This paper surveys the use of mathematical programming models for controlling environmental quality. The scope includes air, water, and land quality, stemming from the first works in the 1960s. It also includes integr...
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This paper surveys the use of mathematical programming models for controlling environmental quality. The scope includes air, water, and land quality, stemming from the first works in the 1960s. It also includes integrated models, generally that are economic equilibrium models which have an equivalent mathematical program or use mathematical programming to compute a fixed point. A primary goal of this survey is to identify interesting research avenues for people in mathematical programming with an interest in applying it to help control our environment with as little economic sacrifice as possible.
In 1965 Helmut Lerchs and Ingo Grossmann presented to the mining community an algorithm to find the optimum design for an open pit mine. In their words, "the objective is to design the contour of a pit so as to m...
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In 1965 Helmut Lerchs and Ingo Grossmann presented to the mining community an algorithm to find the optimum design for an open pit mine. In their words, "the objective is to design the contour of a pit so as to maximize the difference between total mine value of the ore extracted and the total extraction cost of ore and waste". They modeled the problem in graph theoretic terms and showed that an optimal solution of the ultimate pit problem is equivalent to finding the maximum closure of their graph based model. In this paper, we develop a network flow algorithm based on the dual to solve the same problem. We show how this algorithm is closely related to Lerchs and Grossmann's and how the steps in their algorithm can be viewed in mathematical programming terms. This analysis adds insight to the algorithm of Lerchs and Grossmann and shows where it can be made more efficient. As in the case Lerchs and Grossmann, our algorithm allows us to use very efficient data structures based on graphs that represent the data and constraints. (C) 1998 Elsevier Science B.V.
This paper presents two complementary mathematical programming based approaches for the accurate safety assessment of semirigid elastoplastic frames under quasistatic loads. The inelastic behavior of the flexible conn...
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This paper presents two complementary mathematical programming based approaches for the accurate safety assessment of semirigid elastoplastic frames under quasistatic loads. The inelastic behavior of the flexible connections and material plasticity are accommodated through piecewise linearized nonlinear yield surfaces. As is necessary for this class of structures, geometric nonlinearity is taken into account. Moreover, only a 2nd-order geometric approximation is included as this is sufficiently accurate for practical structures. The work described has a twofold contribution. First, we develop an algorithm that can robustly and efficiently process the complete (path-dependent) nonholonomic response of the structure in a stepwise (path-independent) holonomic fashion. The governing formulation is cast in mixed static-kinematic variables and lead:;naturally to what is known in the mathematical programming literature as a mixed complementarity problem (MCP). The novelty of the proposed algorithm is that it processes the MCP directly without using some iterative (and often cumbersome) predictor-corrector procedure. Second, in the spirit of simplified analyses, the classical limit analysis approach is extended to compute the limit load multiplier under the simultaneous influence of joint flexibility, material and geometric nonlinearities, and limited ductility. Our formulation is an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints (MPEC). Various nonlinear programming based algorithms are proposed to solve the MPEC. Finally, four numerical examples, concerning practical structures and benchmark cases, are provided to illustrate application of the analyses as well as to validate the accuracy and robustness of the proposed schemes. (C) 2010 Elsevier Ltd. All rights reserved.
In data mining, regression analysis is a computational tool that predicts continuous output variables from a number of independent input variables, by approximating their complex inner relationship. A large number of ...
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In data mining, regression analysis is a computational tool that predicts continuous output variables from a number of independent input variables, by approximating their complex inner relationship. A large number of methods have been successfully proposed, based on various methodologies, including linear regression, support vector regression, neural network, piece-wise regression, etc. In terms of piece-wise regression, the existing methods in literature are usually restricted to problems of very small scale, due to their inherent non-linear nature. In this work, a more efficient piece-wise linear regression method is introduced based on a novel integer linear programming formulation. The proposed method partitions one input variable into multiple mutually exclusive segments, and fits one multivariate linear regression function per segment to minimise the total absolute error. Assuming both the single partition feature and the number of regions are known, the mixed integer linear model is proposed to simultaneously determine the locations of multiple break-points and regression coefficients for each segment. Furthermore, an efficient heuristic procedure is presented to identify the key partition feature and final number of break-points. 7 real world problems covering several application domains have been used to demonstrate the efficiency of our proposed method. It is shown that our propbsed piece-wise regression method can be solved to global optimality for datasets of thousands samples, which also consistently achieves higher prediction accuracy than a number of state-of-the-art regression methods. Another advantage of the proposed method is that the learned model can be conveniently expressed as a small number of if-then rules that are easily interpretable. Overall, this work proposes an efficient rule-based multivariate regression method based on piece-wise functions and achieves better prediction performance than state-of-the-arts approaches. This novel method
Fuzzy regression models are widely used to investigate the relationship between explanatory and response variables for many decision-making applications in fuzzy environments. To include more fuzzy information in obse...
