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Mathematical Program (mathematical + program)
Selected AbstractsDesign and Management Strategies for Mixed Public Private Transportation Networks: A Meta-Heuristic ApproachCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 4 2009Avinash Unnikrishnan In this study, private companies are assumed to have a degree of control over highway sections on which they perform maintenance and rehabilitation and capacity expansion activities. The private investors recover the cost of construction by levying tolls. The public agency is assumed to maintain the rest of the network with the objective of minimizing total system generalized cost. The bi-directional impact of roadway utilization on deterioration and deterioration on utilization is modeled in this study. The model accounts for route choice of users and all users are assumed to choose routes that have equal and minimal experienced generalized cost. The nonconvex and discontinuous multi-objective mathematical program is solved using nondominant sorting genetic algorithm-II and the pareto-optimal trade-off surface between the profit of the private company and the total system cost is generated. Computational runs are conducted to demonstrate the suitability and flexibility of the developed framework in modeling various policy decisions such as the presence of noncompete clauses. [source] Numerical simulation of the forest impact on aquifersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2004A. Leontiev Abstract Here we propose a numerical method for the computer simulation of forest impact on aquifers. With this phenomenon we understand changes in the level of groundwater table beneath the areas recovered by trees. The mathematical model of the forest impact includes a boundary value problem with free and contact boundary conditions. Considering this free-contact boundary problem as a shape optimization problem we perform boundary elements discretization. Assuming the state and free boundary variables as independents, we treat the discretized problem as a non-linear mathematical program and apply interior point algorithm to solve it. Numerical results for an illustrative 2D test problem are discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source] Designing man-portable power generation systems for varying power demandAICHE JOURNAL, Issue 5 2008Mehmet Yunt Abstract Portable electronic devices operate at varying power demand levels. This variability of power demand must be considered explicitly in the design of man-portable power generation systems for acceptable performance and portability. In this regard, a mathematical programming based design method is proposed. The method transcribes optimal operation of the system at a given power demand into a mathematical program. The power demand specific programs are incorporated into another upper level mathematical program encoding design requirements to form a final two-stage formulation. The design and operational parameters of the power generation system comprise a solution of the formulation. Unlike designs, based on a nominal power demand, the design guarantees that each power demand and all operational requirements can be satisfied. A detailed study of a microfabricated fuel-cell based system is performed. The proposed method produces smaller designs with significantly better performances than nominal power demand based approaches. © 2008 American Institute of Chemical Engineers AIChE J, 2008 [source] A mathematical programming approach for improving the robustness of least sum of absolute deviations regressionNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 4 2006Avi Giloni Abstract This paper discusses a novel application of mathematical programming techniques to a regression problem. While least squares regression techniques have been used for a long time, it is known that their robustness properties are not desirable. Specifically, the estimators are known to be too sensitive to data contamination. In this paper we examine regressions based on Least-sum of Absolute Deviations (LAD) and show that the robustness of the estimator can be improved significantly through a judicious choice of weights. The problem of finding optimum weights is formulated as a nonlinear mixed integer program, which is too difficult to solve exactly in general. We demonstrate that our problem is equivalent to a mathematical program with a single functional constraint resembling the knapsack problem and then solve it for a special case. We then generalize this solution to general regression designs. Furthermore, we provide an efficient algorithm to solve the general nonlinear, mixed integer programming problem when the number of predictors is small. We show the efficacy of the weighted LAD estimator using numerical examples. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006 [source] Optimal Price and Quantity of Refurbished ProductsPRODUCTION AND OPERATIONS MANAGEMENT, Issue 3 2006Jumpol Vorasayan Many retail product returns can be refurbished and resold, typically at a reduced price. The price set for the refurbished products affects the demands for both new and refurbished products, while the refurbishment and resale activities incur costs. To maximize profit, a manufacturer in a competitive market must carefully choose the proportion of returned products to refurbish and their sale price. We model the sale, return, refurbishment, and resale processes in an open queueing network and formulate a mathematical program to find the optimal price and proportion to refurbish. Examination of the optimality conditions reveals the different situations in which it is optimal to refurbish none, some, or all of the returned products. Refurbishing operations may increase profit or may be required to relieve a manufacturing capacity bottleneck. A numerical study identifies characteristics of the new product market and refurbished products that encourage refurbishing and some situations in which small changes in the refurbishing cost and quality provoke large changes in the optimal policy. [source] On the convergence of stationary sequences in topology optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 1 2005Anton Evgrafov Abstract We consider structural topology optimization problems including unilateral constraints arising from non-penetration conditions in contact mechanics. The resulting non-convex non-smooth problems are instances of mathematical programs with equilibrium constraints (MPEC), or bi-level programs. Applying nested (implicit programming) algorithms to this class of problems is problematic owing to the singularity of the feasible set. We propose a perturbation strategy combining the relaxation of the equilibrium constraint with the restriction of the design domain to its regular part only. This strategy allows us to attack the problem numerically using standard non-linear programming algorithms. We rigorously study the optimality conditions for the original singular problem as well as the convergence of stationary points and globally optimal solutions to approximating problems towards respective stationary points and globally optimal solutions to the original problem. A limited numerical benchmarking of the algorithm is performed. Copyright © 2005 John Wiley & Sons, Ltd. [source] Solution of fuzzy matrix games: An application of the extension principleINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 8 2007Shiang-Tai Liu Conventional game theory is concerned with how rational individuals make decisions when they are faced with known payoffs. This article develops a solution method for the two-person zero-sum game where the payoffs are only approximately known and can be represented by fuzzy numbers. Because the payoffs are fuzzy, the value of the game is fuzzy as well. Based on the extension principle, a pair of two-level mathematical programs is formulated to obtain the upper bound and lower bound of the value of the game at possibility level ,. By applying a dual formulation and a variable substitution technique, the pair of two-level mathematical programs is transformed to a pair of ordinary one-level linear programs so they can be manipulated. From different values of ,, the membership function of the fuzzy value of the game is constructed. It is shown that the two players have the same fuzzy value of the game. An example illustrates the whole idea of a fuzzy matrix game. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 891,903, 2007. [source] Modified relaxation method for mathematical programs with complementarity constraintsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2007Gui-Hua Lin Abstract In this paper, we suggest a new relaxation method for solving mathematical programs with complementarity constraints. This method can be regarded as a modification of a method proposed in a recent paper (J. Opt. Theory Appl. 2003; 118:81,116). We show that the main results remain true for the modified method and particularly, some conditions assumed in the previous paper can be removed. Copyright © 2007 John Wiley & Sons, Ltd. [source] | |||||||||||||