Linear Programming Software Research Articles

The essential multiobjectivity of linear programming

It is argued that any non-trivial real world problems involve multiple objectives. The simplistic approach of combining objectives in linear form can generate highly misleading and biased results, and is poor operational research practice. Such biases are illustrated by means of a simple example, and it is demonstrated that two simple approaches based on goal programming and piecewise linear value functions can largely resolve these problems. These methods require careful attention to problem structuring but are easily implemented by use of standard linear programming (LP) packages.

Visual LinProg: A web‐based educational software for linear programming

AbstractVisual LinProg is an educational tool that solves linear problems (LPs), using animation and visualization techniques. The core of the proposed software includes the well‐known class of simplex type algorithms. This tool is a Web‐based software and hence platform independent. Visual LinProg was initially invented to be used in mathematical programming courses to supplement the teaching. The user‐student can solve his own general LPs, view the solution process step‐by‐step, and import or export his own examples in an easy way to read format. The solution process is covered scholastically through textual information and also the necessary steps from the pseudo code are depicted, using multiple views. In this study, we describe Visual LinProg and how it is used in educational purposes. Finally, we present an evaluation of the proposed educational tool. © 2007 Wiley Periodicals, Inc. Comput Appl Eng Educ 15: 1–14, 2007; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20084

Genome-scale in silico aided metabolic analysis and flux comparisons of Escherichia coli to improve succinate production

In the post-genome era, it is one challenge to understand the cellular metabolism at the systematic levels. Mathematical modeling of microorganisms and subsequent computer simulation are effective tools for systems biology. In this paper, based on the genome-scale Escherichia coli stoichiometric model iJR904, through the GAMS linear programming package, the in silico maximal succinate yield was estimated to be 1.714 mol/mol glucose. When another two constraints were added, the maximal succinate yield dropped to 1.60 mol/mol glucose. Further analysis substantiated the uniqueness of the flux distribution under such constraints. After comparisons with the metabolic flux analysis (MFA) results computed from the wet experimental data of the three kinds of E. coli, three potential improvement target sites, the glucose phosphotransferase transport system, the pyruvate carboxylase, and the glyoxylate shunt, were identified and selected for the genetic modifications. All the three genetic modified strains showed increased succinate yield. The final strain TUQ19/pQZ6 had a high yield of 1.29 mol succinate/mol glucose and high productivity. The success of the above experiments proved that this in silico optimal succinate production pathway is reasonable and practical. This method may also be used as a general strategy to help enhance the yields of other favorable metabolites in E. coli.

Massive Data Classification via Unconstrained Support Vector Machines

A highly accurate algorithm, based on support vector machines formulated as linear programs (Refs. 1–2), is proposed here as a completely unconstrained minimization problem (Ref. 3). Combined with a chunking procedure (Ref. 4), this approach, which requires nothing more complex than a linear equation solver, leads to a simple and accurate method for classifying million-point datasets. Because a 1-norm support vector machine underlies the proposed approach, the method suppresses input space features as well. A state-of-the-art linear programming package (CPLEX, Ref. 5) fails to solve problems handled by the proposed algorithm.

E-learning technologies: employing Matlab web server to facilitate the education of mathematical programming

This paper presents new web-based educational software (webNetPro) for Linear Network Programming. It includes many algorithms for Network Optimization problems, such as shortest path problems, minimum spanning tree problems, maximum flow problems and other search algorithms. Therefore, webNetPro can assist the teaching process of courses such as Graph Theory or Network Optimization, Algorithms or Data Structures. Since the Matlab web server is part of the underlying infrastructure, the end user need not use Matlab directly. The approach exploits transparently the benefits of the Matlab programming environment through a straightforward web interface. Furthermore, webNetPro is platform independent. Thus, it can be viewed as a powerful supplement to traditional instruction techniques and can be used without significant difficulties in distance education. Benefits and drawbacks are thoroughly described in order to support the significance of this tool in distance learning.

