Quek - One of the best experts on this subject based on the ideXlab platform.
-
Heterogeneous Cellular Networks Using Wireless Backhaul: Fast Admission Control and Large System Analysis
IEEE Journal on Selected Areas in Communications, 2015Co-Authors: Jian Zhao, Tony Q.s. QuekAbstract:We consider a heterogeneous cellular network with densely underlaid small cell access points (SAPs). Wireless backhaul provides the data connection from the core network to SAPs. To serve as many SAPs and their corresponding users as possible with guaranteed data rates, admission control of SAPs needs to be performed in wireless backhaul. Such a Problem involves joint design of transmit beamformers, power control, and selection of SAPs. In order to tackle such a difficult Problem, we apply $\ell_1$ -relaxation and propose an iterative algorithm for the $\ell_1$ -Relaxed Problem. The selection of SAPs is made based on the outputs of the iterative algorithm, and we prove such an algorithm converges locally. Furthermore, this algorithm is fast and enjoys low complexity for small-to-medium sized systems. However, its solution depends on the actual channel state information, and resuming the algorithm for each new channel realization may be unrealistic for large systems. Therefore, we make use of the random matrix theory and also propose an iterative algorithm for large systems. Such a large-system iterative algorithm can produce the asymptotically optimum solution for the $\ell_1$ -Relaxed Problem, which only requires large-scale channel coefficients irrespective of the actual channel realization. Near optimum results are achieved by our proposed algorithms in simulations.
-
heterogeneous cellular networks using wireless backhaul fast admission control and large system analysis
arXiv: Information Theory, 2015Co-Authors: Jian Zhao, Tony Q.s. Quek, Zhongding LeiAbstract:We consider a heterogeneous cellular network with densely underlaid small cell access points (SAPs). Wireless backhaul provides the data connection from the core network to SAPs. To serve as many SAPs and their corresponding users as possible with guaranteed data rates, admission control of SAPs needs to be performed in wireless backhaul. Such a Problem involves joint design of transmit beamformers, power control, and selection of SAPs. In order to tackle such a difficult Problem, we apply $\ell_1$-relaxation and propose an iterative algorithm for the $\ell_1$-Relaxed Problem. The selection of SAPs is made based on the outputs of the iterative algorithm. This algorithm is fast and enjoys low complexity for small-to-medium sized systems. However, its solution depends on the actual channel state information, and resuming the algorithm for each new channel realization may be unrealistic for large systems. Therefore, we make use of random matrix theory and also propose an iterative algorithm for large systems. Such a large system iterative algorithm produces asymptotically optimum solution for the $\ell_1$-Relaxed Problem, which only requires large-scale channel coefficients irrespective of the actual channel realization. Near optimum results are achieved by our proposed algorithms in simulations.
Peter B Luh - One of the best experts on this subject based on the ideXlab platform.
-
an effective subgradient method for scheduling a steelmaking continuous casting process
IEEE Transactions on Automation Science and Engineering, 2015Co-Authors: Kun Mao, Quanke Pan, Tianyou Chai, Peter B LuhAbstract:The steelmaking-continuous-casting (SCC) process, which includes steelmaking, refining and continuous casting, is one of the major bottlenecks of iron and steel production. Efficient and effective scheduling of this process is essential to improve the productivity and reduce the production costs of the entire production system. We present a time-index formulation for this scheduling Problem and a Lagrangian relaxation (LR) approach based on the relaxation of the machine capacity constraints. The Relaxed Problem is solved using an efficient polynomial dynamic programming algorithm. The corresponding Lagrangian dual (LD) Problem is solved using a deflected conditional subgradient level method. Unlike the conventional subgradient algorithms for the LD Problem, our method guarantees convergence using the Brannlund's level control strategy to replace the strict convergence condition that the optimum of the dual Problem is known a priori. Furthermore, our method enhances the efficiency by introducing a deflected conditional subgradient to weaken the zigzagging phenomena that slows the convergence of conventional subgradient algorithms. The computational results demonstrate that the approaches can quickly obtain high-quality solutions and are notably promising for the SCC scheduling.
