Linear Computer Program Research Articles

Optimization: From Its Inception

Optimization has been one of the most fundamental and extensive contributions of management science/operations research, with an enormous number of contributions and subfields developed by many researchers and practitioners. When the journal Management Science launched in 1954, little was known about optimization, including some results in nonlinear optimization and the simplex method and duality developed for linear programming. However, linear programming computations were limited to problems with at most 101 linear constraints. Then some early contributions by seminal researchers began to develop foundations for the field. I will review a few of these early contributions, focusing on the traveling sales problem and integer programming, decomposition, and column generation. I will summarize some research and applied contributions since then, including the enormous development of computations. I will focus on linear and integer programs with some material on combinatorial optimization. This paper was accepted by David Simchi-Levi, Special Section of Management Science: 65th Anniversary.

Optimization of soil movements when planning terrain

Earth work is considered when planning the terrain at the initial stage of construction. Instead of a manual method for calculating the volume of soil transportation, it is proposed to switch to the use of linear programming methods and computer solutions in the environment of the computing complex Matlab. The problem is stated, algorithms and a computer program are developed. The optimal plan for transporting soil masses from dredges to embankments was found for a specific task.

Operator- and user-based rebalancing strategy for bike-sharing systems

Leveraging their networks, bike rental companies usually provide customers with services for renting and returning bikes at different bike stations. Over time, however, rental networks may encounter problems with unbalanced bike stocks. The potential imbalance between supply and demand at bike stations may result in lost sales for stations with relatively high demand and underutilization for stations with relatively low demand. This paper proposed a constrained mixed-integer programming model that uses operator-based redistribution and user-based price approach to rebalance bikes across bike stations. This paper aims to maximize total profit over a planning horizon by determining operator-based bike transfers and dynamic pricing. The proposed model is a non-deterministic polynomial-time problem, and thus, a heuristic was developed based on linear programming and evolutionary computation to perform model solving. Numerical experiments reveal that the proposed method performed better than Lingo, a well-known commercial software. Sensitivity analyses were also performed to investigate the impact of changes in system parameters on computational results.

Secure Optimization Computation Outsourcing in Cloud Computing: A Case Study of Linear Programming

Cloud computing enables an economically promising paradigm of computation outsourcing. However, how to protect customers confidential data processed and generated during the computation is becoming the major security concern. Focusing on engineering computing and optimization tasks, this paper investigates secure outsourcing of widely applicable linear programming (LP) computations. Our mechanism design explicitly decomposes LP computation outsourcing into public LP solvers running on the cloud and private LP parameters owned by the customer. The resulting flexibility allows us to explore appropriate security/efficiency tradeoff via higher-level abstraction of LP computation than the general circuit representation. Specifically, by formulating private LP problem as a set of matrices/vectors, we develop efficient privacy-preserving problem transformation techniques, which allow customers to transform the original LP into some random one while protecting sensitive input/output information. To validate the computation result, we further explore the fundamental duality theorem of LP and derive the necessary and sufficient conditions that correct results must satisfy. Such result verification mechanism is very efficient and incurs close-to-zero additional cost on both cloud server and customers. Extensive security analysis and experiment results show the immediate practicability of our mechanism design.

Linear programming computation

Introduction.- Geometry of the Feasible Region.- Simplex Method.- Duality principle and dual simplex method.- Implementation of the Simplex Method.- Sensitivity Analysis and Parametric LP.- Variants of the Simplex Method.- Decomposition Method.- Interior Point Method.- Integer Linear Programming (ILP).- Pivot Rule.- Dual Pivot Rule.- Simplex Phase-I Method.- Dual Simplex Phase-l Method.- Reduced Simplex Method.- Improved Reduced Simplex Method.- D-Reduced Simplex Method.- Criss-Cross Simplex Method.- Generalizing Reduced Simplex Method.- Deficient-Basis Method.- Dual Deficient-Basis Method.- Face Method.- Dual Face Method.- Pivotal interior-point Method.- Special Topics.- Appendix.- References.