A Comparison of Discrete Algorithms for Fuzzy Weighted Average

Fuzzy weighted average (FWA), which can be applied to various fields such as engineering design, decision analysis, etc., and as function of fuzzy numbers, is suitable for the problem of multiple occurrences of fuzzy parameters. Additional fuzziness may be introduced in the alpha-cut arithmetic. This paper reviews and compares discrete algorithms for the FWAs in both theoretical comparison and numerical comparisons, as opposed to the linear programming algorithms that may be efficient but require the help of linear programming software. An alternative efficient algorithm is also proposed. The algorithm introduces an all-candidate (criteria ratings) weights-replaced benchmark adjusting procedure other than a binary (dichotomy) search in the existing methods. The theoretical worst-case comparison shows that the algorithms of Guu and Guh and our alternative algorithm require the same order of calculation complexity O(n), where n is the number of FWA terms. Yet, the Guh algorithm always requires 2(n-1) calculations to be performed. The algorithm of Guu requires the elemental comparison complexity O(n), and is superior to the other algorithms, in the worst case. On the other hand, our alternative algorithm and Lee and Park algorithm have the same comparison complexity O(n log n). Yet, our alternative algorithm requires O(n) calculation complexity which is better than O(n log n) of the Lee and Park algorithm. The numerical experiments show that the algorithm of Guu and our alternative algorithm generally perform and converge faster by requiring fewer calculations than that of Lee and Park's algorithm. The alternative algorithm requires a slightly smaller number of calculations than that of the Guu algorithm, due to the use of the convergent benchmark adjustment procedure rather than a somewhat fixed binary search. Conversely, in the number of element comparisons, Lee and Park's algorithm is shown numerically generally slightly better than the alternative algorithm due to the simple binary search scheme used. The alternative algorithm also requires fewer comparisons than that of the Guu algorithm. Furthermore, in comparison of the average CPU time requirements, the ranks of the results of these algorithms are consistent with those of the algorithms for the average numbers of calculations. In general, the alternative algorithm may provide an efficient alternative algorithm to the FWAs. In the worse-case situation, the Guu algorithm still may be considered as an efficient alternative

Multiple Weighted Objectives Heuristic for the Redundancy Allocation Problem

A new heuristic is proposed and tested for system reliability optimization. The multiple weighted objective heuristic is based on a transformation of the problem into a multiple objective optimization problem, and then ultimately, transformation into a different single objective problem. The multiple objectives are to simultaneously maximize the reliability of each individual subsystem. This is a logical approach because system reliability is the product of the subsystem reliabilities, so if they are maximized, the system reliability will also be high. This new formulation and associated heuristic are then based on solving a sequence of linear programming problems. It is one of the very few optimization approaches that allow for linear programming algorithms and software to be used for the redundancy allocation problem when mixing of functionally equivalent components is allowed. Thus, it represents an efficient solution method that relies on readily available optimization tools. The heuristic is tested on many example problems, and compared to competing solution approaches. Overall, the heuristic performance is observed to be very good on the tested problem, and superior to the max-min heuristic regarding both efficiency, and performance

Minimum cost dimensioning of ring optical networks

We consider the problem of traffic grooming of low-rate traffic circuits in WDM rings where circuits are associated with a set of heterogeneous granularities. While networks are no longer limited by transmission bandwidth, the key issue in WDM network design has evolved towards the processing capabilities of electronic switches, routers and multiplexers. Therefore, we focus here on traffic grooming with minimum interconnecting equipment cost. We first formulate the problem as an integer linear programming (ILP) or a mixed integer linear programming (MILP) problem depending on the design specifications: UPSR vs BLSR, fixed vs variable wavelength capacities, non-bifurcated vs bifurcated flows, wavelength continuity vs possible signal regeneration on a different wavelength. Considering the case study of the second SONET ring generation with MSPP like interconnection equipment, we define the cost by a function of the number of transport blades, taking into account that the number of MSPP transport blades makes up a significant portion of the overall network design cost. Using the CPLEX linear programming package, we next compare the optimal solutions of the ILP or MILP programs for different design assumptions, including the classical ring network design scheme with a single hub where the lightpaths directly connect the hub to all other nodes.

Energy efficiency assessment for the Antalya Region hotels in Turkey

The hotels in the Antalya Region of Turkey have become a major consumer of energy, water and other resources. However, at present, there are no existing guidelines for the efficient use and management of these resources. Energy management includes increasing in profitability due to the reduced operational costs and it is also a potential for improved market share. Many different evaluation models have been published in energy management literature. However there have been not so many systematic approaches to compare the relative efficiency of the systems. Data envelopment analysis is a special linear programming model for deriving the comparative efficiency of multiple-input multiple-output decision-making units. An evaluation of energy efficiency in 32 five-star hotels in the Antalya Region has been carried out and the results are discussed in this paper. According to this study eight hotels are efficient and twenty-four hotels are inefficient. Also for these 24 inefficient hotels, ideal energy consumptions (electricity, water and liquefied petroleum gas consumptions) are proposed to become efficient these hotels. In this study data envelopment analysis models are evaluated by using a linear programming package LINGO 5.0.

