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objective functions AND MODELS OF CORPORATE OPTIMIZATION

QUARTERLY JOURNAL OF ECONOMICS 1961年第3期75卷 345-375页

作者： SHUBIK, M Yale University

This article focuses on the objective functions and models of corporate optimization. The problems of formulation of objectives have given rise to new terminology. For example, the phrase 'objective function' has made its way into the literature of economics, operations research and management science by the route of linear programming. In a linear program the objective function is the expression to be maximized or minimized. The typical programming problem is one in which the prices of the final products are given, the capacity limitations on production are specified, technology is assumed to be known and the goal is to maximize a revenue or equivalently, minimize a cost subject to constraints. Unfortunately in problems involving more than a few aspects of the meaning of a complex organization such as the modern firm, it becomes most difficult to describe the objective function. As the complexity of the organization grows the so-called objective function becomes more and more subjective and less quantitative as multiple goals, social and political goals and uncertainty and ill-perception of the environment are taken into account.

关键词： Corporations Economic theory Economic models Game theory Revenue Economic policy Oligopolies Shareholders objective functions

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Uncertainty analysis of coupling multiple hydrologic models and multiple objective functions in Han River, China

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WATER SCIENCE AND TECHNOLOGY 2013年第3期68卷 506-513页

作者： Dong, Leihua Xiong, Lihua Zheng, Yanfeng Wuhan Univ State Key Lab Water Resources & Hydropower Engn S Wuhan 430072 Peoples R China

Three different hydrological models are chosen to simulate rainfall-runoff relationships under each of three objective functions including mean squared errors of squared transformed flows, squared root transformed flows and logarithmic transformed flows;thus nine individual models are constructed. By weighted averaging over these nine models, the method of Bayesian model averaging (BMA) was used to provide both the mean value and the uncertainty intervals of flow prediction. Three kinds of uncertainty information can be generated: the uncertainty of individual member model's predictions;the total uncertainty of BMA mean prediction;the between-model and within-model uncertainties in the BMA scheme. Based on the estimated results in this study, the coupling of multiple models with multiple objective functions in general offers better results for both the mean prediction and the uncertainty intervals for the runoffs in a selected basin in Han River, China, than the individual models.

关键词： between-model uncertainty hydrological models model combination objective functions uncertainty analysis

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Comparative assessment of GPGPU technologies to accelerate objective functions: A case study on parsimony

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JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 2019年 126卷 67-81页

作者： Santander-Jimenez, Sergio Vega-Rodriguez, Miguel A. Vicente-Viola, Jorge Sousa, Leonel Univ Lisbon Inst Engn Sistemas & Comp Invest & Desenvolviment Inst Super Tecn P-1000029 Lisbon Portugal Univ Extremadura Dept Comp & Commun Technol Escuela Politecn Campus Univ S-N Caceres 10003 Spain

objective functions provide measurements of solution quality that represent the core calculations required to tackle NP-hard optimization problems. Since their complexity keeps growing with the introduction of more realistic data, research efforts have turned their interest into the proposal of efficient objective function implementations that take advantage of potential parallelism. This work explores GPGPU technologies to accelerate objective functions, considering as a case study the parallelization of phylogenetic parsimony calculations from DNA data. We undertake the comparative evaluation of different GPU programming models and architectures, highlighting the benefits and drawbacks of each approach through experimentation on six real-world biological datasets. Experimental results shed light on the strong relationship between the characteristics of the input data and the effective utilization of GPU resources. Furthermore, comparisons with other parallel architectures and methods point out how current and future optimization scenarios can benefit from the use of accurate, efficient GPU approaches. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Parallel algorithms GPGPU objective functions Bioinformatics

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An approach for minimizing the number of objective functions in the optimization of vehicle suspension systems

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JOURNAL OF SOUND AND VIBRATION 2018年 435卷 149-169页

作者： Papaioannou, Georgios Koulocheris, Dimitrios Natl Tech Univ Athens Sch Mech Engn Vehicles Lab Zografou Campus 9 Athens 15780 Greece

In recent studies, the suspension parameters of a vehicle model are estimated using multi-objective optimization procedures with genetic algorithms in order to overcome the well known conflict of ride comfort and road holding. However, the researchers sometimes end up using more than one objective function representing the same requirement, growing the dimension of the optimization problem. Thus, the optimization procedure becomes very quickly ineffective and the merits of the GAs are put aside because of the increased computational time of the simulations. This work focuses on indicating that the inconsiderate selection of objective functions noticed in the literature, in order to obtain the optimum solution of a suspension design, doesn't lead to extra quality in the solution. In this direction, six objective functions widely used in the literature depicting the ride comfort and the road holding, were selected. In our experiments, various SOO approaches (Part A) and two MOO approaches (Part B and C) were selected, where Part B is proposing a novel way of handling the optimization objectives. All the MOO approaches presented combine GAs for obtaining the Pareto set and a sorting algorithm for pointing out their optimum solution among the Pareto alternatives. The optimum solutions of the two approaches are presented and compared in terms of convergence and computational time, concluding to the fact that the economy in the objective functions could provide not only a better solution but also could save significant computational time. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Vehicle suspensions Multi objective optimization Ride comfort Road holding objective functions