Implementation of Secure Cloud Storage Gateway using Symmetric Key Algorithm

Focusing on engineering computing and optimization tasks, this paper investigates secure outsourcing of widely applicable linear programming (LP) computations. In order to achieve practical efficiency, our mechanism design explicitly decomposes the LP computation outsourcing into public LP solvers running on the cloud and private LP parameters owned by the customer. The resulting flexibility allows us to explore appropriate security/ efficiency tradeoff via higher-level abstraction of LP computations than the general circuit representation. In particular, by formulating private data owned by the customer for LP problem as a set of matrices and vectors, we are able to develop a set of efficient privacy-preserving problem transformation techniques, which allow customers to transform original LP problem into some arbitrary one while protecting sensitive input/output information. To validate the computation result, we further explore the fundamental duality theorem of LP computation and derive the necessary and sufficient conditions that correct result must satisfy. Such result verification mechanism is extremely efficient and incurs close-to-zero additional cost on both cloud server and customers. Extensive security analysis and experiment results show the immediate practicability of our mechanism design. Keywords: cloud customer, cloud server,fully homomorphic encryption (FHE), linearprogramming,

Data Security in Cloud Computing Using Linear Programming

Cloud computing has great potential of providing robust computational power to the society at reduced cost. It enables customers with limited computational resources to outsource their large computation workloads to the cloud, and economically enjoy the massive computational power, bandwidth, storage, and even appropriate software that can be shared in a pay-per-use manner. Despite the tremendous benefits, security is the primary obstacle that prevents the wide adoption of this promising computing model, especially for customers when their confidential data are consumed and produced during the computation. Treating the cloud as an intrinsically insecure computing platform from the viewpoint of the cloud customers, We must design mechanisms that not only protect sensitive information by enabling computations with encrypted data, but also protect customers from malicious behaviors by enabling the validation of the computation result. Such a mechanism of general secure computation outsourcing was recently shown to be feasible in theory, but to design mechanisms that are practically efficient remains a very challenging problem. Focusing on engineering computing and optimization tasks, this paper investigates secure outsourcing of widely applicable linear programming (LP) computations. In order to achieve practical efficiency, our mechanism design explicitly decomposes the LP computation outsourcing into public LP solvers running on the cloud and private LP parameters owned by the customer. The resulting flexibility allows us to explore appropriate security/efficiency tradeoff via higher-level abstraction of LP computations than the general circuit representation. In particular, by formulating private data owned by the customer for LP problem as a set of matrices and vectors, we are able to develop a set of efficient privacy-preserving problem transformation techniques, which allow customers to transform original LP problem into some arbitrary one while protecting sensitive input/output information. To validate the computation result, we further explore the fundamental duality theorem of LP computation and derive the necessary and sufficient conditions that correct result must satisfy. Such result verification mechanism is extremely efficient and incurs close-to-zero additional cost on both cloud server and customers. Extensive security analysis and experiment results show the immediate practicability of our mechanism design.

Optimization Problem of Excel Programming Calculation for Mayonnaise Prescription

The method combining linear programming theory and computer technology, affords the possibility for the Optimization problem of food prescription in engineering design. Excel's Solver function may be used to solve problems with up to 200 decision variables, enough to calculate the most problems about food prescription. Combined design requirement of mayonnaise prescription, the decision variables, constraint condition and mathematics model of cost are established. The optimization prescription of minimum cost is gotten through the function of Excel programming calculation. It may provide valuable reference for the application of computer in prescription design.

A New Fuzzy Approach on Planning and Decision Making in Engineering and Construction Industry

In recent years engineering and construction industry faces formidable challenges in control project and optimization of management decision making. The requirements and challenges of today's world have made managers to explore new methods in dealing with solving management problems, methods with high flexibility, which can adopt plans to real conditions can help one to make a decision at right time. This paper proposes a new method to obtain the optimal solution in construction environment with uncertainty and dynamic. Since linear programming is the most natural mechanism for formulating a vast array of problems with the modest effort, we use fuzzy linear programming and Matlab computation to solve this problem. In this research, we are modeling uncertainty and dynamic of engineering and construction industry with fuzzy theory. The considerable ratio of data about uncertainties is linguistic data and cannot be formulated with classical mathematics, so we use fuzzy theory for the computational model of the linguistic term of expert. After preparation of the dynamic fuzzy linear programming model (DFLP) we solve the optimization problem. Dynamics of the DFLP model able the system to provide decision making in environmental changes.

