Mathematical Programming-based Approach Research Articles

AxOMaP : Designing FPGA-based A ppro x imate Arithmetic O perators using Ma thematical P rogramming

With the increasing application of machine learning (ML) algorithms in embedded systems, there is a rising necessity to design low-cost computer arithmetic for these resource-constrained systems. As a result, emerging models of computation, such as approximate and stochastic computing, that leverage the inherent error-resilience of such algorithms are being actively explored for implementing ML inference on resource-constrained systems. Approximate computing (AxC) aims to provide disproportionate gains in the power, performance, and area (PPA) of an application by allowing some level of reduction in its behavioral accuracy (BEHAV). Using approximate operators (AxOs) for computer arithmetic forms one of the more prevalent methods of implementing AxC. AxOs provide the additional scope for finer granularity of optimization, compared to only precision scaling of computer arithmetic. To this end, the design of platform-specific and cost-efficient approximate operators forms an important research goal. Recently, multiple works have reported the use of AI/ML-based approaches for synthesizing novel FPGA-based AxOs. However, most of such works limit the use of AI/ML to designing ML-based surrogate functions that are used during iterative optimization processes. To this end, we propose a novel data analysis-driven mathematical programming-based approach to synthesizing approximate operators for FPGAs. Specifically, we formulate mixed integer quadratically constrained programs based on the results of correlation analysis of the characterization data and use the solutions to enable a more directed search approach for evolutionary optimization algorithms. Compared to traditional evolutionary algorithms-based optimization, we report up to 21% improvement in the hypervolume, for joint optimization of PPA and BEHAV, in the design of signed 8-bit multipliers. Further, we report up to 27% better hypervolume than other state-of-the-art approaches to DSE for FPGA-based application-specific AxOs.

사용자 유사도 및 지역사회 운동 효과 기반 유사 요통 환자 추천에 관한 연구

In order to return to a healthy daily life of individuals who need rehabilitation exercise, it is necessary to provide continuous individualized rehabilitation exercise services after discharge at the hospital. However, in reality, it is difficult to provide services for the entire rehabilitation cycle of individuals because hospital and community rehabilitation data are not shared. In this paper, we consider the problem of providing a top-k similar patient list under the assumption that rehabilitation medical care and community exercise service are shared. The considered problem differs from the typical recommender system problems due to the lack of labels representing any two patients share the same or similar characteristics, which means that it is challenging to apply the existing recommender algorithms. We present a mathematical programming-based approach that enables us to identify the optimal feature set and similarity between patients. Then, a two-step algorithm was developed by utilizing the presented mathematical formulation, which results in a user-based collaborative filtering system. We report the experimental results for 12 experimental options using real-life clinical data of low back pain patients.

Sequencing two classes of jobs on a machine with an external no-idle constraint

In this paper, we deal with a special type of scheduling problem. There are two classes of jobs to be processed on a single machine. Jobs of class A are directly delivered to the customers and we want to minimise their total flow time. Jobs of class B do not contribute to the objective function but must respect a no-idle constraint (i.e. they are required to keep an external downstream machine busy). This problem arises in some real-world production environments where the downstream process must not be interrupted because of technological constraints, economic viability or because the firm is bound to keep the external process continuously active (e.g. a contract with a downstream firm imposing penalties if the supply is interrupted). We prove that the general problem is NP-Hard. We introduce two mathematical programming-based approaches and some constructive heuristics. The various approaches are compared on the basis of a large computational campaign.

IoT Ecosystem on Exploiting Dynamic VNF Orchestration and Service Chaining: AI to the Rescue?

