During the last years, interest on hybrid metaheuristics has risen considerably in the field of optimization and machine learning. The best results found for many optimization problems in science and industry are obta...
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During the last years, interest on hybrid metaheuristics has risen considerably in the field of optimization and machine learning. The best results found for many optimization problems in science and industry are obtained by hybrid optimization algorithms. Combinations of optimization tools such as metaheuristics, mathematical programming, constraint programming and machine learning, have provided very efficient optimization algorithms. Four different types of combinations are considered in this paper: (i) Combining metaheuristics with complementary metaheuristics. (ii) Combining metaheuristics with exact methods from mathematical programming approaches which are mostly used in the operations research community. (iii) Combining metaheuristics with constraint programming approaches developed in the artificial intelligence community. (iv) Combining metaheuristics with machine learning and data mining techniques.
With the fast-growing demand in the electricity market of the last decades, attention has been focused on alternative and flexible sources of energy such as hydro valleys. Managing the hydroelectricity produced by the...
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With the fast-growing demand in the electricity market of the last decades, attention has been focused on alternative and flexible sources of energy such as hydro valleys. Managing the hydroelectricity produced by the plants in hydro valleys is called the hydro unit commitment problem. This problem consists in finding the optimal power production schedule of a set of hydro units while meeting several technical, physical, and strategic constraints. The hydro unit commitment has always been a crucial and challenging optimization problem, not only because of its strong nonlinear and combinatorial aspects, but also because it is a large-scale problem that has to be solved to (near) optimality in a reasonable amount of time. This paper presents a review on mathematical programming approaches for the deterministic hydro unit commitment problem. We first provide a survey of the different variants of the problem by exposing a variety of the assumptions, objectives, and constraints considered in the literature. Then, we review the main contributions on resolution approaches with a particular focus on methods based on mathematical programming techniques.
In the coming decades, an increasing competition for global land and water resources can be expected, due to rising demand for food and bio-energy production, biodiversity conservation, and changing production conditi...
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In the coming decades, an increasing competition for global land and water resources can be expected, due to rising demand for food and bio-energy production, biodiversity conservation, and changing production conditions due to climate change. The potential of technological change in agriculture to adapt to these trends is subject to considerable uncertainty. In order to simulate these combined effects in a spatially explicit way, we present a model of agricultural production and its impact on the environment (MAgPIE). MAgPIE is a mathematical programming model covering the most important agricultural crop and livestock production types in 10 economic regions worldwide at a spatial resolution of three by three degrees, i.e., approximately 300 by 300 km at the equator. It takes regional economic conditions as well as spatially explicit data on potential crop yields and land and water constraints into account and derives specific land-use patterns for each grid cell. Shadow prices for binding constraints can be used to valuate resources for which in many places no markets exist, especially irrigation water. In this article, we describe the model structure and validation. We apply the model to possible future scenarios up to 2055 and derive required rates of technological change (i.e., yield increase) in agricultural production in order to meet future food demand.
Two-parameter (TP) estimators are more advantageous to their one-parameter competitors since they have two biasing parameters that serve different purposes in linear regression model. At least one of these biasing par...
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Two-parameter (TP) estimators are more advantageous to their one-parameter competitors since they have two biasing parameters that serve different purposes in linear regression model. At least one of these biasing parameters intends to gain a remedial impact for multicollinearity. Within this respect, we define a new TP estimator to eliminate the disorder originated from multicollinearity. Also, we perform theoretical comparisons for new TP estimator according to mean square error criterion. By minimizing the mean square error, we derive optimal estimators for both of the biasing parameters of this new estimator. Moreover, we recommend a mathematical programming approach to determine two biasing parameters, simultaneously. In this approach, we minimize the mean square error and improve the length of the newly defined TP estimator. In application part, computations regarding the estimations of the biasing parameters and mean square errors, and the length of the estimated coefficients are examined.
Large practical linear and integer programming problems are not always presented in a form which is the most compact representation of the problem. Such problems are likely to posses generalized upper bound(GUB) and r...
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Large practical linear and integer programming problems are not always presented in a form which is the most compact representation of the problem. Such problems are likely to posses generalized upper bound(GUB) and related structures which may be exploited by algorithms designed to solve them *** steps of an algorithm which by repeated application reduces the rows, columns, and bounds in a problem matrix and leads to the freeing of some variables are first presented. The ‘unbounded solution’ and ‘no feasible solution’ conditions may also be detected by this. Computational results of applying this algorithm are presented and *** algorithm to detect structure is then described. This algorithm identifies sets of variables and the corresponding constraint relationships so that the total number of GUB-type constraints is maximized. Comparisons of computational results of applying different heuristics in this algorithm are presented and discussed.