Optimal Residential Load Control With Price Prediction in Real-Time Electricity Pricing Environments

Real-time electricity pricing models can potentially lead to economic and environmental advantages compared to the current common flat rates. In particular, they can provide end users with the opportunity to reduce their electricity expenditures by responding to pricing that varies with different times of the day. However, recent studies have revealed that the lack of knowledge among users about how to respond to time-varying prices as well as the lack of effective building automation systems are two major barriers for fully utilizing the potential benefits of real-time pricing tariffs. We tackle these problems by proposing an optimal and automatic residential energy consumption scheduling framework which attempts to achieve a desired trade-off between minimizing the electricity payment and minimizing the waiting time for the operation of each appliance in household in presence of a real-time pricing tariff combined with inclining block rates. Our design requires minimum effort from the users and is based on simple linear programming computations. Moreover, we argue that any residential load control strategy in real-time electricity pricing environments requires price prediction capabilities. This is particularly true if the utility companies provide price information only one or two hours ahead of time. By applying a simple and efficient weighted average price prediction filter to the actual hourly-based price values used by the Illinois Power Company from January 2007 to December 2009, we obtain the optimal choices of the coefficients for each day of the week to be used by the price predictor filter. Simulation results show that the combination of the proposed energy consumption scheduling design and the price predictor filter leads to significant reduction not only in users' payments but also in the resulting peak-to-average ratio in load demand for various load scenarios. Therefore, the deployment of the proposed optimal energy consumption scheduling schemes is beneficial for both end users and utility companies.

A note on minimizing absolute percentage error in combined forecasts

In this note, two new approaches of combined forecasts are proposed. One approach minimizes mean absolute percentage error while the other approach minimizes the maximum absolute percentage error. A goal programming model is used to obtain the weights to combine different forecasts to minimize the mean absolute percentage error. This formulation can be solved readily by any linear programming computer code. The other approach, minimizing the maximum absolute percentage error, can also be formulated as a goal programming model. Scope and purposeMean absolute percentage error has been widely used as a performance measure in forecasting. One of the major reasons for its popularity is that it is easy to interpret and understand and it becomes a good alternative to mean squared error. Our proposed linear programming models can provide solutions of the minimum mean absolute percentage error and the minimum of the maximum absolute percentage error in combined forecasts. The models we proposed could be solved readily by any linear programming computer code.

Imprecise Reliability of General Structures

This paper discusses the important aspects of the reliability of systems with an imprecise general model of the structure function. It is assumed that the information about reliability behavior of components is restricted by the mean levels of component performance. In this case the classical reliability theory cannot provide a way for analyzing the reliability of systems. The theory of imprecise probabilities may be a basis in developing a general reliability theory which allows us to solve such problems. The basic tool for computing new reliability measures is the natural extension which can be regarded as a linear optimization problem. However, the linear programming computations will become impracticable when the number of components in the system is large. Therefore, the main aim of this paper is to obtain explicit expressions for computing the system reliability measures. We analyze the reliability of general structures and typical systems. The numerical examples illustrate the usefulness of the presented approach to reliability analyzing.

Nutritional analysis and complementation of a food basket derived from consumption

The DISEASE & PROCON Basket (DPB) is a list of basic foodstuffs, drawn up on the basis of a Standard of Living and Work Research project in S. Paulo city, Brazil. Seeing that it has been used as a standard for price variations, it is desirable that such an economic instrument as this, should also represent a truly healthy standard of nutrition. Thus, this study seeks to verify the adequacy of the food products in the DPB in relation to the nutritional needs of a typical reference family in S. Paulo city. It also proposes some techniques for dietary complementation. A demographic census, undertaken in 1991 has been used to establish the reference family, as well as 2/3rds of RDA as corresponding to its nutritional needs, and the food composition tables of McCance & Widdowson to analyse the nutrient content of the DPB. Dietary complementation were undertaken by three different methods: Ad Hoc (direct suggestions), Linear Programming (computer software was utilized to minimize costs), and Hybrid (a combination of the first two). Food items in the DPB showed insufficient values for vitamins A, C, B2 and B6, and for minerals Ca, Mg, Fe, Zn, I and Se; besides, a relatively high fat content was found. The Hybrid Method of food complementation seems to present the best results, associating low cost and local dietary habits. A relation between the dietary deficiencies of the DPB and the nutritional transition in the developing countries may be infered. The epidemiological risks associated with these changes in eating patterns should not be incorporated into a reliable economic instrument.