An efficient automated virtual network function (VNF) deployment and service function chaining (SFC) can induce a significant improvement in the overall performance of various IoT services. Few concerns regarding the latency benefits, energy consumption expenditure, and migration costs are required to be taken into consideration collaboratively for the solution method to accommodate supreme privileges for both users and providers. However, most of the works existing in the literature emphasize these issues exclusively. Additionally, they focus on employing traditional mathematical programming-based approaches to find optimal solutions that are computationally expensive. Thus, state-of-the-art methods are infeasible and not prompt enough to provide real-time solutions for massive IoT services. In this article, we propose the utilization of different deep learning and reinforcement learning techniques (e.g., artificial neural networks, convolutional neural networks, deep Q-networks, and federated learning) for swift VNF orchestration and SFC. Moreover, we identify some challenges and their potential solutions associated with these sophisticated learning models. Then we present some simulation results on a VNF deployment case study demonstrating that deep learning techniques can be a significant breakthrough with promising potential to resolve most of the mentioned concerns incorporated with the VNF orchestration and SFC generation problem.

Optimization of the Supply Chain in the Production of Ethanol from Agricultural Biomass Using Mixed-Integer Linear Programming (MILP): A Case Study

The production of biofuels from agricultural biomass has attracted much attention from researchers in recent years. Biomass residues generated from agricultural production of corn and barley represent an essential source of raw material for the production of biofuels, and a mathematical programming-based approach can be used to establish an efficient supply chain. This paper proposes a model of mixed-integer linear programming (MILP) that seeks to minimize the total cost of the bioethanol supply chain. The proposal allows determining the optimal number and location of storage centers, biorefineries, and mixing plants, as well as the flow of biomass and bioethanol between the facilities. To show the proposed approach, we present a case study developed in the region of Tulancingo, Hidalgo, in Mexico (case study), considering the potential of biomass (corn and barley residues) in the region. The results show the costs for the production of bioethanol, transportation, and refining and total cost of the bioethanol supply chain, besides a sensitivity analysis on the costs of the bioethanol supply chain which is presented by mixing different percentages of bioethanol with fossil fuel to satisfy the demand. We conclude that the proposed approach is viable in the process of configuring the supply chain within the proposed study region.

Qualification Management in Wafer Fabs: Optimization Approach and Simulation-Based Performance Assessment

Machines need to be individually qualified to run lots of certain families in semiconductor wafer fabrication facilities (wafer fabs). A qualification time window that lasts a couple of days is associated with each family and each tool. The time window can be reinitialized with additional qualification effort as needed and can be extended by on-time processing of qualified families. A mixed-integer linear programming formulation is proposed. The objective function takes into account the backlog costs and inventory holding costs. Moreover, it penalizes qualifications. The optimization approach is applied in a rolling horizon setting using a wafer fab simulation model. The demand for a planning window of several periods is derived using feedback from the shop floor. The results of the simulation experiments demonstrate that an appropriate tradeoff between production objectives and performed qualifications can be achieved by an appropriate configuration of the model. Note to Practitioners —In this article, we propose a mathematical programming-based approach to decide when the tools in wafer fabs have to be qualified for a certain family. These decisions have high practical relevance because qualifications are expensive and time-consuming. A dispatching scheme to implement the qualification decisions is designed. The overall approach is assessed in a rolling horizon setting using a simulation model of a large-scale wafer fab. An appropriate tradeoff between production and qualification goals can be achieved using the proposed approach.

Emission utilization permission based on environmental efficiency analysis.

Emission utilization permission is an interesting but complex issue regarding the environmental effect of pollution. This paper proposes a mathematical programming-based approach to emission utilization permission taking environmental efficiency into consideration. We use this approach for an environmental efficiency analysis and emission utilization permission (extra emission permission) of selected economic sectors in Iran, namely, agriculture, oil, industry, transportation, and domestic, commercial, and public. We use a gradually decreasing scheme for the process of emission utilization permission to investigate the condition of each sector during the process. The result reveals a vital need of improvement for two sectors, namely, oil sector and transportation sector, at the end of emission utilization permission process that is very tight in terms of emission permission.

