Rounding Strategy Research Articles

Towards high performance low bitwidth training for deep neural networks

The high performance of the state-of-the-art deep neural networks (DNNs) is acquired at the cost of huge consumption of computing resources. Quantization of networks is recently recognized as a promising solution to solve the problem and significantly reduce the resource usage. However, the previous quantization works have mostly focused on the DNN inference, and there were very few works to address on the challenges of DNN training. In this paper, we leverage dynamic fixed-point (DFP) quantization algorithm and stochastic rounding (SR) strategy to develop a fully quantized 8-bit neural networks targeting low bitwidth training. The experiments show that, in comparison to the full-precision networks, the accuracy drop of our quantized convolutional neural networks (CNNs) can be less than 2%, even when applied to deep models evaluated on ImageNet dataset. Additionally, our 8-bit GNMT translation network can achieve almost identical BLEU to full-precision network. We further implement a prototype on FPGA and the synthesis shows that the low bitwidth training scheme can reduce the resource usage significantly.

Mixed-integer minimax dynamic optimization for structure identification of glycerol metabolic network

Cell metabolism is a dynamic regulation process, in which its network structure and/or regulatory mechanisms can change constantly over time due to internal and external perturbations. This paper models glycerol metabolism in continuous fermentation as a nonlinear mixed-integer dynamic system by defining the time-varying metabolic network structure as an integer-valued function. To identify the dynamic network structure and kinetic parameters, we establish a mixed-integer minimax dynamic optimization problem with concentration robustness as its objective functional. By direct multiple shooting strategy and a decomposition approach consisting of convexification, relaxation and rounding strategy, the optimization problem is transformed into a large-scale approximate multistage parameter optimization problem. It is then solved using a competitive particle swarm optimization algorithm. We also show that the relaxation problem yields the best lower bound for the optimization problem, and its solution can be arbitrarily approximated by the solution obtained from rounding strategy. Numerical results indicate that the proposed mixed-integer dynamic system can better describe cellular self-regulation and response to intermediate metabolite inhibitions in continuous fermentation of glycerol. These numerical results show that the proposed numerical methods are effective in solving the large-scale mixed-integer dynamic optimization problems.

Computation of an eigendecomposition-based discrete fractional Fourier transform with reduced arithmetic complexity

In this paper, we introduce a method for computing an eigendecomposition-based discrete fractional Fourier transform (DFrFT) with reduced arithmetic complexity, when compared to the O(N2) complexity of the corresponding direct computation. Our approach exploits properties of a recently introduced closed-form Hermite-Gaussian-like discrete Fourier transform eigenbasis, which is used to define the DFrFT, and includes a rounding strategy. The proposed (exact) technique requires a slightly lower number of multiplications and half or less additions than what is required by other state-of-the-art methods; if the referred rounding strategy is applied, up to 65% of multiplications can be avoided. We validate our results by means of computer experiments where the application of the transform in signal filtering and compact representation is considered.

A Shape Optimization Algorithm for Interface Identification Allowing Topological Changes

In this work we investigate a combination of classical PDE constrained optimization methods and a rounding strategy based on shape optimization for the identification of interfaces. The goal is to identify radioactive regions in a groundwater flow represented by a control that is either active or inactive. We use a relaxation of the binary problem on a coarse grid as initial guess for the shape optimization with higher resolution. The result is a computationally cheap method that does not have to perform large shape deformations. We demonstrate that our algorithm is moreover able to change the topology of the initial guess.

Simple heuristic for the strategic supply chain design of large-scale networks: A Brazilian case study

We propose a simple heuristic method for the strategic Supply Chain Network Design (SCND) problem of a Brazilian tire company with four layers, multi-product in a single-period. Although several solution methods have been developed to solve this problem, mainly based on heuristic techniques, they have serious limitations in the number of warehouses, products, and consumer zones they can handle. This issue restrains their practical applications to the specific addressed real-world problem, involving hundreds of elements in these dimensions. The heuristic approach, combining a multi-start mechanism and a rounding strategy, is specially developed to solve large-scale problems in reasonable time. The rounding strategy solves the models proposed by the multi-start mechanism. This integration allows the required diversification in the solution search, avoiding stagnation in a local optimum. The heuristic method is first evaluated using randomly generated instances, with different sizes in terms of the number of suppliers, factories, warehouses, products, and customer zones. The obtained results show the solution method is competitive, compared with previous developed approaches, with the advantage of solving larger instances efficiently and effectively. The heuristic is then applied to the company, aiming to restructure its supply chain due to the overture of a new factory. The proposed heuristic approach proves appropriate to solve this practical application, involving an unprecedented number of warehouses, products, and customers.