The augmented system variant of IPMs in two-stage stochastic linear programming computation

The application of interior point methods (IPM) to solve the deterministic equivalent of two-stage stochastic linear programming problems is a known and natural idea. Experiments have proved that among the interior point methods, the augmented system approach gives the best performance on these problems. However, most of their implementations encounter numerical difficulties in certain cases, which can result in loss of efficiency. We present a new approach for the decomposition of the augmented system, which ‘automatically’ exploits the special behavior of the problems. We show that the suggested approach can be implemented in a fast and numerically robust way by solving a number of large-scale two-stage stochastic linear programming problems. The comparison of our solver with fo1aug, which is considered as a state-of-the-art augmented system implementation of interior point methods, is also given.

Clarification to “The Sudbury structure: Controversial or misunderstood?”

Journal of Geophysical Research: PlanetsVolume 98, Issue E11 p. 20903-20904 CorrectionsFree Access Clarification to “The Sudbury structure: Controversial or misunderstood?” R. A. F. Grieve, R. A. F. GrieveSearch for more papers by this authorD. Stöffler, D. StöfflerSearch for more papers by this authorA. Deutsch, A. DeutschSearch for more papers by this author R. A. F. Grieve, R. A. F. GrieveSearch for more papers by this authorD. Stöffler, D. StöfflerSearch for more papers by this authorA. Deutsch, A. DeutschSearch for more papers by this author First published: 25 November 1993 https://doi.org/10.1029/93JE02139Citations: 1AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article. References Deutsch, A., P. Brockmeyer, D. Buhl, Sudbury again: New and old isotope data, Lunar Planet Sci. Conf., XXI, 282– 283, 1990. Fairbairn, H. W., P. M. Hurley, W. H. Pinson, Rb-Sr whole rock age of the Sudbury 1opolith and basin sediments, Can. J. Earth Sci., 5, 707– 714, 1968. Gibbins, W. A., R. H. McNutt, Rubidium-Strontium mineral ages and polymetamorphism at Sudbury, Ontario: The age of the Sudbury nickel irruptive and the Murray Granite, Can. J. Earth Sci., 12, 1990– 003, 1975. Grieve, R. A. F., R. J. Floran, The Manicouagan impact melt, Quebec, 2, Chemical interrelations with basement and formational processes, J. Geophys. Res., 83, 2761– 2771, 1978. Stöckelmann, D., W. U. Reimold, The HMX mixing calculation program, Math. Geol., 21, 853– 860, 1989. Wright, T. L., P. C. Doherty, A linear programming and least squares computer method for solving petrologic mixing problems, Geol. Soc. Am. Bull., 81, 1995– 2008, 1970. Citing Literature Volume98, IssueE1125 November 1993Pages 20903-20904 ReferencesRelatedInformation

Optimization of transmission line planning including security constraints

The authors describe an automatic way of finding the least-cost method of securing a given power system. The objective is to minimize the present cost of building additional lines to make the system secure due to single contingencies, subject to the technical constraints with and without line outages. A second approach to the problem, heuristic in nature, is also illustrated and compared to the results of the first method. All network synthesis is based on the DC power flow model. A six-bus network is used to illustrate the methods, and solutions obtained using a standard mixed-integer linear programming computer package, MIP/370, are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fast and efficient linear programming and linear least-squares computations