Two Mathematical Programming-Based Approaches for Wireless Mobile Robot Deployment in Disaster Environments

This paper addresses the issue of the wireless mobile robot deployment for the ad hoc network establishment in disaster environments, which aims to maximize the important locations covered by the established ad hoc network so as to improve the performance of task allocation. In many disaster environments, the number of wireless mobile robots usually is much less than the number of important locations in the environment so that maximizing the important locations covered by the established ad hoc network is the primary objective of wireless mobile robot deployment approaches. To maximize the coverage of important locations, most of the current approaches were developed based on greedy algorithms. Due to the myopia of greedy algorithms, these approaches can only maximize the coverage of important locations of each wireless mobile robot rather than the whole network. To this end, two mathematical programming-based wireless mobile robot deployment approaches are proposed for ad hoc network establishment in disaster environments. The proposed approach can create suitable deployment locations for all wireless mobile robots in a disaster environment. The experimental results demonstrate that ad hoc networks established by the proposed approaches can cover more important locations in a disaster environment than those established by greedy algorithm-based approaches.

A mathematical programming-based approach in piecewise regression optimisation by simultaneous considering variables

Piecewise regression is one of the linear regression types which control variables could break. In this paper, we propose a new mathematical programming-based approach to optimise the piecewise regression model by simultaneous considering variables. To this aim, the break point and the regression model parameters so determined that the absolute error of prediction is minimised. Note that existing methods are designed only based on independent variables and simultaneous effects of variable are not considered in piecewise regression. Accordingly, in this paper, a new approach is developed to optimise the piecewise regression model by simultaneous considering variables. Results show that proposed method has better performance than the existing methods for fitting data with correlated control variables.

A mathematical programming-based approach in piecewise regression optimisation by simultaneous considering variables

Piecewise regression is one of the linear regression types which control variables could break. In this paper, we propose a new mathematical programming-based approach to optimise the piecewise regression model by simultaneous considering variables. To this aim, the break point and the regression model parameters so determined that the absolute error of prediction is minimised. Note that existing methods are designed only based on independent variables and simultaneous effects of variable are not considered in piecewise regression. Accordingly, in this paper, a new approach is developed to optimise the piecewise regression model by simultaneous considering variables. Results show that proposed method has better performance than the existing methods for fitting data with correlated control variables.

An innovative data structure to handle the geometry of nesting problems

As in many other combinatorial optimisation problems, research on nesting problems (aka irregular packing problems) has evolved around the dichotomy between continuous (time consuming) and discrete (memory consuming) representations of the solution space. Recent research has been devoting increasing attention to discrete representations for the geometric layer of nesting problems, namely in mathematical programming-based approaches. These approaches employ conventional regular meshes, and an increase in their precision has a high computational cost. In this paper, we propose a data structure to represent non-regular meshes, based on the geometry of each piece. It supports non-regular discrete geometric representations of the shapes, and by means of the proposed data structure, the discretisation can be easily adapted to the instances, thus overcoming the precision loss associated with discrete representations and consequently allowing for a more efficient implementation of search methods for the nesting problem. Experiments are conducted with the dotted-board model – a recently published mesh-based binary programming model for nesting problems. In the light of both the scale of the instances, which are now solvable, and the quality of the solutions obtained, the results are very promising.

A corn-stover harvest scheduling problem arising in cellulosic ethanol production

In this paper, we address a corn-stover harvest scheduling problem (CSHSP) that arises when a cellulosic ethanol plant contracts with farmers to harvest corn stover after the grain harvest has been completed. The plant contracts a fleet of harvesting crews, which must be assigned by the plant scheduler to harvest fields as they are called in by the farmers over the harvest season. First, we study the static CSHSP, in which the call in times for the fields are assumed known at the beginning of the season, and propose a mathematical programming-based approach that we show to generate solutions with an average optimality gap of only 6.1% for real-life-inspired instances. We also consider the dynamic CSHSP, in which the call in times are not known at the beginning of the harvest season and the requests arrive randomly over time. The method that we develop for the solution of this problem incurs costs that are about 4.8% higher, on average, than those incurred for the static case. These results exhibit the proposed approach to be robust for use by a plant scheduler in his/her efforts to optimize harvest scheduling as the actual season unfolds. Our proposed approach can also effectively deal with uncertainties encountered in a commercial harvest.