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Fuzzy regression models are widely used to investigate the relationship between explanatory and response variables for many decision-making applications in fuzzy environments. To include more fuzzy information in observations, this study uses intuitionistic fuzzy numbers (IFNs) to characterize the explanatory and response variables in formulating intuitionistic fuzzy regression (IFR) models. Different from traditional solution methods, such as the least-squares method, in this study, mathematical programming problems are built up based on the criterion of least absolute deviations to establish IFR models with intuitionistic fuzzy parameters. The proposed approach has the advantages that the model formulation is not limited to the use of symmetric triangular IFNs and the signs of the parameters are determined simultaneously in the model formulation process. The prediction performance of the obtained models is evaluated in terms of similarity and distance measures. Comparison results of the performance measures indicate that the proposed models outperform an existing approach.
This paper presents a review of advances that have taken place in the mathematical programming approach to process design and synthesis. A review is first presented on the algorithms that are available for solving MIN...
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This paper presents a review of advances that have taken place in the mathematical programming approach to process design and synthesis. A review is first presented on the algorithms that are available for solving MINLP problems, and its most recent variant, Generalized Disjunctive programming models. The formulation of superstructures, models and solution strategies is also discussed for the effective solution of the corresponding optimization problems. The rest of the paper is devoted to reviewing recent mathematical programming models for the synthesis of reactor networks, distillation sequences, heat exchanger networks, mass exchanger networks, utility plants, and total flowsheets. As will be seen from this review, the progress that has been achieved in this area over the last decade is very significant.
This study proposes a mathematical programming framework to model and quantitatively compare different maintenance strategies for network-level highway pavements. The study develops mixed-integer linear programming mo...
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This study proposes a mathematical programming framework to model and quantitatively compare different maintenance strategies for network-level highway pavements. The study develops mixed-integer linear programming models for various maintenance strategies that are commonly adopted in practice and in the literature. In developing these models, traffic, pavement age, and maintenance actions with heterogeneous effects are considered. The strategies include optimization-based, worst-first, best-first, and threshold based strategies. To demonstrate the flexibility of the framework and present a practical situation in which engineering judgment is sometimes incorporated in pavement maintenance strategies, we further develop a mixed strategy. A solution procedure combining the off-shelf mixed-integer programming solver, greedy algorithms, and Lagrangian relaxation algorithms is developed to efficiently solve the models. Finally, a numerical example of a hypothetical network is established. Different maintenance strategies are applied given different budget levels, traffic loadings, and initial pavement conditions. The results of the numerical example are reasonable, and they provide insights into the efficient implementation of maintenance strategies. Results also show that the framework has the potential to aid maintenance agencies in evaluating maintenance strategies before they are implemented, improving pavement conditions, and reducing the budget for transportation infrastructure. (C) 2018 Elsevier Ltd. All rights reserved.
This paper describes the accomplishment of an operations research project concerning the development of petroleum fields and transport systems. All phases of the project are reported--the first contact with the client...
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This paper describes the accomplishment of an operations research project concerning the development of petroleum fields and transport systems. All phases of the project are reported--the first contact with the client, the discussions that lead to the formulation of a mathematical programming model, the choice of solution techniques, and the computer implementation of a user-friendly system to be used by planners as a means of decision support. [ABSTRACT FROM AUTHOR]
The optimization of stochastic Discrete Event Systems (DESs) is a critical and difficult task. The search for the optimal system configuration (optimization problem) requires the assessment of the system performance (...
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The optimization of stochastic Discrete Event Systems (DESs) is a critical and difficult task. The search for the optimal system configuration (optimization problem) requires the assessment of the system performance (simulation problem), resulting in a simulation-optimization problem. In the past ten years, a noticeable research effort has been devoted to this area. Recently, mathematical programming has been proposed to integrate simulation and optimization for multi-stage open queueing networks. This paper proposes the application of this approach to closed queueing networks. In particular, the optimal pallet allocation problem is tackled through linear mathematical programming models for simulation-optimization.
Effective engineering of large systems requires a careful delineation of major areas of responsibility for design and development. Some important considerations are critical interdependencies in performing the system ...
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Effective engineering of large systems requires a careful delineation of major areas of responsibility for design and development. Some important considerations are critical interdependencies in performing the system mission, major data flows within the system, and similarities in technology between different parts of the system. This partitioning activity is viewed in two stages: synthesis-derivation of a reasonably small number of candidate partitions- and evaluation-more thorough investigation of detailed trade-offs. Partition synthesis is addressed by means of mathematical programming. A series of formulations are given, ranging in complexity from a simple linear transportation problem to quadratic integer programs requiring maximization of a convex function. Selection among alternative formulations depends on the actual partitioning criteria applied as well as the degree of preselection desired from the synthesis.
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