基于整数线性规划的VLIW DSP指令分簇调度

在分簇VLIW DSP上,指令分簇是一项对程序性能有重要影响的编译优化,但现有的指令分簇算法只能处理顺序的程序区域,且难以获得最佳的分簇方案。针对这些问题,提出一种基于整数线性规划的统一指令分簇与指令调度的方法。该方法使用零一决策变量表示函数中指令的分簇、指令的局部调度以及簇间传输指令的全局调度,并将指令之间的依赖关系和对处理器资源的竞争关系构造为线性约束,最终得到一个以最小化函数的估计执行时间为目标的整数线性规划模型。实验结果表明,求解该模型得到的分簇调度方案对程序性能的优化显著强于现有算法,并且求解模型所耗费的时间是可接受的。     

A Hybrid approach for integer programming combining genetic algorithms, linear programming and ordinal optimization

Hybrid methods are promising tools in integer programming, as they combine the best features of different methods in a complementary fashion. This paper presents such a framework, integrating the notions of genetic algorithm, linear programming, and ordinal optimization in an effort to shorten computation times for large and/or difficult integer programming problems. Capitalizing on the central idea of ordinal optimization and on the learning capability of genetic algorithms to quickly generate good feasible solutions, and then using linear programming to solve the problem that results from fixing the integer part of the solution, one may be able to obtain solutions that are close to optimal. Indeed ordinal optimization guarantees the quality of the solutions found. Numerical testing on a real-life complex scheduling problem demonstrates the effectiveness and efficiency of this approach.     

Integer linear programming for a cutting problem in the wood-processing industry: a case study

In this paper, the authors present a case study from the wood-processing industry. It focuses on a cutting process in which material from stock is cut down in order to provide the items required by the customers in the desired qualities, sizes, and quantities. In particular, two aspects make this cutting process special. Firstly, the cutting process is strongly interdependent, with a preceding handling process, which, consequently, cannot be planned independently. Secondly, if the trim loss is of a certain minimum size, it can be returned into stock and used as input to subsequent cutting processes. In order to reduce the cost of the cutting process, a decision support tool has been developed that incorporates an integer linear programming model as a central feature. The model is described in detail, and experience from the application of the tool is reported.     

Gamma deployment problem in grids: hardness and new integer linear programming formulation

Vehicular networks are mobile networks designed for the domain of vehicles and pedestrians. These networks are an essential component of intelligent transportation systems and have the potential to ease traffic management, lower accident rates, and offer other solutions to smart cities. One of the most challenging aspects in the design of a vehicular network is the distribution of its infrastructure units, which are called roadside units (RSUs). In this work, we tackle the gamma deployment problem that consists of deploying the minimum number of RSUs in a vehicular network in accordance with a quality of service metric called gamma deployment. This metric defines a vehicle as covered if it connects to some RSUs at least once in a given time interval during its whole trip. Then, the metric parameterizes the minimum percentage of covered vehicles necessary to make a deployment acceptable or feasible. In this paper, we prove that the decision version of the gamma deployment problem in grids is NP‐complete. Moreover, we correct the multiflow integer linear programming formulation present in the literature and introduce a new formulation based on set covering that is at least as strong as the multiflow formulation. In experiments with a commercial solver, the set covering formulation widely outperforms the multiflow formulation with respect to running time and linear programming relaxation gap.     

Stability radius of an efficient solution of a vector problem of integer linear programming in the Gölder metric

A vector (multicriterion) problem of integer linear programming is considered on a finite set of feasible solutions. A metric l_p, 1 ≤ p ≤ ∞, is defined on the parameter space of the problem. A formula of the maximum permissible level of perturbations is obtained for the parameters that preserve the efficiency (Pareto optimality) of a given solution. Necessary and sufficient conditions of two types of stability of the problem are obtained as corollaries. This work has been carried out with financial support from the Belgosuniversity within the framework of the Intercollegiate Program “Fundamental and Applied Investigations” (project No. 492/28). __________ Translated from Kibernetika I Sistemnyi Analiz, No. 4, pp. 175–181, July–August 2006.     