The Unit Commitment Problem With AC Optimal Power Flow Constraints

We propose a mathematical programming-based approach to optimize the unit commitment problem with alternating current optimal power flow (ACOPF) network constraints. This problem is a nonconvex mixed-integer nonlinear program (MINLP) that we solve through a solution technique based on the outer approximation method. Our solution technique cooptimizes real and reactive power scheduling and dispatch subject to both unit commitment constraints and ACOPF constraints. The proposed approach is a local solution method that leverages powerful linear and mixed-integer commercial solvers. We demonstrate the relative economic and operational impact of more accurate ACOPF constraint modeling on the unit commitment problem, when compared with copperplate and DCOPF constraint modeling approaches; we use a six-bus, the IEEE RTS-79, and the IEEE-118 test systems for this analysis. Our approach can be extended to solve larger scale power systems as well as include security constraints or uncertainty through decomposition techniques.

Algorithms for Generalized Clusterwise Linear Regression

Clusterwise linear regression (CLR), a clustering problem intertwined with regression, finds clusters of entities such that the overall sum of squared errors from regressions performed over these clusters is minimized, where each cluster may have different variances. We generalize the CLR problem by allowing each entity to have more than one observation and refer to this as generalized CLR. We propose an exact mathematical programming-based approach relying on column generation, a column generation–based heuristic algorithm that clusters predefined groups of entities, a metaheuristic genetic algorithm with adapted Lloyd’s algorithm for K-means clustering, a two-stage approach, and a modified algorithm of Späth [Späth (1979) Algorithm 39 clusterwise linear regression. Comput. 22(4):367–373] for solving generalized CLR. We examine the performance of our algorithms on a stock-keeping unit (SKU)-clustering problem employed in forecasting halo and cannibalization effects in promotions using real-world retail data from a large supermarket chain. In the SKU clustering problem, the retailer needs to cluster SKUs based on their seasonal effects in response to promotions. The seasonal effects result from regressions with predictors being promotion mechanisms and seasonal dummies performed over clusters generated. We compare the performance of all proposed algorithms for the SKU problem with real-world and synthetic data. The online supplement is available at https://doi.org/10.1287/ijoc.2016.0729 .

Mathematical programming-based approaches for multi-facility glass container production planning

This paper introduces a mathematical model (together with a relaxed version) and solution approaches for the multi-facility glass container production planning (MF-GCPP) problem. The glass container industry covers the production of glass packaging (bottle and jars), where a glass paste is continuously distributed to a set of parallel molding machines that shape the finished products. Each facility has a set of furnaces where the glass paste is produced in order to meet the demand. Furthermore, final product transfers between facilities are allowed to face demand. The objectives include meeting demand, minimizing inventory investment and transportation costs, as well as maximizing the utilization of the production facilities. A novel mixed integer programming formulation is introduced for MF-GCPP and solution approaches applying heuristics and meta-heuristics based on mathematical programming are developed. A multi-population genetic algorithm defines for each individual the partitions of the search space to be optimized by the MIP solver. A variant of the fix-and-optimize improvement heuristic is also introduced. The computational tests are carried on instances generated from real-world data provided by a glass container company. The results show that the proposed methods return competitive results for smaller instances, comparing to an exact solver method. In larger instances, the proposed methods are able to return high quality solutions.

Minimizing the total tardiness for the tool change scheduling problem on parallel machines

This paper deals with the total tardiness minimization problem in a parallel machines manufacturing environment where tool change operations have to be scheduled along with jobs. The mentioned issue belongs to the family of scheduling problems under deterministic machine availability restrictions. A new model that considers the effects of the tool wear on the quality characteristics of the worked product is proposed. Since no mathematical programming-based approach has been developed by literature so far, two distinct mixed integer linear programming models, able to schedule jobs as well as tool change activities along the provided production horizon, have been devised. The former is an adaptation of a well-known model presented by the relevant literature for the single machine scheduling problem with tool changes. The latter has been specifically developed for the issue at hand. After a theoretical analysis aimed at revealing the differences between the proposed mathematical models in terms of computational complexity, an extensive experimental campaign has been fulfilled to assess performances of the proposed methods under the CPU time viewpoint. Obtained results have been statistically analyzed through a properly arranged ANOVA analysis.