-
convergence of the surrogate lagrangian relaxation method
Journal of Optimization Theory and Applications, 2015Co-Authors: Mikhail A Bragin, Peter B Luh, Joseph H Yan, Gary A SternAbstract:Studies have shown that the surrogate subgradient method, to optimize non-smooth dual functions within the Lagrangian relaxation framework, can lead to significant computational improvements as compared to the subgradient method. The key idea is to obtain surrogate subgradient directions that form acute angles toward the optimal multipliers without fully minimizing the Relaxed Problem. The major difficulty of the method is its convergence, since the convergence proof and the practical implementation require the knowledge of the optimal dual value. Adaptive estimations of the optimal dual value may lead to divergence and the loss of the lower bound property for surrogate dual values. The main contribution of this paper is on the development of the surrogate Lagrangian relaxation method and its convergence proof to the optimal multipliers, without the knowledge of the optimal dual value and without fully optimizing the Relaxed Problem. Moreover, for practical implementations, a stepsizing formula that guarantees convergence without requiring the optimal dual value has been constructively developed. The key idea is to select stepsizes in a way that distances between Lagrange multipliers at consecutive iterations decrease, and as a result, Lagrange multipliers converge to a unique limit. At the same time, stepsizes are kept sufficiently large so that the algorithm does not terminate prematurely. At convergence, the lower-bound property of the surrogate dual is guaranteed. Testing results demonstrate that non-smooth dual functions can be efficiently optimized, and the new method leads to faster convergence as compared to other methods available for optimizing non-smooth dual functions, namely, the simple subgradient method, the subgradient-level method, and the incremental subgradient method.
-
an alternative framework to lagrangian relaxation approach for job shop scheduling
European Journal of Operational Research, 2003Co-Authors: Haoxun Chen, Peter B LuhAbstract:Abstract A new Lagrangian relaxation (LR) approach is developed for job shop scheduling Problems. In the approach, operation precedence constraints rather than machine capacity constraints are Relaxed. The Relaxed Problem is decomposed into single or parallel machine scheduling subProblems. These subProblems, which are NP-complete in general, are approximately solved by using fast heuristic algorithms. The dual Problem is solved by using a recently developed “surrogate subgradient method” that allows approximate optimization of the subProblems. Since the algorithms for subProblems do not depend on the time horizon of the scheduling Problems and are very fast, our new LR approach is efficient, particularly for large Problems with long time horizons. For these Problems, the machine decomposition-based LR approach requires much less memory and computation time as compared to a part decomposition-based approach as demonstrated by numerical testing.
Kun Mao - One of the best experts on this subject based on the ideXlab platform.
-
an effective subgradient method for scheduling a steelmaking continuous casting process
IEEE Transactions on Automation Science and Engineering, 2015Co-Authors: Kun Mao, Quanke Pan, Tianyou Chai, Peter B LuhAbstract:The steelmaking-continuous-casting (SCC) process, which includes steelmaking, refining and continuous casting, is one of the major bottlenecks of iron and steel production. Efficient and effective scheduling of this process is essential to improve the productivity and reduce the production costs of the entire production system. We present a time-index formulation for this scheduling Problem and a Lagrangian relaxation (LR) approach based on the relaxation of the machine capacity constraints. The Relaxed Problem is solved using an efficient polynomial dynamic programming algorithm. The corresponding Lagrangian dual (LD) Problem is solved using a deflected conditional subgradient level method. Unlike the conventional subgradient algorithms for the LD Problem, our method guarantees convergence using the Brannlund's level control strategy to replace the strict convergence condition that the optimum of the dual Problem is known a priori. Furthermore, our method enhances the efficiency by introducing a deflected conditional subgradient to weaken the zigzagging phenomena that slows the convergence of conventional subgradient algorithms. The computational results demonstrate that the approaches can quickly obtain high-quality solutions and are notably promising for the SCC scheduling.