In computations related to mathematical programming problems, one often has to consider approximate, rather than exact, solutions satisfying the constraints of the problem and the optimality criterion with a certain e...
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In computations related to mathematical programming problems, one often has to consider approximate, rather than exact, solutions satisfying the constraints of the problem and the optimality criterion with a certain error. For determining stopping rules for iterative procedures, in the stability analysis of solutions with respect to errors in the initial data, etc., a justified characteristic of such solutions that is independent of the numerical method used to obtain them is needed. A necessary delta-optimality condition in the smooth mathematical programming problem that generalizes the Karush-Kuhn-Tucker theorem for the case of approximate solutions is obtained. The Lagrange multipliers corresponding to the approximate solution are determined by solving an approximating quadratic programming problem.
During the last years, interest on hybrid metaheuristics has risen considerably in the field of optimization and machine learning. The best results found for many optimization problems in science and industry are obta...
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During the last years, interest on hybrid metaheuristics has risen considerably in the field of optimization and machine learning. The best results found for many optimization problems in science and industry are obtained by hybrid optimization algorithms. Combinations of optimization tools such as metaheuristics, mathematical programming, constraint programming and machine learning, have provided very efficient optimization algorithms. Four different types of combinations are considered in this paper: (1) Combining metaheuristics with complementary metaheuristics. (2) Combining metaheuristics with exact methods from mathematical programming approaches which are mostly used in the operations research community. (3) Combining metaheuristics with constraint programming approaches developed in the artificial intelligence community. (4) Combining metaheuristics with machine learning and data mining techniques.
The coefficient of variation is a useful statistical measure, which has long been widely used in many areas. In real-world applications, there are situations where the observations are inexact and imprecise in nature ...
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The coefficient of variation is a useful statistical measure, which has long been widely used in many areas. In real-world applications, there are situations where the observations are inexact and imprecise in nature and they have to be estimated. This paper investigates the sample coefficient of variation (CV) with uncertain observations, which are represented by interval values. Since the observations are interval-valued, the derived CV should be interval-valued as well. A pair of mathematical programs is formulated to calculate the lower bound and upper bound of the CV. Originally, the pair of mathematical programs is nonlinear fractional programming problems, which do not guarantee to have global optimum solutions. By model reduction and variable substitutions, the mathematical programs are transformed into a pair of quadratic programs. Solving the pair of quadratic programs produces the global optimum solutions and constructs the interval of the CV. The given example shows that the proposed model is indeed able to help the manufacturer select the most suitable manufacturing process with interval-valued observations.
A finite cutting plane procedure is proposed for generating feasible points for the extreme point mathematical programming (EPMP) problem. It is demonstrated that the proposed procedure can be used for the solution o...
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A finite cutting plane procedure is proposed for generating feasible points for the extreme point mathematical programming (EPMP) problem. It is demonstrated that the proposed procedure can be used for the solution of nonconvex programs of other types as well. A finite method is described for the EPMP problem, and computational experience on EPMP and concave minimization problems is included. Computational experience demonstrates that, using certain stragegies, the Majthay-Whinston (1974) concave minimization cutting plane technique may be significantly more effective than that of Tuy (1964). The implication is that the use of the original vertex finding procedures at solving special nonconvex programming problems is interesting both from the point of view of finiteness and also from the possibility of speeding up existing cutting plane techniques.
In this paper, we establish a strong convergence theorem for hierarchical problems, an equivalent relation between a multiple sets split feasibility problem and a fixed point problem. As applications of our results, w...
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In this paper, we establish a strong convergence theorem for hierarchical problems, an equivalent relation between a multiple sets split feasibility problem and a fixed point problem. As applications of our results, we study the solution of mathematical programming with fixed point and multiple sets split feasibility constraints, mathematical programming with fixed point and multiple sets split equilibrium constraints, mathematical programming with fixed point and split feasibility constraints, mathematical programming with fixed point and split equilibrium constraints, minimum solution of fixed point and multiple sets split feasibility problems, minimum norm solution of fixed point and multiple sets split equilibrium problems, quadratic function programming with fixed point and multiple set split feasibility constraints, mathematical programming with fixed point and multiple set split feasibility inclusions constraints, mathematical programming with fixed point and split minimax constraints.
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