A Mathematical Programming-Based Approach to Determining Objective Functions from Qualitative and Subjective Comparisons

The solutions or states of optimization problems or simulations are evaluated by using objective functions. The weights for these objective functions usually have to be estimated from experts' evaluations, which are likely to be qualitative and somewhat subjective. Although such estimation tasks are normally regarded as quite suitable for machine learning, we propose a mathematical programming-based method for better estimation. The key idea of our method is to use an ordinal scale for measuring paired differences of the objective values as well as the paired objective values. By using an ordinal scale, experts' qualitative and subjective evaluations can be appropriately expressed with simultaneous linear inequalities, and which can be handled by a mathematical programming solver. This allows us to extract more information from experts' evaluations compared to machine-learning-based algorithms, which increases the accuracy of our estimation. We show that our method outperforms machine-learning-based algorithms in a test of finding appropriate weights for an objective function.

Design, modeling, and analysis of a feedstock logistics system

Given the location of a bio-energy plant for the conversion of biomass to bio-energy, a feedstock logistics system that relies on the use of satellite storage locations (SSLs) for temporary storage and loading of round bales is proposed. Three equipment systems are considered for handling biomass at the SSLs, and they are either placed permanently or are mobile and thereby travel from one SSL to another. A mathematical programming-based approach is utilized to determine SSLs and equipment routes in order to minimize the total cost. The use of a Side-loading Rack System results in average savings of 21.3% over a Densification System while a Rear-loading Rack System is more expensive to operate than either of the other equipment systems. The utilization of mobile equipment results in average savings of 14.8% over the equipment placed permanently. Furthermore, the Densification System is not justifiable for transportation distances less than 81km.

Design and operation of a future hydrogen supply chain: Multi-period model

Introducing hydrogen as the fuel of the future necessitates a comprehensive, widespread supply chain network that is capable of producing, distributing, storing, and dispensing hydrogen to end users. Most of the early attempts to design and model the future hydrogen supply chain (HSC) were either limited to examining an individual component of the supply chain or focused on a predetermined hydrogen pathway. In these studies, a simulation-based approach has commonly been adopted rather than using a mathematical programming-based approach. The work presented here is an extension of an early attempt to design and operate a deterministic, steady-state HSC network using a mathematical modelling approach. In this paper, however, the model is developed to consider the availability of energy sources (i.e. raw materials) and their logistics, as well as the variation of hydrogen demand over a long-term planning horizon leading to phased infrastructure development. The proposed model is formulated as a mixed-integer linear programming (MILP) and solved via a commercial software tool, GAMS. The results show that the optimal design of the future HSC network of Great Britain (GB) starts with small-size plant together with using the hydrogen currently produced by chemical processing plants. As demand grows, more plants of different sizes should be built to meet the demand. The hydrogen produced will be transported using liquid hydrogen trucks and stored in different sizes of storage facilities.

Economic Life of Capital Equipments in a Cellular Manufacturing System

This paper is aimed to investigate the economic life of the capital equipment in a cellular manufacturing system (CMS). The capital equipment is prone to degradation during the usage and this degradation can be measured by increase in the operation and maintenance (O&M) costs. Economic life refers to the optimal replacement age of the equipment in which the total discounted costs is at its minimum value. To our best knowledge, the traditional cell formation methods are built on the principle of economy of scale without considering the economic life and discounted costs of the capital equipment. On the other hand, due to a known drawback of the CMSs of imbalance cell utilization (Rheault, 1995), resulting from the unbalance workload distributed between machines within the cells, the machines within different cells have various degradation rates and consequently different economic lives. A mathematical programming-based approach is used to form the cells considering the life cycle costs of the machines and material handling equipment over a long horizon. The performance of the proposed model is verified by a comprehensive numerical example.