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A study on formulation of objective functions for determining material models

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INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES 2008年第2期50卷 193-204页

作者： Cao, J. Lin, J. Univ Birmingham Sch Engn Dept Mech & Mfg Engn Birmingham B15 2TT W Midlands England

Optimisation techniques have been developed and used to determine material constants arising in unified creep/viscoplastic constitutive equations based on experimental data. objective functions (OF) have been formulated as pointers to the quality of fit between the equations and experimental data and a set of criteria is presented to assess the suitability of the objective functions. Convergence features of two existing objective functions are analysed. The problems of using these objective functions are studied. To overcome difficulties arising in the existence of different scales of individual sub-objectives, a novel error definition is introduced, which has a natural unitless form and can provide a measure for "true" error. A novel weighting technique is introduced, which can also be chosen automatically to compensate the loss of credits in individual data points and curves. Using these techniques, a novel objective function is formulated, which meets the set criteria. The objective function, together with an evolutionary programming (EP) solver, are employed to determine material constants in three sets of unified constitutive equations which are formulated to match experimental data. The convergent features of the objective functions are compared and analysed. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： optimisation constitutive equations materials modelling objective functions evolutionary algorithms

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Estimating groundwater recharge rates in the Upper Awash Basin, Ethiopia under different combinations of model complexity and objective functions

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HYDROLOGY RESEARCH 2024年第3期55卷 263-279页

作者： Redda, Muauz Amare Birhanu, Behailu Hussien, Bediru Addis Ababa Univ Ethiopian Inst Water Resource Addis Ababa Ethiopia Addis Ababa Univ Sch Earth Sci Addis Ababa Ethiopia Addis Ababa Sci & Technol Univ Sch Earth Sci & Engn Addis Ababa Ethiopia

Reliable quantification of groundwater recharge rate is crucial for the sustainable utilization of groundwater resources. However, little information is documented about the uncertainty associated with recharge rate estimation from the different combinations of model complexity and objective function perspectives. Therefore, this study aims to (i) analyze the sensitivity of the model parameters under different combinations of model complexities and objective functions and (ii) estimate the groundwater recharge rate in the Hombele catchment, Upper Awash Basin, Ethiopia, for different combinations of objective functions and model complexities. The effect of these model complexities in estimating groundwater recharge rate and parametrizing model parameters was quantified for the period 1986-2013. A total of 10 combinations of model complexities and objective functions were used for the analysis. The Kling-Gupta efficiency (Nash-Sutcliffe efficiency) values for calibration, validation, and the whole period are 0.89 (0.80), 0.80 (0.73), and 0.87 (0.77), respectively, when a semi-distributed HBV-light model was used. For all objective functions, we found that the average annual recharge rate of the study catchment ranges from 185.9 to 280.5 mm when the HBV-light model was considered as a semi-distributed model. In contrast, the average annual recharge rate ranges from 185.3 to 321.7 mm when applying the HBV-light model as a lumped model.

关键词： groundwater recharge HBV-light model model complexity objective functions

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On an open problem related to the strict local minima of multilinear objective functions

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1997年第11期42卷 1564-1566页

作者： Liang, XB Wu, LD Department of Computer Science Fudan University Shanghai China

This paper gives a combinatorial proof of a ''yes'' answer to an open question presented in [1], stated as follows: ''given a multilinear polynomial E(x): [0, 1](n) --> R, is it true that E-b(x) = E(x) - b(t)z has a strict local minimum over the discrete set {0,1}(n) for almost all b of sufficiently small norm?'' The given combinatorial proof is completed directly by providing a sufficient condition for a conjecture on the strict local minima of multilinear polynomials also postulated in [1] to hold. In addition, a simple counterexample is presented to demonstrate that the conjecture may be not true if the provided sufficient condition is not satisfied.

