Showing papers on "Linear-fractional programming published in 2007"

Municipal Solid Waste Management Under Uncertainty: A Mixed Interval Parameter Fuzzy-Stochastic Robust Programming Approach

Abstract: A mixed interval parameter fuzzy-stochastic robust programming (MIFSRP) model is developed and applied to the planning of solid waste management systems under uncertainty The MIFSRP can explicitly address system uncertainties with multiple presentations It can be used as an extension of the existing interval-parameter fuzzy robust programming, interval-parameter linear programming, and chance constraint programming methods In this MIFSRP model, the hybrid uncertainties can be directly communicated into the optimization process and resulting solution through representing the uncertain parameters as interval numbers and fuzzy membership functions with random characteristics Highly uncertain information arising from simultaneous appearance of fuzziness and randomness for the lower and upper bounds of interval parameters can be effectively addressed through integrating chance constraint programming, interval linear programming, and fuzzy robust programming methods into a general optimization framework Th

An exact primal---dual penalty method approach to warmstarting interior-point methods for linear programming

Abstract: One perceived deficiency of interior-point methods in comparison to active set methods is their inability to efficiently re-optimize by solving closely related problems after a warmstart. In this paper, we investigate the use of a primal---dual penalty approach to overcome this problem. We prove exactness and convergence and show encouraging numerical results on a set of linear and mixed integer programming problems.

Linear programming with MATLAB

Abstract: 1. Introduction 2. Linear algebra 3. The simplex method 4. Duality 5. Solving large linear programs 6. Sensitivity and parametric linear programming 7. Quadratic programming and complementarity problems 8. Interior point methods 9. Approximation and classification A. Linear algebra, convexity, and nonlinear functions B. Summary of available MATLAB Commands Bibliography Index.

Inter and intra-modal deformable registration: continuous deformations meet efficient optimal linear programming

Abstract: In this paper we propose a novel non-rigid volume registration based on discrete labeling and linear programming. The proposed framework reformulates registration as a minimal path extraction in a weighted graph. The space of solutions is represented using a set of a labels which are assigned to predefined displacements. The graph topology corresponds to a superimposed regular grid onto the volume. Links between neighborhood control points introduce smoothness, while links between the graph nodes and the labels (end-nodes) measure the cost induced to the objective function through the selection of a particular deformation for a given control point once projected to the entire volume domain. Higher order polynomials are used to express the volume deformation from the ones of the control points. Efficient linear programming that can guarantee the optimal solution up to (a user-defined) bound is considered to recover the optimal registration parameters. Therefore, the method is gradient free, can encode various similarity metrics (simple changes on the graph construction), can guarantee a globally sub-optimal solution and is computational tractable. Experimental validation using simulated data with known deformation, as well as manually segmented data demonstrate the extreme potentials of our approach.

Formulating Integer Linear Programs: A Rogues' Gallery

Abstract: “Convincing yourself is easy, persuading a colleague is harder, but proving it to a computer is hardest of all!”---R. Hamming, ca 1985. The art of formulating linear and integer linear programs is, well, an art: It is hard to teach, and even harder to learn. To help demystify this art, we present a set of modeling building blocks that we call “formulettes.” Each formulette consists of a short verbal description that must be expressed in terms of variables and constraints in a linear or integer linear program. These formulettes can better be discussed and analyzed in isolation from the much more complicated models they comprise. Not all models can be built from the formulettes we present. Rather, these are chosen because they are the most frequent sources of mistakes. We also present Naval Postgraduate School NPS format; a define-before-use formulation guide we have followed for decades to express a complete formulation.