A Randomized Rounding Algorithm for Sparse PCA

We present and analyze a simple, two-step algorithm to approximate the optimal solution of the sparse PCA problem. In the proposed approach, we first solve an ℓ 1 -penalized version of the NP-hard sparse PCA optimization problem and then we use a randomized rounding strategy to sparsify the resulting dense solution. Our main theoretical result guarantees an additive error approximation and provides a tradeoff between sparsity and accuracy. Extensive experimental evaluation indicates that the proposed approach is competitive in practice, even compared to state-of-the-art toolboxes such as Spasm.

Strategy selection in Alzheimer patients: A study in arithmetic

Objective: We compared Alzheimer’s disease (AD) patients’ and elderly controls’ abilities to select the best strategy on each item and determined whether AD patients tended to repeat the same strategy across consecutive items more often than controls. Method: A total of 60 participants (30 healthy older adults, HOA; 30 AD patients) were asked to select the best rounding strategy to estimate products of multiplication problems (e.g., estimating 42 × 76 by rounding operands down or up, like doing 40 × 70 = 2800 or 50 × 80 = 3200). We identified strategies used on each problem and measured solution latencies and percentage errors with each strategy as a function of problem characteristics. Results: Older adults and AD patients were able to use both available strategies. However, AD patients were less able to select the best strategy than HOA, especially on problems for which selecting the best strategy was most difficult. Moreover, AD patients significantly repeated the preceding strategies across successive problems more often than HOA. Conclusions: Our findings have important implications for further our understanding of dementia-related differences in strategic aspects of cognitive performance.

An iterative rounding search-based algorithm for the disjunctively constrained knapsack problem

This article proposes an iterative rounding search-based algorithm for approximately solving the disjunctively constrained knapsack problem. The problem can be viewed as a variant of the well-known knapsack problem with some sets of incompatible items. The algorithm considers two key features: a rounding strategy applied to the fractional variables of a linear relaxation and a neighbouring strategy used for improving the quality of the solutions at hand. Both strategies are iterated into a process based on adding a series of (i) valid cardinality constraints and (ii) lower bounds used for bounding the objective function. The proposed algorithm is analysed computationally on a set of benchmark instances of the literature. The proposed algorithm outperforms the Cplex solver and the results obtained improve on most existing solutions.

An efficient heuristic approach for a multi-period logistics network redesign problem

In this paper, a multi-period logistics network redesign problem arising in the context of strategic supply chain planning is studied. Several aspects of practical relevance are captured, namely, multiple echelons with different types of facilities, product flows between facilities in the same echelon, direct shipments to customers, and facility relocation. A two-phase heuristic approach is proposed to obtain high-quality feasible solutions to the problem, which is initially modeled as a large-scale mixed-integer linear program. In the first phase of the heuristic, a linear programming rounding strategy is applied to find initial values for the binary location variables. The second phase of the heuristic uses local search to correct the initial variable choices when a feasible solution is not identified, or to improve the initial feasible solution when its quality does not meet given criteria. The results of a computational study are reported for randomly generated instances comprising a variety of logistics networks.

A distance-based rounding strategy for post-imputation ordinal data

Multiple imputation has emerged as a widely used model-based approach in dealing with incomplete data in many application areas. Gaussian and log-linear imputation models are fairly straightforward to implement for continuous and discrete data, respectively. However, in missing data settings which include a mix of continuous and discrete variables, correct specification of the imputation model could be a daunting task owing to the lack of flexible models for the joint distribution of variables of different nature. This complication, along with accessibility to software packages that are capable of carrying out multiple imputation under the assumption of joint multivariate normality, appears to encourage applied researchers for pragmatically treating the discrete variables as continuous for imputation purposes, and subsequently rounding the imputed values to the nearest observed category. In this article, I introduce a distance-based rounding approach for ordinal variables in the presence of continuous ones. The first step of the proposed rounding process is predicated upon creating indicator variables that correspond to the ordinal levels, followed by jointly imputing all variables under the assumption of multivariate normality. The imputed values are then converted to the ordinal scale based on their Euclidean distances to a set of indicators, with minimal distance corresponding to the closest match. I compare the performance of this technique to crude rounding via commonly accepted accuracy and precision measures with simulated data sets.