Optimal scheduling for flexible job shop operation

This paper presents a new integer linear programming (ILP) model to schedule flexible job shop, discrete parts manufacturing industries that operate on a make-to-order basis. The model considers groups of parallel homogeneous machines, limited intermediate buffers and negligible set-up effects. Orders consist of a number of discrete units to be produced and follow one of a given number of processing routes. The model allows re-circulation to take place, an important issue in practice that has received scant treatment in the scheduling literature. Good solution times were obtained using commercial mixed-integer linear programming (MILP) software to solve realistic examples of flexible job shops to optimality. This supports the claim that recent advances in computational power and MILP solution algorithms are making this approach competitive with others traditionally applied in job shop scheduling.

Fractional programming with absolute-value functions: a fuzzy goal programming approach

Fuzzy goal programming (FGP) is an important technique for solving many decision/management problems. Following the philosophy of FGP, this paper proposes a new approach to solve fractional programming with absolute-value functions (FP-A). The major contribution of this paper is that the FP-A problem can be converted to the linearized FGP problem. Then, the linearized FGP problem can be easily solved by commercialized linear programming packages. In addition, illustrative examples are included to demonstrate the correctness of the proposed method.

The linear multiple choice knapsack problem with equity constraints

In this paper, we introduce an important variation of a well known problem, the linear multiple choice knapsack problem with equity constraints, which finds application in the allocation of funds to highway improvements. The multiple choice constraints are used to model the interactions that arise among different improvements. The equity constraints are introduced to ensure a balance on the budget amounts allocated to different sets of improvements. We present the mathematical formulation and show that this problem structure has several fundamental properties. These are used to develop an optimal two phase greedy algorithm for its solution. We report computational results which indicate that the algorithm is more efficient than a commercial linear programming package and the outperformance increases with problem size.

A new approach to O&D revenue management based on scenario trees

Origin and destination (O&D) revenue management (RM), either leg-based or PNR based, has become a standard in the airline industry. This paper presents a new approach to O&D RM which does not make any assumptions on demand distributions or on the correlations of the booking process. Protection levels are determined for all origin—destination itineraries, fare classes, points of sale and data collection points (DCPs), and for a variety of demand patterns over the complete booking period. This approach to the seat inventory problem is modelled as a multistage stochastic program, where its stages correspond to the DCPs of the booking horizon. The stochastic passenger demand process is approximated by a scenario tree generated from historical data by a recursive scenario reduction procedure. The stochastic program represents a specially structured large scale linear program (LP) that may be solved by standard LP software (eg CPLEX). Preliminary numerical experience is reported.

Docking of Atomic Clusters Through Nonlinear Optimization

The problem of molecular docking is defined as that of finding a minimum energy configuration of a pair of molecular structures (usually consisting of proteins, DNA or RNA fragments). It is often assumed that the two interacting structures can be considered as rigid bodies and that it is of interest to researchers to develop methods which enable to discover the potential binding sites. Many different models have been proposed in the literature for the definition of the potential energy between two molecular structures, most of which contain at least a term (known as Van Der Waals interaction) which accounts for pairwise attraction between atoms, a repulsion term and a term which takes into account electrostatic forces (Coulomb interaction). Some well known models, and in particular those used in rigid docking, are based on the assumption that the only terms which are relevant in the process of docking are pairwise interactions between atoms belonging to the two different parts of the structure. In this paper the problem of finding the lowest energy configuration of a pair of biomolecular structures, considered as rigid bodies, is defined and formulated as a global optimization problem. In terms of dimension of the search space this formulation is not 'high-dimensional', as there are only six degrees of freedom: 3 translation and 3 rotation parameters. However the energy surface of the docking problem is characterized by a huge number of local minima; moreover each function evaluation is quite expensive (interesting structures usually possess a few thousand atoms each). So there is a strong need both of local and of global optimization procedures. In this paper a local optimization technique, based upon standard non linear programming software and a penalized objective function, is introduced and its potential usefulness in the context of global optimization is outlined.