Inter‐sample avoidance in trajectory optimizers using mixed‐integer linear programming

This paper proposes an extension to trajectory optimization using mixed‐integer linear programming. The purpose of the extension is to ensure that avoidance constraints are respected at all times between discrete samples, not just at the sampling times themselves. The method is very simple and involves applying the same switched constraints at adjacent time steps. This requires fewer additional constraints than the existing approach and is shown to reduce computation time. A key benefit of efficient inter‐sample avoidance is the facility to reduce the number of time steps without having to compensate by enlarging the obstacles. A further extension to the principle is presented to account for curved paths between samples, proving useful in cases where narrow passageways are traversed. Copyright © 2013 John Wiley & Sons, Ltd.     

The scheduling of maintenance. A resource-constraints mixed integer linear programming model

The scheduling of preventive maintenance is crucial in reliability and maintenance engineering. Hundreds of parts compose complex machines that require replacement and/or repairing. Maintenance involves the machine vendor (1), the machine user (2) and the service maintenance provider (3). The vendor and the maintenance service provider have to guarantee a high level of availability and productivity of the machines and maintain their down-time at a minimum even though they are installed worldwide and usually far from the vendor’s headquarters and/or the locations of the provider’s regional service offices. Moreover, many companies have great profits from maintenance and spare parts management.This study aims to illustrate an original mixed integer linear programming (MILP) model for the cost-based, reliability-based and resource-constraints scheduling of preventive maintenance actions. The model minimizes the total cost function made of spare parts contributions, the cost of the execution of the preventive actions and the cost of the additional repair activity in case of unplanned failure. The cost of the personnel of the producer and/or the maintenance service provider is also included. Finally, the paper presents a case study in a what-if environment demonstrating the effectiveness and the novelty of this study in real and complex applications.     

Improving the efficiency of a mixed integer linear programming based approach for multi-class classification problem

Data classification is one of the fundamental issues in data mining and machine learning. A great deal of effort has been done for reducing the time required to learn a classification model. In this research, a new model and algorithm is proposed to improve the work of Xu and Papageorgiou (2009). Computational comparisons on real and simulated patterns with different characteristics (including dimension, high overlap or heterogeneity in the attributes) confirm that, the improved method considerably reduces the training time in comparison to the primary model, whereas it generally maintains the accuracy. Particularly, this speed-increase is significant in the case of high overlap. In addition, the rate of increase in training time of the proposed model is much less than that of the primary model, as the set-size or the number of overlapping samples is increased.     

Referee assignment in the Chilean football league using integer programming and patterns

This article uses integer linear programming to address the referee assignment problem in the First Division of the Chilean professional football league. The proposed approach considers balance in the number of matches each referee must officiate, the frequency of each referee being assigned to a given team, the distance each referee must travel over the course of a season, and the appropriate pairings of referee experience or skill category with the importance of the matches. Two methodologies are studied, one traditional and the other a pattern‐based formulation inspired by the home‐away patterns for scheduling season match calendars. Both methodologies are tested in real‐world and experimental instances, reporting results that improve significantly on the manual assignments. The pattern‐based formulation attains major reductions in execution times, solving real instances to optimality in just a few seconds, while the traditional one takes anywhere from several minutes to more than an hour.     

Applying software engineering techniques in the development and management of linear and integer programming applications

This work addresses characteristics of software environments for mathematical modeling and proposes a system for developing and managing models of linear and integer programming (IP) problems. The main features of this modeling environment are: version control of models and data; client‐server architecture, which allows the interaction among modelers and decision makers; the use of a database to store information about the models and data scenarios; and the use of remote servers of optimization, which allows the optimization problems to be solved on different machines. The modeling environment proposed in this work was validated using mathematical programming models that exploit different characteristics, such as the treatment of conditions for generating variables and constraints, the use of calculated parameters derived from other parameters, and the use of integer and continuous variables in mixed IP models among others. This validation showed that the proposed environment is able to treat models found in various application areas of operations research and to solve problems with tens of thousands of variables and constraints.     