We present a new parallel algorithm for computing a least-squares solution to a sparse overdetermined system of linear equations A x = b such that the m × n matrix A is sparse and the graph, G = ( V, E), of the matrix H= I A T A O has an s( m + n)-separator family, i.e. either | V| < n 0 for a fixed constant n 0 or, by deleting a separator subset S of vertices of size ⩽ s( m + n), G can be partitioned into two disconnected subgraphs having vertex sets V 1, V 2 of size ⩽ 2 3 (m + n) , and each of the two resulting subgraphs induced by the vertex sets S U ́ V i, i = 1, 2 , can be recursively s(|S U ́ V i|) -separated in a similar way. Our algorithm uses O(log ( m + n) log 2 s ( m + n)) steps and ⩽ s 3( m + n) processors; it relies on our recent parallel algorithm for solving sparse linear systems and has several immediate applications of interest, in particular to mathematical programming, to sparse nonsymmetric systems of linear equations and to the path algebra computations. We most closely examine the impact on the linear programming problem (LPP) which requires maximizing c T y subject to A T y ⩽ b, y ⩾ 0 , where A is an m × n matrix. Hereafter it is assumed that m ⩾ n. The recent algorithm by Karmarkar gives the best-known upper estimate [ O ( m 3.5 L) arithmetic operations, where L is the input size] for the cost of the solution of this problem in the worst case. We prove an asymptotic improvement of that result in the case where the graph of the associated matrix H has an s ( m + n)-separator family; then our algorithm can be implemented using O ( mL log m log 2 s ( m + n)) parallel arithmetic steps, s 3 ( m + n) processors and a total of O ( mLs 3 ( m + n) log m log 2 s ( m + n)) arithmetic operations. In many cases of practical importance this is a considerable improvement on the known estimates: for example, s ( m + n) = √8 ( m + n) if G is planar [as occurs in many operations research applications; for instance, in the problem of computing the maximum multicommodity flow with a bounded number of commodities in a network having an s ( m + n)-separator family], so that the processor bound is only 8 √8 ( m + n) 1.5 and the total number of arithmetic steps is O ( m 2.5 L). Similarly, Karmakar's algorithm and the known algorithms for the solution of overdetermined linear systems are accelerated in the case of dense input matrices via our recent parallel algorithms for the inversion of dense k × k matrices using O (log 2 k) steps and k 3 processors. Combined with a modification of Karmarkar's algorithm, this implies solution of the LPP using O ( Lm log 2 m) steps and m 2.5 processors. The stated results promise some important practical applications. Theoretically, the above processor bounds can be reduced for dense matrix inversion to o ( k 2.5) and for the LPP to o ( m 2.165) in the dense case and to o ( s 2.5 ( m + n)) in the sparse case (preserving the same number of parallel steps); this also decreases the known sequential time bound for the LPP by a factor of m 0.335, i.e. to O ( Lm 3.165).

Efficient parallel linear programming

Linear programming and least squares computations are accelerated using author's parallel algorithms for solving linear systems. The implications on the performance of the Karmarkar and the simplex algorithms for dense and sparse linear programs are examined. The results have further applications to combinatorial algorithms.

Electricity and gas supply in south-eastern Australia, 1980–2020

A linear programming computer model, MENSA, was used to examine the energy systems of the south-eastern states of Australia. A regime of stable extraction costs for primary fuels was assumed and capital and operating costs for energy technologies were assumed to remain constant in real terms over the 40 year period 1980–2020. Particular attention was focused on the final demand sectors which consume electricity and natural gas. The costs and benefits attributeble to various proposed linkages of the gas supply networks and the electricity grids were examined, using minimum overall system cost as the criterion for deciding optimal configurations. The only gas pipeline which proved viable within the assumptions and data presented to the model was a low-capacity link between the existing systems of New South Wales and Victoria. A number of options for supplying South Australian electricity needs after the year 2000 were studied. Nuclear power was found to give the greatest system savings but at considerable capital cost. An alternative scheme involving a high-capacity link with the Victorian grid was also investigated. Within the model, this link proved viable if nuclear power continued to be proscribed.

A chance-constrained multiobjective model for mental health services planning

Mental health services planning, and particularly the planning for deinstitutionalization, is a very complex problem. This paper suggests a chance-constrained goal programming (CCGP) approach to mental health services planning. The CCGP approach is based on the sequential solution of a linear programming formulation, allowing efficient solution of large-scale planning problems using commercially available linear programming computer codes. The procedure is demonstrated with a case example and implementation of the approach is discussed.