Decomposition techniques for the minimum toll revenue problem

AbstractThe objective of the minimum toll revenue (MINREV) problem is to find tolls that simultaneously cause users to use the transportation network efficiently and minimize the total toll revenues that must be collected. This article investigates the Dantzig‐Wolfe (DW) decomposition as an approach for solving the MINREV problem and establishes its relationships with a cutting plane algorithm and other proposed approaches. The article also identifies the variant of DW decomposition most suitable for implementation. Numerical experiments with real transportation networks suggest that DW decomposition is robust and should be used when the problems are too large for standard linear programming software. Although transportation planning is the application emphasized in this article, it should be noted that the MINREV problem also has applications in telecommunication network design and control. © 2004 Wiley Periodicals, Inc. NETWORKS, Vol. 44(2), 142–150 2004

A Feature Selection Newton Method for Support Vector Machine Classification

A fast Newton method, that suppresses input space features, is proposed for a linear programming formulation of support vector machine classifiers. The proposed stand-alone method can handle classification problems in very high dimensional spaces, such as 28,032 dimensions, and generates a classifier that depends on very few input features, such as 7 out of the original 28,032. The method can also handle problems with a large number of data points and requires no specialized linear programming packages but merely a linear equation solver. For nonlinear kernel classifiers, the method utilizes a minimal number of kernel functions in the classifier that it generates.

The Numerical Solution of Minimum Time Maneuvering Problems by a NLP Method

It is a great concerning problem for a mariner to know how maneuvering method is the best for his ship. Moreover it is also important for a ship builder in the meaning how the designed ship shows the maneuvering performance in full conditions. A minimum time maneuvering yields an answer about this problem. The minimum time maneuvering problem of ship can be formulated as two point boundary problem. The author has solved this non linear problem using the Sequential Conjugate Gradient-Restoration Algorithm (SCGRA) by Wu and Miel. This numerical method was a powerful solving method. However, a tedious programming method was needed. In this paper, the author proposes to treat this problem in a non linear programming formulation. According to this, our problem is transformed to more easy one and we can solve the transformed one by using a general Non Linear Programming (NLP) package. In this paper, the author solves a minimum time changing course problem and a Williamson's turning (man over board) one which are described by non linear mathematical maneuvering model.

Iteratively reweighted least-squares implementation of the WLAV state-estimation method

An implementation of the weighted least absolute value (WLAV) method for obtaining an estimate of the state of the power system is presented. Most of the known WLAV methods use some form of linear programming software to find the best estimate. The paper shows that it is possible to obtain a WLAV estimate by simply applying the Newton-Raphson method to the set of equations that yield the critical points. The resulting iterative scheme corresponds to solving a sequence of linear weighted least-squares (WLS) problems. The proposed implementation enables the use of well-known techniques of WLS estimation and, consequently, facilitates the integration of the WLAV function in an energy management system. Test results on standard IEEE test systems reveal that the proposed implementation is competitive with a standard WLAV algorithm that uses a state-of-the-art implementation of an interior-point method.

Junk food or genuine nourishment: The nutritional value of some of South African fast-food chains

Integer programming is used to test the nutritional completeness of two fast-food chains operating in South Africa. McDonald's and Kentucky Fried Chicken. It is shown that a fully nutritional and varied daily diet can be made up from McDonald's menu items, but the same is not true for Kentucky Fried Chicken. This exercise is highly suited to introduce students to mathematical programming: skills learned include formulating mathematical programming problems, mastering linear programming software and exploring the Internet for relevant data.

A combinatorial approximation algorithm for concurrent flow problem and its application

The multi-commodity flow problem involves simultaneous shipping several different commodities from sources to sinks in a directed network with total amount of flow going through an edge limited by its capacity. The optimization version of the multi-commodity flow problem is the maximum concurrent flow problem, which finds a flow with the minimum congestion. For any positive ε, the ε-optimal concurrent flow problem is to find a solution whose the congestion value is no more than (1+ ε) times the minimum congestion. In recent years, a few fast combinatorial approximation algorithms for the ε-optimal concurrent flow problem have been presented. In this paper we propose a new variant of the combinatorial approximation algorithm: CACF with a tighter computation bound in decreasing the values of congestion and the potential function. Numerical comparisons are made between the results obtained by the combinatorial approximation algorithms and those did by the linear programming package CPLEX on large-scale test networks. The application of CACF to efficiently solving the system-optimal network flow problem is given where good results have been obtained. It has shown the capacity of the CACF in dealing with problems of concurrent flow associated.