-
an effective lagrangian relaxation approach for rescheduling a steelmaking continuous casting process
Control Engineering Practice, 2014Co-Authors: Kun Mao, Quanke Pan, Xinfu Pang, Tianyou ChaiAbstract:Abstract This paper studies a steelmaking-continuous casting (SCC) rescheduling Problem with machine breakdown and processing time variations. Two objectives are considered in this study: the efficiency objective and the stability objective. The former refers to the total weighted completion time and total sojourn time, whereas the latter refers to the number of operations processed on different machines in the initial and revised schedules. We develop a time-index formulation and an effective Lagrangian relaxation (LR) approach with machine capacity relaxation to address the rescheduling Problem. The LR approach decomposes the Relaxed Problem into batch-level subProblems with variable processing times. A polynomial two-stage dynamic programming algorithm is proposed to solve the batch-level subProblems. An efficient subgradient algorithm with global convergence is presented to solve the corresponding Lagrangian dual (LD) Problem. Computational experiments based on practical production data show that the proposed approach not only produces a high quality schedule within an acceptable time but also performs much better than a practical SCC rescheduling method from a large iron and steel enterprise in China.
-
a novel lagrangian relaxation approach for a hybrid flowshop scheduling Problem in the steelmaking continuous casting process
European Journal of Operational Research, 2014Co-Authors: Kun Mao, Quanke Pan, Xinfu Pang, Tianyou ChaiAbstract:Abstract One of the largest bottlenecks in iron and steel production is the steelmaking-continuous casting (SCC) process, which consists of steel-making, refining and continuous casting. The SCC scheduling is a complex hybrid flowshop (HFS) scheduling Problem with the following features: job grouping and precedence constraints, no idle time within the same group of jobs and setup time constraints on the casters. This paper first models the scheduling Problem as a mixed-integer programming (MIP) Problem with the objective of minimizing the total weighted earliness/tardiness penalties and job waiting. Next, a Lagrangian relaxation (LR) approach relaxing the machine capacity constraints is presented to solve the MIP Problem, which decomposes the Relaxed Problem into two tractable subProblems by separating the continuous variables from the integer ones. Additionally, two methods, i.e. , the boundedness detection method and time horizon method, are explored to handle the unboundedness of the decomposed subProblems in iterations. Furthermore, an improved subgradient level algorithm with global convergence is developed to solve the Lagrangian dual (LD) Problem. The computational results and comparisons demonstrate that the proposed LR approach outperforms the conventional LR approaches in terms of solution quality, with a significantly shorter running time being observed.
Adolfo Arroyorabasa - One of the best experts on this subject based on the ideXlab platform.
-
relaxation and optimization for linear growth convex integral functionals under pde constraints
Journal of Functional Analysis, 2017Co-Authors: Adolfo ArroyorabasaAbstract:Abstract We give necessary and sufficient conditions for the minimality of generalized minimizers of linear-growth integral functionals of the form F [ u ] = ∫ Ω f ( x , u ( x ) ) d x , u : Ω ⊂ R d → R N , where f : Ω × R N → R is a convex integrand and u is an integrable function satisfying a general PDE constraint. Our analysis is based on two ideas: a relaxation argument into a subspace of the space of bounded vector-valued Radon measures M ( Ω ; R N ) , and the introduction of a set-valued pairing on M ( Ω ; R N ) × L ∞ ( Ω ; R N ) . By these means we are able to show an intrinsic relation between minimizers of the Relaxed Problem and maximizers of its dual formulation also known as the saddle-point conditions. In particular, our results can be applied to relaxation and minimization Problems in BV, BD and divergence-free spaces.
-
relaxation and optimization for linear growth convex integral functionals under pde constraints
arXiv: Analysis of PDEs, 2016Co-Authors: Adolfo ArroyorabasaAbstract:We give necessary and sufficient conditions for minimality of generalized minimizers for linear-growth functionals of the form \[ \mathcal F[u] := \int_\Omega f(x,u(x)) \, \text{d}x, \qquad u:\Omega \subset \mathbb R^N\to \mathbb R^d, \] where $u$ is an integrable function satisfying a general PDE constraint. Our analysis is based on two ideas: a relaxation argument into a subspace of the space of bounded vector-valued Radon measures $\mathcal M(\Omega;\mathbb R^d)$, and the introduction of a set-valued pairing in $\mathcal M(\Omega;\mathbb R^N) \times {\rm L}^\infty(\Omega;\mathbb R^N)$. By these means we are able to show an intrinsic relation between minimizers of the Relaxed Problem and maximizers of its dual formulation also known as the saddle-point conditions. In particular, our results can be applied to relaxation and minimization Problems in BV, BD.
