Automating Mathematical Program Transformations

Agarwal, Ashish; Bhat, Sooraj; Gray, Alexander; Grossmann, Ignacio E.

doi:10.1007/978-3-642-11503-5_12

Cited by 14 publications

(7 citation statements)

References 11 publications

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“…We can simplify the objective function by omitting item x 0 iL and x 0 iR , which are constants for a specific hit point combination. In addition, we also need to convert constraints (1g)-(1i) to linear constraints based on the big-M transformation [29].…”

Section: Sadp-aware Pin Accessmentioning

confidence: 99%

Self-Aligned Double Patterning Aware Pin Access and Standard Cell Layout Co-Optimization

Cline

Yeric

et al. 2015

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Self-aligned double patterning (SADP) is being considered for use at the 10-nm technology node and below for routing layers with pitches down to ∼50 nm because it has better line edge roughness and overlay control compared to other multiple patterning candidates. To date, most of the SADPrelated literature has focused on enabling SADP-legal routing in physical design tools while few attempts have been made to address the impact SADP routing has on local, standard cell (SC) I/O pin access. At the same time, via layers are used to connect the local SADP routing layers to the I/O pins on lower metal layers. Due to the high via density on the Via-1 layer, the litho-etch-litho-etch (LELE)-aware Via-1 design becomes a necessity to achieve legal pin access at the SC level. In this paper, we present the first study on SADP-aware pin access and layout optimization at the SC level. Accounting for SADP-specific and Via-1 design rules, we propose a coherent framework that uses depth first search, mixed integer linear programming, and backtracking method to enable LELE friendly Via-1 design and simultaneously optimize SADP-based local pin access and within-cell connections. Our experimental results show that, compared with the conventional approach, our framework effectively improves pin access of the SCs and maximizes the pin access flexibility for routing.Index Terms-Double patterning, pin access, self-aligned double patterning (SADP), standard cell (SC) layout, Via-1 assignment.

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Section: Sadp-aware Pin Accessmentioning

confidence: 99%

Self-Aligned Double Patterning Aware Pin Access and Standard Cell Layout Co-Optimization

Cline

Yeric

et al. 2015

IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst.

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Section: Milp Formulationmentioning

confidence: 99%

Self-aligned double patterning aware pin access and standard cell layout co-optimization

Cline

Yeric

et al. 2014

Proceedings of the 2014 on International Symposium on Physical Design

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Self-Aligned Double Patterning (SADP) is being considered for use at the 10nm technology node and below for routing layers with pitches down to ∼50nm because it has better LER and overlay control compared to other multiple patterning candidates. To date, most of the SADP-related literature has focused on enabling SADP-legal routing in physical design tools while few attempts have been made to address the impact SADP routing has on local, standard cell (SC) I/O pin access. In this paper, we present the first study on SADP-aware pin access and layout optimization at the SC level. Accounting for SADP-specific design rules, we propose a coherent framework that uses Mixed Integer Linear Programming (MILP) and branch and bound method to simultaneously optimize SADP-based local pin access and within-cell connections. Our experimental results show that, compared with the conventional approach, our framework effectively improves pin access of the standard cells and maximizes the pin access flexibility for routing.

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“…The implication symbol “⇒” in () means that the constraint is only enforced when the corresponding binary variable is equal to one. This implication and the subsequent ones may be implemented in a MIQP framework using the “big‐M” technique 43 . A brief tutorial on how to implement implications in a mixed‐integer programming framework through “big‐M” is presented in Appendix E.…”

Section: Optimal Control Formulationmentioning

confidence: 99%

Mixed‐integer quadratic programming for automatic walking footstep placement, duration, and rotation

Máximo

Afonso

2020

Optim Control Appl Methods

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Summary This paper presents a mixed‐integer model predictive controller for walking. In the proposed scheme, mixed‐integer quadratic programs (MIQP) are solved online to simultaneously decide center of mass jerks, footsteps positions, durations, and rotations while respecting actuation, geometry, and contact constraints. Most walking controllers require preplanned footstep rotations to avoid dealing with the nonlinearity introduced by foot rotation decision. The main contribution of this work is an optimization formulation where feet rotations are automatically planned to attain a reference speed rotation. Finally, simulation results are shown to present and discuss the capabilities of the proposed formulation.

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Automating Mathematical Program Transformations

Cited by 14 publications

References 11 publications

Self-Aligned Double Patterning Aware Pin Access and Standard Cell Layout Co-Optimization

Self-Aligned Double Patterning Aware Pin Access and Standard Cell Layout Co-Optimization

Self-aligned double patterning aware pin access and standard cell layout co-optimization

Mixed‐integer quadratic programming for automatic walking footstep placement, duration, and rotation

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