Solving parametric fuzzy systems of linear equations by a nonlinear programming method

Linear systems of equations, with uncertainty on the parameters, play a major role in various problems in economics and finance. In this paper parametric fuzzy linear systems of the general form A ₁ x + b ₁ = A ₂ x + b ₂, with A ₁, A ₂, b ₁ and b ₂ matrices with fuzzy elements, are solved by means of a nonlinear programming method. The relation between this methodology and the algorithm proposed in Muzzioli and Reynaerts [(2006) Fuzzy Sets and Systems, in press] is highlighted. The methodology is finally applied to an economic and a financial problem.     

Applying fuzzy multi-objective linear programming to project management decisions with the interactive two-phase method

The aim of this paper is to develop an interactive two-phase method that can help the Project Manager (PM) with solving the fuzzy multi-objective decision problems. Therefore, in this paper, we first revisit the related papers and focus on how to develop an interactive two-phase method. Next, we establish to consider the imprecise nature of the data by fulfilling the possibilistic programming model, and we also assume that each objective work has a fuzzy goal. Finally, for reaching our objective, the detailed numerical example is presented to illustrate the feasibility of applying the proposed approach to PM decision problems at the end of this paper. Results show that our model can be applied as an effective tool. Furthermore, we believe that this approach can be applied to solve other multi-objective decision making problems.     

大数据环境下MES作业计划与调度能力云服务化研究

云制造技术给制造企业带来机遇的同时,也为其制造执行系统MES的设计与实现带来了新的挑战。为了解决单件小批MES中作业计划与调度优化问题,首先设计了一个从作业计划静态制定,到作业执行情况实时监控与主动感知,再到异常事件智能响应,最后到作业调度动态调节的闭环体系结构。接着针对异常信息实时获取与异常事件发现、异常事件智能化处理以及作业计划与调度优化算法计算能力服务化三个子问题,依次进行了问题分析并给出了技术解决方案。最后,以哈尔滨电机厂为案例对象,综合利用IEC/ISO 62264标准、大数据分析与挖掘方法以及由虚拟化、服务化和SOA等组成的云计算技术实现了单件小批MES作业计划与调度综合优化系统,验证了上述理论与方法的有效性。     

OOESAlgorithm.jl: a julia package for optimizing a linear function over the set of efficient solutions for biobjective mixed integer linear programming

We present OOESAlgorithm.jl , a package for optimizing a linear function over the efficient set of biobjective mixed integer linear programs. The proposed package extends our recent study (see Sierra‐Altamiranda and Charkhgard [INFORMS Journal on Computing, https://doi.org/10.1287/ijoc.2018.0851]) by adding two main features: (a) in addition to CPLEX, the package allows employing any single‐objective solver supported by MathProgBase.jl , for example, GLPK, CPLEX, and SCIP; (b) the package supports execution on multiple processors and is compatible with the JuMP modeling language. An extensive computational study shows the efficacy of the package and its features.     

Target setting with minimum improving costs in data envelopment analysis: A mixed integer linear programming approach

This study addresses a problem called cost‐minimizing target setting in data envelopment analysis (DEA) methodology. The problem is how to make an inefficient decision‐making unit efficient by allocating to it as few organizational resources as possible, assuming that the marginal costs of reducing inputs or increasing outputs are known and available, which is different from previous furthest and closest DEA targets setting methods. In this study, an existed cost minimizing target setting heuristics approach based on input‐oriented model is examined to show that there exist some limitations. This study develops a simple mixed integer linear programming to determine the desired targets on the strongly efficient frontier based on non‐oriented DEA model considering the situation in the presence of known marginal costs of reducing inputs and increasing outputs simultaneously. Some experiments with the simulated datasets are conducted, and results show that the proposed model can obtain more accurate projections with lower costs compared with those from furthest and closest target setting approaches. Besides, the proposed model can be realistic and efficient in solving cost‐minimizing target setting problem.     

