Incremental Lagrangian Relaxation Based Discrete Gate Sizing and Threshold Voltage Assignment

Timing closure remains one of the most critical challenges of a physical synthesis flow, especially when the design operates under multiple operating conditions. Even if timing is almost closed at the end of the flow, last-mile placement and routing congestion optimizations may introduce new timing violations. Correcting such violations needs minimally disruptive techniques such as threshold voltage reassignment and gate sizing that affect only marginally the placement and routing of the almost finalized design. To this end, we transform a powerful Lagrangian-relaxation-based optimizer, used for global timing optimization early in the design flow, into a practical incremental timing optimizer that corrects small timing violations with fast runtime and without increasing the area/power of the design. The proposed approach was applied to already optimized designs of the ISPD 2013 benchmarks assuming that they experience new timing violations due to local wire rerouting. Experimental results show that in single corner designs, timing is improved by more than 36% on average, using 45% less runtime. Correspondingly, in a multicorner context, timing is improved by 39% when compared to the fully-fledged version of the timing optimizer.

A bi-level mathematical model for logistic management considering the evolutionary game with environmental feedbacks

PurposeThis paper proposed a bi-level mathematical model for location, routing and allocation of medical centers to distribution depots during the COVID-19 pandemic outbreak. The developed model has two players including interdictor (COVID-19) and fortifier (government). Accordingly, the aim of the first player (COVID-19) is to maximize system costs and causing further damage to the system. The goal of the second player (government) is to minimize the costs of location, routing and allocation due to budget limitations.Design/methodology/approachThe approach of evolutionary games with environmental feedbacks was used to develop the proposed model. Moreover, the game continues until the desired demand is satisfied. The Lagrangian relaxation method was applied to solve the proposed model.FindingsEmpirical results illustrate that with increasing demand, the values of the objective functions of the interdictor and fortifier models have increased. Also, with the raising fixed cost of the established depot, the values of the objective functions of the interdictor and fortifier models have raised. In this regard, the number of established depots in the second scenario (COVID-19 wave) is more than the first scenario (normal COVID-19 conditions).Research limitations/implicationsThe results of the current research can be useful for hospitals, governments, Disaster Relief Organization, Red Crescent, the Ministry of Health, etc. One of the limitations of the research is the lack of access to accurate information about transportation costs. Moreover, in this study, only the information of drivers and experts about transportation costs has been considered. In order to implement the presented solution approach for the real case study, high RAM and CPU hardware facilities and software facilities are required, which are the limitations of the proposed paper.Originality/valueThe main contributions of the current research are considering evolutionary games with environmental feedbacks during the COVID-19 pandemic outbreak and location, routing and allocation of the medical centers to the distribution depots during the COVID-19 outbreak. A real case study is illustrated, where the Lagrangian relaxation method is employed to solve the problem.

Joint Power Allocation and Bit-Loading for Multicarrier Systems with Discrete Modulation

In this paper, we propose two algorithms for joint power allocation and bit-loading in multicarrier systems using discrete modulations. The objective is to maximize the data rate under the constraint of a suitable Bit Error Rate per subcarrier. The first algorithm is based on the Lagrangian Relaxation of the discrete optimization problem in order to find an initial solution. A discrete solution is found by bit truncation followed by an iterative modulation adjustment. The second algorithm is based on Discrete Coordinate Ascent framework with iterative modulation increment of one selected subcarrier at each iteration. A simple cost function related to the power increment per bit is used for subcarrier selection. A sub-optimal low complexity Discrete Coordinate Ascent algorithm is proposed that overcome the limitations of the Hughes-Hartogs algorithm. The Lagrangian Relaxation algorithm provides a suboptimal solution for non-coded system using M-QAM modulations, whereas the low complexity Discrete Coordinate Ascent algorithm provides a near optimal solution for coded as well as for non-coded system using an arbitrary modulation set. Numerical results show the efficiency of the proposed algorithms in comparison with traditional methods.

Enabling Retrain-free Deep Neural Network Pruning Using Surrogate Lagrangian Relaxation

Network pruning is a widely used technique to reduce computation cost and model size for deep neural networks. However, the typical three-stage pipeline, i.e., training, pruning and retraining (fine-tuning) significantly increases the overall training trails. In this paper, we develop a systematic weight-pruning optimization approach based on Surrogate Lagrangian relaxation (SLR), which is tailored to overcome difficulties caused by the discrete nature of the weight-pruning problem while ensuring fast convergence. We further accelerate the convergence of the SLR by using quadratic penalties. Model parameters obtained by SLR during the training phase are much closer to their optimal values as compared to those obtained by other state-of-the-art methods. We evaluate the proposed method on image classification tasks using CIFAR-10 and ImageNet, as well as object detection tasks using COCO 2014 and Ultra-Fast-Lane-Detection using TuSimple lane detection dataset. Experimental results demonstrate that our SLR-based weight-pruning optimization approach achieves higher compression rate than state-of-the-arts under the same accuracy requirement. It also achieves a high model accuracy even at the hard-pruning stage without retraining (reduces the traditional three-stage pruning to two-stage). Given a limited budget of retraining epochs, our approach quickly recovers the model accuracy.

Improved CP-Based Lagrangian Relaxation Approach with an Application to the TSP

CP-based Lagrangian relaxation (CP-LR) is an efficient optimization technique that combines cost-based filtering with Lagrangian relaxation in a constraint programming context. The state-of-the-art filtering algorithms for the WeightedCircuit constraint that encodes the traveling salesman problem (TSP) are based on this approach. In this paper, we propose an improved CP-LR approach that locally modifies the Lagrangian multipliers in order to increase the number of filtered values. We also introduce two new algorithms based on the latter to filter WeightedCircuit. The experimental results on TSP instances show that our algorithms allow significant gains on the resolution time and the size of the search space when compared to the state-of-the-art implementation.