Interactive fuzzy programming for decentralized two-level linear fractional programming (DTLLFP) problems

Abstract: This paper presents two new interactive fuzzy programming approaches for a decentralized two-level linear fractional programming (DTLLFP) problem with a single decision maker ( DM 0 ) at the upper level and multiple DMs ( DM i , i = 1 , … , k ) at the lower level. In the first approach, DM 0 specifies the minimal satisfactory level for own objective without considering the satisfactory levels of own decision variables and decreases it in favour of objectives at the lower level. Whereas, in the second approach, DM 0 does not specify the minimal satisfactory level for own objective, but instead DM 0 transfers the degree of satisfaction for not only own objective but also the own decision variables to the lower level. In both our approaches, with the help of analytic hierarchy process (AHP) method [Saaty TL. The analytical hierarchy process. New York: McGraw-Hill, 1980], DM 0 assigns weights w 1 , w 2 , … , w k to objectives at the lower level. The most important idea to be emphasized is that equivalence is established such that the satisfactory levels of all objectives are proportional to their own weights. To obtain an overall satisfactory balance between both levels, by updating the satisfactory degree of the DM 0 which is in the first approach or the tolerances of the DM 0 's decision variables which is in the second approach, transformed main problems are constructed corresponding to DTLLFP. Maximizing the least degree of equivalent satisfaction among all DMs, they efficiently find a satisfactory or compromise solution from a Pareto optimal set for DTLLFP problem. If the DM 0 is not satisfied with this solution, a strongly efficient satisfactory solution can be reached by interacting with him or her. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed methods.

Acceptable optimality in linear fractional programming with fuzzy coefficients

Abstract: Based on the specified grades of satisfaction, we propose two new concepts of (?, β)-acceptable optimal solution and (?, β)-acceptable optimal value of a fuzzy linear fractional programming problem with fuzzy coefficients, and develop a method to compute them. An example is provided to demonstrate the method.

A New Methodology for the General Multiparametric Mixed-Integer Linear Programming (MILP) Problems

Abstract: In this paper, a general algorithm is developed to address the multiparametric mixed-integer linear programming (mpMILP) problem with uncertain parameters in the left-hand side (LHS), right-hand si...

An Optimization Approach to Petri Net Monitor Design

Abstract: This note addresses the problem of enforcing generalized mutual exclusion constraints on a Petri net plant. First, we replace the classical partition of the event set into controllable and uncontrollable events from supervisory control theory, by associating a control and observation cost to each event. This leads naturally to formulate the supervisory control problem as an optimal control problem. Monitor places which enforce the constraint are devised as a solution of an integer linear programming problem whose objective function is expressed in terms of the introduced costs. Second, we consider timed models for which the monitor choice may lead to performance optimization. If the plant net belongs to the class of mono-T-semiflow nets, we present an integer linear fractional programming approach to synthesize the optimal monitor so as to minimize the cycle time lower bound of the closed loop net. For strongly connected marked graphs the cycle time of the closed-loop net can be minimized

Simplex Method For Solving Linear Programming Problems With Fuzzy Numbers

Abstract: The fuzzy set theory has been applied in many fields, such as operations research, control theory, and management sciences, etc. In particular, an application of this theory in decision making problems is linear programming problems with fuzzy numbers. In this study, we present a new method for solving fuzzy number linear programming problems, by use of linear ranking function. In fact, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.

Linear fractional programming and duality

Abstract: This paper presents a dual of a general linear fractional functionals programming problem. Dual is shown to be a linear programming problem. Along with other duality theorems, complementary slackness theorem is also proved. A simple numerical example illustrates the result.

An adaptive genetic algorithm for solving bilevel linear programming problem

Abstract: Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the genetic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes may be infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references.

An Infinite-Dimensional Linear Programming Algorithm for Deterministic Semi-Markov Decision Processes on Borel Spaces

Abstract: We devise an algorithm for solving the infinite-dimensional linear programs that arise from general deterministic semi-Markov decision processes on Borel spaces. The algorithm constructs a sequence of approximate primal-dual solutions that converge to an optimal one. The innovative idea is to approximate the dual solution with continuous piecewise linear ridge functions that naturally represent functions defined on a high-dimensional domain as linear combinations of functions defined on only a single dimension. This approximation gives rise to a primal/dual pair of semi-infinite programs, for which we show strong duality. In addition, we prove various properties of the underlying ridge functions.