Reduction in the number of binary variables for inter‐sample avoidance in trajectory optimizers using mixed‐integer linear programming

This note proposes the use of a tuple encoding scheme to reduce the number of binary variables involved in trajectory optimization problems with inter‐sample avoidance constraints. Copyright © 2016 John Wiley & Sons, Ltd.     

Scheduling resumable simple linear deteriorating jobs on a single machine with an availability constraint to minimize makespan

We consider a single-machine scheduling problem in which the processing time of each job is a simple linear deteriorating function of its waiting time. The machine is subject to an availability constraint. Jobs interrupted by machine unavailability can resume their processing. The objective is to minimize the makespan. We first show that the problem can be solved optimally by 0–1 integer programming. We then prove that the problem is NP-hard in the ordinary sense and there exists a fully polynomial time approximation scheme for it.     

Stochastic programming analysis and solutions to schedule overcrowded operating rooms in China

As a result of the growing demand for health services, China's large city hospitals have become markedly overstretched, resulting in delicate and complex operating room scheduling problems. While the operating rooms are struggling to meet demand, they face idle times because of (human) resources being pulled away for other urgent demands, and cancellations for economic and health reasons. In this research we analyze the resulting stochastic operating room scheduling problems, and the improvements attainable by scheduled cancellations to accommodate the large demand while avoiding the negative consequences of excessive overtime work. We present a three-stage recourse model which formalizes the scheduled cancellations and is anticipative to further uncertainty. We develop a solution method for this three-stage model which relies on the sample average approximation and the L-shaped method. The method exploits the structure of optimal solutions to speed up the optimization. Scheduled cancellations can significantly and substantially improve the operating room schedule when the costs of cancellations are close to the costs of overtime work. Moreover, the proposed methods illustrate how the adverse impact of cancellations (by patients) for economic and health reasons can be largely controlled. The (human) resource unavailability however is shown to cause a more than proportional loss of solution value for the surgery scheduling problems occurring in China's large city hospitals, even when applying the proposed solution techniques, and requires different management measures.     

Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis

A mixed integer linear model for selecting the best decision making unit (DMU) in data envelopment analysis (DEA) has recently been proposed by Foroughi [Foroughi, A. A. (2011a). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550–554], which involves many unnecessary constraints and requires specifying an assurance region (AR) for input weights and output weights, respectively. Its selection of the best DMU is easy to be affected by outliers and may sometimes be incorrect. To avoid these drawbacks, this paper proposes three alternative mixed integer linear programming (MILP) models for identifying the most efficient DMU under different returns to scales, which contain only essential constraints and decision variables and are much simpler and more succinct than Foroughi’s. The proposed alternative MILP models can make full use of input and output information without the need of specifying any assurance regions for input and output weights to avoid zero weights, can make correct selections without being affected by outliers, and are of significant importance to the decision makers whose concerns are not DMU ranking, but the correct selection of the most efficient DMU. The potential applications of the proposed alternative MILP models and their effectiveness are illustrated with four numerical examples.     

Task allocation and trajectory planning for multiple agents in the presence of obstacle and connectivity constraints with mixed‐integer linear programming

This article addresses the problem of maneuvering multiple agents that must visit a number of target sets, while enforcing connectivity constraints and avoiding obstacle as well as interagent collisions. The tool to cope with the problem is a formulation of model predictive control including binary decision variables. In this regard, two mixed‐integer linear programming formulations are presented, considering a trade‐off between optimality and scalability between them. Simulation results are also shown to illustrate the main features of the proposed approaches.