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Methods for Valuing Producers' Uses of Water
Published in Robert A. Young, John B. Loomis, Determining the Economic Value of Water, 2014
Robert A. Young, John B. Loomis
where Πi represents net income or rent per activity i; Xi is a vector of production activities; the elements of the A matrix are production coefficients; and B is a vector of constraints on production inputs such as labor, capital, and natural resources. The objective function can be linear or nonlinear (e.g. quadratic). In addition, the models can be made dynamic with the allocation of resources changing over time if future prices of particular inputs or output are expected to change over time. A tractable way to do this is in a multi-stage optimization model (Marques et al. 2005). In addition, the usual assumption in many programming models that the production coefficients are fixed at a known level can also be relaxed to account for uncertainty of these production coefficients. These types of stochastic models explicitly incorporate uncertainty in the model coefficients via some random parameters (Feiring et al. 1998). In addition, dynamic stochastic models can be constructed that deal with temporal dimensions and uncertainty (Marques et al. 2005).
Mine ventilation system planning esing genetic algorithms
Published in Vladimír Strakoš, Vladimír Kebo, Radim Farana, Lubomír Smutný, Mine Planning and Equipment Selection 1997, 2020
N. M. Lilić, R. M. Stanković, I. M. Obradović
A genotype is an explicit genetic structure of chromosomes, while a phenotype is the real, physical representation of the genotype. The objective function is the function being optimized, i.e. the function whose minimum or maximum is required. The feasibility measure, i.e. the fitness of an individual demonstrates, in the optimization case, how well that individual, i.e. the solution represented by the chromosome optimizes the objective function. In the case of minimization, the fitness value is inversely proportional to the value of the objective function, and in the maximization task, the values of the objective function and fitness are proportional. A chromosome can contain groups of genes with common characteristics which are called schemes, an sometimes pools.
Optimization Methods
Published in B K Bala, Energy Systems Modeling and Policy Analysis, 2022
The standard form of linear programming consists of two parts: (1) objective function and (2) constraints. Objective function defines the quantity to be optimized, and constraints defines the restrictions on achieving the objectives. For linear programming, the objective function may be stated as maximize or minimize the objective function (de Neufville, 1990): Z=∑CiXi
Using an optimisation strategy to design a supercritical CO2 radial inflow turbine transonic stator
Published in Engineering Applications of Computational Fluid Mechanics, 2022
Jianhui Qi, Bingkun Ma, Kan Qin, Kuihua Han, Jiangwei Liu, Jinliang Xu, Yueming Yang, Yongqing Xiao, Xujiang Wang
It is essential correctly to define the objective function for an optimisation problem, which delivers the targets to the optimiser. Considering that the outlet flow fields are the most important for the stator, as they affect the operation of the downstream rotor, the objective functions are set based on the stator outlet flow properties. Figure 1 presents an example of the stator geometry and flow fields. In this project, six different targets (highlighted in bold font in Table 1) leading to a multi-objective optimisation problem need to be reached, and the linear combination of objects can be addressed as where Φ should be minimised. is the cost term related to different targets, and is the corresponding weight.
Optimal prioritization of rain gauge stations for areal estimation of annual rainfall via coupling geostatistics with artificial bee colony optimization
Published in Journal of Spatial Science, 2019
Mahdi Attar, Mohammad Javad Abedini, Reza Akbari
For the past three decades or so, hydrologists have assumed a variety of procedures to obtain more accurate results in designing a typical rain gauge network (Chebbi et al. 2013, Putthividhya and Tanaka 2013, Adhikary et al. 2015, Feki et al. 2017). These procedures associated with the objective function are classified as variance-based methods (Bastin et al. 1984, Kassim and Kottegoda 1991, Cheng et al. 2008, Haggag et al. 2016), entropy-based techniques (Krstanovic and Singh 1992, Al-Zahrani and Husain 1998, Yoo et al. 2008, Vivekanandan et al. 2012, Xu et al. 2015), fractal-based approaches (Mazzarella and Tranfaglia 2000, Capecchi et al. 2012), distance-based styles (Van Groenigen et al. 2000) and a combination of two of the above methodologies (Chen et al. 2008, Awadallah 2012, Mahmoudi-Meimand et al. 2016, Xu et al. 2018). After selecting the objective function, an optimization algorithm should be implemented to minimize or maximize the corresponding objective function. Thus, there is a close interaction between the objective function and the corresponding optimization algorithm used.
Modelling and simulation of energy consumption of ceramic production chains with mixed flows using hybrid Petri nets
Published in International Journal of Production Research, 2018
Hongcheng Li, Haidong Yang, Bixia Yang, Chengjiu Zhu, Sihua Yin
A sensitivity analysis will be implemented based on the perturbation analysis theory of the linear programming model. In theory, a sensitivity analysis refers to the study of how optimal solutions change with the changes of the given linear programing terms of the coefficients of the matrix, the right-hand side and the objective function (Ignizio and Cavalier 1994). Assuming q = [q0 ⋯ qp]T is the uncertain parameter vector in a ceramic production chain, the optimal solution of Equation (19) (using the simplex method) can be written as Equation (20) for a given value of q. The corresponding optimal basis B is a set of l variables, and the optimal basis matrix AB can be obtained by taking only those columns of A whose corresponding variables are in B. The variables in B are the basic variables, while the others are called non-basic (their set is denoted as N). It is worth noting that the optimal solution in Equation (20) is degenerate because many bases are associated with it.