A Linear Programming Approach to Semidefinite Programming Problems

Abstract: A semidefinite programming problem can be regarded as a convex nonsmooth optimization problem, so it can be represented as a semi-infinite linear programming problem Thus, in principle, it can be solved using a cutting plane approach; we describe such a method The cutting plane method uses an interior point algorithm to solve the linear programming relaxations approximately, because this resulted in the generation of better constraints than a simplex cutting plane method Further, the bundle method of Helmberg and Rendl can be used to generate a set of linear constraints Typically, these alone are not sufficient to give a good linear programming relaxation Nonetheless, if they are used in conjunction with some families of problem specific constraints, tight LP relaxations can be obtained Solving SDP via LP 2

Continuous Thrust Orbit Transfer Optimization Using Large-Scale Linear Programming

Abstract: A new technique is developed to optimize continuous medium- and low-thrust orbit transfers. This approach combines large-scale linear programming algorithms with discretization of the trajectory dynamics on segments and a set of pseudoimpulses or control for each segment. The set is a discrete approximation with a small mesh width for a space of possible thrust directions. Boundary conditions are presented as a linear matrix equation. A matrix inequality on the sum of characteristic velocities for the pseudoimpulses is used to transform the problem into a linear programming form. The number of decision variables is on the order of tens of thousands. In modern linear programming methods there are interior-point algorithms to solve such problems. In the general case, the continuous burns include a number of adjacent segments and a postprocessing of the linear programming solutions is needed to form a sequence of the burns. An optimal number of the burns is automatically determined in the postprocessing. A maintenance of a 24-hour elliptical orbit, long-term transfer from a geo-transfer to geostationary orbit, and a one-revolution, medium-thrust transfer between two elliptical noncoplanar orbits are considered as application examples. In the last two examples an iterative solution method was used. The presented method can be used effectively for trajectory optimization in a wide range of space missions.

Primal-Dual Simplex Method for Multiobjective Linear Programming

Abstract: We develop a primal-dual simplex algorithm for multicriteria linear programming. It is based on the scalarization theorem of Pareto optimal solutions of multicriteria linear programs and the single objective primal-dual simplex algorithm. We illustrate the algorithm by an example, present some numerical results, give some further details on special cases and point out future research.

Mixed-Integer Linear Programming Algorithm for a Computational Protein Design Problem

Abstract: The computational protein design problem or the side-chain positioning problem is a central part in computational methods for predicting protein structure and designing protein sequences. However, the computational protein design problem is NP-complete, and it is also NP-complete to find a reasonable approximate solution to this problem. Here, we present a critical finding that the network flow structure embedded in the integer linear programming formulation of the computational protein design problem makes it equivalent to a mixed-integer linear programming formulation with fewer binary variables. This novel formulation effectively reduces the combinatorial difficulty of the computational protein design problem, thereby allowing the sequence selection of the global minimum energy conformation for large proteins to become tractable by using the standard optimization algorithms. Our preliminary calculation results for 20 core redesigned proteins show that the mixed-integer linear programming algorithm with...

On Optimization over the Efficient Set in Linear Multicriteria Programming

Abstract: The efficient set of a linear multicriteria programming problem can be represented by a reverse convex constraint of the form g(z)≤0, where g is a concave function. Consequently, the problem of optimizing some real function over the efficient set belongs to an important problem class of global optimization called reverse convex programming. Since the concave function used in the literature is only defined on some set containing the feasible set of the underlying multicriteria programming problem, most global optimization techniques for handling this kind of reverse convex constraint cannot be applied. The main purpose of our article is to present a method for overcoming this disadvantage. We construct a concave function which is finitely defined on the whole space and can be considered as an extension of the existing function. Different forms of the linear multicriteria programming problem are discussed, including the minimum maximal flow problem as an example.

Harmonic grammar with linear programming

Abstract: Harmonic Grammar (HG) is a model of linguistic constraint interaction in which well-formedness is calculated as the sum of weighted constraint violations. We show how linear programming algorithms can be used to determine whether there is a weighting for a set of constraints that fits a set of linguistic data. Our associated software package HaLP provides a practical tool for studying large and complex linguistic systems in the HG framework, and thus it can be valuable for comparing HG’s linear model to the model of constraint ranking assumed in Optimality Theory. We describe the translation from linguistic systems to linear systems, and we report on some recent work modeling HG typologies using HaLP.