Semi-definite programming-based method for security-constrained unit commitment with operational and optimal power flow constraints

Considering the economics and securities for the operation of a power system, a semi-definite programming (SDP) model for the security-constrained unit commitment (SCUC) problem is described here, which is directly solved by the interior-point method for SDP within the polynomial times. The proposed method is promising for the SCUC problems because of its excellent convergence and the ability of handling the non-covex integer variables. No model decomposition and initial relaxation are needed when applying the SDP-based method. When the solution contains minor mismatches in the integer variables, a simple rounding strategy is used to correct the non-integer into integer efficiently. Different test cases from 6 to 118 buses over a 24 h horizon are presented. Extensive numerical simulations have shown that the proposed method is capable of obtaining the optimal UC schedules without any network and bus voltage violations, and minimising the operation cost as well.

Modeling and solving a Crew Assignment Problem in air transportation

A typical problem arising in airline crew management consists in optimally assigning the required crew members to each flight segment of a given time period, while complying with a variety of work regulations and collective agreements. This problem called the Crew Assignment Problem ( CAP) is currently decomposed into two independent sub-problems which are modeled and solved sequentially: (a) the well-known Crew Pairing Problem followed by (b) the Working Schedules Construction Problem. In the first sub-problem, a set of legal minimum-cost pairings is constructed, covering all the planned flight segments. In the second sub-problem, pairings, rest periods, training periods, annual leaves, etc. are combined to form working schedules which are then assigned to crew members. In this paper, we present a new approach to the Crew Assignment Problem arising in the context of airline companies operating short and medium haul flights. Contrary to most previously published work on the subject, our approach is not based on the concept of crew-pairings, though it is capable of handling many of the constraints present in crew-pairing-based models. Moreover, contrary to crew-pairing-based approaches, one of its distinctive features is that it formulates and solves the two sub-problems (a) and (b) simultaneously for the technical crew members (pilots and officers) with specific constraints. We show how this problem can be formulated as a large scale integer linear program with a general structure combining different types of constraints and not exclusively partitioning or covering constraints as usually suggested in previous papers. We introduce then, a formulation enhancement phase where we replace a large number of binary exclusion constraints by stronger and less numerous ones: the clique constraints. Using data provided by the Tunisian airline company TunisAir, we demonstrate that thanks to this new formulation, the Crew Assignment Problem can be solved by currently available integer linear programming technology. Finally, we propose an efficient heuristic method based on a rounding strategy embedded in a partial tree search procedure. The implementation of these methods (both exact and heuristic ones) provides good solutions in reasonable computation times using CPLEX 6.0.2: guaranteed exact solutions are obtained for 60% of the test instances and solutions within 5% of the lower bound for the others.

Convex quadratic programming relaxations for parallel machine scheduling with controllable processing times subject to release times*

Abstract Scheduling unrelated parallel machines with controllable processing times subject to release times is investigated. Based on the convex quadratic programming relaxation and the randomized rounding strategy, a 2-approximation algorithm is obtained for a special case with the all-or-none property and then a 3-approximation algorithm is presented for general problem.

Rabies and its Control in India

Describe a dose rounding strategy for rabies immune globulin (RIG) administration.Multicenter, retrospective, observational review of patients that received RIG following an exposure from an animal with potential to transmit rabies infection in one health-system from March 2011 through December 2021. The primary outcome was to describe the RIG dose rounding strategy and population of patients that received RIG rounded to the nearest vial size compared to those that did not. Secondary outcomes evaluated additional costs and RIG international units (IU) wasted that could have occurred (rounded group) or did occur (not rounded group), re-presentation to the ED or primary care provider (PCP) within 7 days due to RIG related complaint, and occurrence of rabies infection. Data collection included patient demographics, exposure information, and RIG dose administered. Descriptive data and univariate analyses are reported. Cost and RIG IU wasted were calculated for the dosing strategies.426 patients were included; 373 (88%) had RIG rounded to the nearest vial size and 53 (12%) did not (mean age 36.1 years ±20.5, 51.6% male, most common exposures were bats [50%], type was bite [58%], and category III exposures [92%]). Those that had RIG rounded were younger and had lower total RIG doses, but similar IU/kg doses to those not rounded. A cost savings of $144,815 and prevention of 40,572 RIG IU wasted was calculated from those patients that had RIG rounded. There was no difference in the rate of re-presentation within 7 days and no cases of human rabies infection in the region during the study period.RIG dose rounding to the nearest vial size is associated with cost savings and prevention of wasting RIG IU. There was no association with re-presentation to the ED or PCP with RIG related issues within 7 days from administration.