关键词： analog neural networks discrete optimization problems multilinear polynomials objective functions

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APPLICATION OF PROGRAMS WITH MAXIMIN objective functions TO PROBLEMS OF OPTIMAL RESOURCE-ALLOCATION

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OPERATIONS RESEARCH 1974年第4期22卷 802-807页

作者： KAPLAN, S NYU NEW YORKNY 10003

A mathematical program with a maximin objective function is defined as an optimization problem of the following type: Maxz = mini cixi, subject to AX = b, X ≧ 0. Although the ci can be in the interval (? ∞, ∞), the... 详细信息

A mathematical program with a maximin objective function is defined as an optimization problem of the following type: Maxz = min_i c_ix_i, subject to AX = b, X ≧ 0. Although the c_i can be in the interval (? ∞, ∞), the paper discusses the more common practical case where all c_i ≧ 0. It shows that problems of this type arise in a variety of applications where it is required to maximize a production function of the “fixed proportion” type subject to a set of linear constraints. Although it is well known that the solution to this type of problem can be found by linear programming, this paper shows that, if the existence of a certain condition can be demonstrated, then a simplified method can be used to determine the optimum solution. Many problems of practical interest can be solved by this simplified method; an example involving the readiness of a ship is presented.

关键词： objective functions Maximin Linear programming Food security Production functions Military vehicles Vehicle performance Ammunition

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Evaluation of Different objective functions Used in the SUFI-2 Calibration Process of SWAT-CUP on Water Balance Analysis: A Case Study of the Pursat River Basin, Cambodia

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WATER 2020年第10期12卷 2901-2901页

作者： Sao, Davy Kato, Tasuku Tu, Le Hoang Thouk, Panha Fitriyah, Atiqotun Oeurng, Chantha Tokyo Univ Agr & Technol Dept Agr & Environm Engn United Grad Sch Agr Sci 3-8-5 Saiwai Cho Fuchu Tokyo 1838538 Japan Tokyo Univ Agr & Technol Inst Agr 3-8-5 Saiwai Cho Fuchu Tokyo 1838538 Japan Nong Lam Univ Res Ctr Climate Change Ho Chi Minh City 700000 Vietnam Tokyo Univ Agr & Technol Dept Int Environm & Agr Sci 3-8-5 Saiwai Cho Fuchu Tokyo 1838538 Japan Tokyo Univ Agr & Technol Inst Global Innovat Res 3-8-5 Saiwai Cho Fuchu Tokyo 1838538 Japan Inst Technol Cambodia Fac Hydrol & Water Resources Engn POB 86Russian Confederat Blvd Phnom Penh 12156 Cambodia

Many calibration techniques have been developed for the Soil and Water Assessment Tool (SWAT). Among them, the SWAT calibration and uncertainty program (SWAT-CUP) with sequential uncertainty fitting 2 (SUFI-2) algorithm is widely used and several objective functions have been implemented in its calibration process. In this study, eight different objective functions were used in a calibration of stream flow of the Pursat River Basin of Cambodia, a tropical monsoon and forested watershed, to examine their influences on the calibration results, parameter optimizations, and water resources estimations. As results, many objective functions performed better than satisfactory in calibrating the SWAT model. However, different objective functions defined different fitted values and sensitivity rank of the calibrated parameters, except Nash-Sutcliffe efficiency (NSE) and ratio of standard deviation of observations to root mean square error (RSR) which are equivalent and produced quite identical simulation results including parameter sensitivity and fitted parameter values, leading to the same water balance components and water yields estimations. As they generated reasonable fitted parameter values, either NSE or RSR gave better estimation results of annual average water yield and other water balance components such as annual average evapotranspiration, groundwater flow, surface runoff, and lateral flow according to the characteristics of the river basin and the results and data of previous studies. Moreover, either of them was also better in calibrating base flow, falling limb, and overall the entire flow phases of the hydrograph in this area.

关键词： SWAT model SUFI-2 objective functions calibration water balance components

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Classification-based objective functions

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MACHINE LEARNING 2006年第2期63卷 183-205页

作者： Rimer, M Martinez, T Brigham Young Univ Dept Comp Sci Provo UT 84602 USA

Backpropagation, similar to most learning algorithms that can form complex decision Surfaces, is prone to overfitting. This work presents classification-based objective functions, an approach to training artificial neural networks on classification problems. Classification-based learning attempts to guide the network directly to correct pattern classification rather than using common error minimization heuristics, such as sum-squared error (SSE) and cross-entropy (CE), that do not explicitly minimize classification error. CBI is presented here as a novel objective function for learning classification problems. It seeks to directly minimize classification error by backpropagating error only on misclassified patterns from culprit Output nodes. CB1 discourages weight saturation and overfitting and achieves higher accuracy on classification problems than optimizing SSE or CE. Experiments on a large OCR data set have shown CB1 to significantly increase generalization accuracy over SSE or CE optimization, from 97.86% and 98.10%, respectively, to 99.11%. Comparable results are achieved over several data sets from the UC Irvine Machine Learning Database Repository, with an average increase in accuracy from 90.7% and 91.3% using optimized SSE and CE networks, respectively, to 92.1% for CB1. Analysis indicates that CBI performs a fundamentally different search of the feature space than optimizing SSE or CE and produces significantly different solutions.

关键词： neural networks backpropagation classification objective functions

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