Scalarization in vector optimization is often closely connected to the minimization of Gerstewitz functionals. In this paper, the minimizer sets of Gerstewitz functionals are investigated. Conditions are given under w...
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Scalarization in vector optimization is often closely connected to the minimization of Gerstewitz functionals. In this paper, the minimizer sets of Gerstewitz functionals are investigated. Conditions are given under which such a set is nonempty and compact. Interdependencies between solutions of problems with different parameters or with different feasible point sets are shown. Consequences for the parameter control in scalarization methods are proved. It is pointed out that the minimization of Gerstewitz functionals is equivalent to an optimization problem which generalizes the scalarization by Pascoletti and Serafini. The results contain statements about minimizers of certain Minkowski functionals and norms. Some existence results for solutions of vector optimization problems are derived.
The Lagrangian globalization (LG) method for non-linear equation-solving proposed in [10] is developed through theoretical analysis, the formulation of a particular LG algorithm, and a numerical illustration. New meri...
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The Lagrangian globalization (LG) method for non-linear equation-solving proposed in [10] is developed through theoretical analysis, the formulation of a particular LG algorithm, and a numerical illustration. New merit functions (termed detour potentials) for non-linear equation-solving, which broaden the LG concept, are also defined.
The main aim of this paper is to develop an approach to solving multi-objective bi-matrix games with intuitionistic fuzzy (IF) goals, which are called IF multi-objective bi-matrix games for short. In this paper, the s...
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The main aim of this paper is to develop an approach to solving multi-objective bi-matrix games with intuitionistic fuzzy (IF) goals, which are called IF multi-objective bi-matrix games for short. In this paper, the solution approach for such a game is presented by introducing an aspiration level approach, and IF non-linear programming problem is constructed to find the optimal solution for such types of multi-objective bi-matrix games. Furthermore, it is shown that this multi-objective bi-matrix game with IF goals is an extension of the multi-objective bi-matrix game with fuzzy goals. Finally, a numerical example is incorporated to demonstrate the implementation and applicability process of the proposed approach.
In the pharmaceutical industry, the main components in determining physician-detailing plans are strategic physician-population segmentation, data driven sales-response functions of physician prescribing behavior, and...
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In the pharmaceutical industry, the main components in determining physician-detailing plans are strategic physician-population segmentation, data driven sales-response functions of physician prescribing behavior, and an optimization algorithm for sales call allocation. Using data mining technology in neural networks coupled with non-linear programming, this paper proposes an expert system to effectively allocate sales-force resources for single-product physician-detailing planning. The result shows that this adaptive and easy-to-implement system helps decision makers to outperform the standard industry practice(1) by 10% in profit gain. (C) 2003 Elsevier Ltd. All rights reserved.
In the paper we design a super genetic hybrid algorithm (SuperGHA), an integrated optimization system for simultaneous parametric search and nonlinear optimization. The parametric search machine is implemented as a ge...
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In the paper we design a super genetic hybrid algorithm (SuperGHA), an integrated optimization system for simultaneous parametric search and nonlinear optimization. The parametric search machine is implemented as a genetic superstructure, producing tentative parameter vectors that control the ultimate optimization process. The family of parameter vectors evolves through ordinary genetic operators aimed at producing the best possible parameterization for the underlying optimization problem. In comparison to traditional genetic algorithms, the integrated superstructure involves a twofold ordering of the population of Parameter vectors. The first sorting key is provided by the objective function of the optimization problem at issue. The second key is given by the total mesh time absorbed by the parametric setting. In consequence, SuperGHA is geared at solving an optimization problem, using the best feasible parameterization in terms of optimality and time absorbance. The algorithm combines features from classical nonlinear optimization methodology and evolutionary computation utilizing a powerful accelerator technique. The constrained problem can be cast into multiple representations, supporting the integration of different mathematical programming environments. We show by extensive Monte Carlo simulations that SuperGHA extracts suitable parameter vectors for fast solution of complicated nonlinearprogramming problems.
Simplicial decomposition is an important form of decomposition for large non-linear programming problems with linear constraints. Von Hohenbalken has shown that if the number of retained extreme points is n + 1, where...
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Simplicial decomposition is an important form of decomposition for large non-linear programming problems with linear constraints. Von Hohenbalken has shown that if the number of retained extreme points is n + 1, where n is the number of variables in the problem, the method will reach an optimal simplex after a finite number of master problems have been solved (i.e., after a finite number of major cycles). However, on many practical problems it is infeasible to allocate computer memory for n + 1 extreme points. In this paper, we present a version of simplicial decomposition where the number of retained extreme points is restricted to r , 1 ⩽ r ⩽ n + 1, and prove that if r is sufficiently large, an optimal simplex will be reached in a finite number of major cycles. This result insures rapid convergence when r is properly chosen and the decomposition is implemented using a second order method to solve the master problem.
The cost associated with a direct methanol fuel cell (DMFC) is the main drawback of its commercialization. To address this issue, the main objective of this study is to minimize the cost of micro DMFCs for portable ap...
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The cost associated with a direct methanol fuel cell (DMFC) is the main drawback of its commercialization. To address this issue, the main objective of this study is to minimize the cost of micro DMFCs for portable applications. The model was coupled with a nonlinear constrained optimization to determine an optimum design of the DMFC with respect to the design and geometrical parameters of the anode and cathode, including methanol concentration, power density, catalyst loading, etc. optimization was performed using Matlab to minimize the difference between the power input required and the power optimum via non-linear programming (NLP). The optimum characteristics of DMFC were solved by using an NLP simulation. The outputs were verified by both experimental and modeling results. These dynamic optimization results provided an optimum design parameters for the physical properties of DMFC required to generate the portable application. Lastly, a cost analysis was also considered in this study. (c) 2009 Published by Elsevier Ltd on behalf of Professor T. Neiat Veziroglu.
This paper is the second one of the two papers entitled "Weighted Superposition Attraction (WSA) Algorithm", which is about the performance evaluation of the WSA algorithm in solving the constrained global o...
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This paper is the second one of the two papers entitled "Weighted Superposition Attraction (WSA) Algorithm", which is about the performance evaluation of the WSA algorithm in solving the constrained global optimization problems. For this purpose, the well-known mechanical design optimization problems, design of a tension/compression coil spring, design of a pressure vessel, design of a welded beam and design of a speed reducer, are selected as test problems. Since all these problems were formulated as constrained global optimization problems, WSA algorithm requires a constraint handling method for tackling them. For this purpose we have selected 6 formerly developed constraint handling methods for adapting into WSA algorithm and analyze the effect of the used constraint handling method on the performance of the WSA algorithm. In other words, we have the aim of producing concluding remarks over the performance and robustness of the WSA algorithm through a set of computational study in solving the constrained global optimization problems. Computational study indicates the robustness and the effectiveness of the WSA in terms of obtained results, reached level of convergence and the capability of coping with the problems of premature convergence, trapping in a local optima and stagnation. (C) 2015 Elsevier B.V. All rights reserved.
The primary aim of this research is to investigate the impact of dams constructed in Turkey on the operational policy of the Mosul Dam. The study employs non-linear programming to establish an optimization model for t...
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The primary aim of this research is to investigate the impact of dams constructed in Turkey on the operational policy of the Mosul Dam. The study employs non-linear programming to establish an optimization model for the Mosul Dam reservoir, with the goal of maximizing hydropower generation and determining the optimal operation policy. Statistical tests, including Kendall's Rank Correlation Test and the Standard Normal Homogeneity Test, were used to analyze the direction and identify change points in the time-series. The results indicate a significant decrease in flow during March, April, and May due to dam construction in Turkey, with quantities ranging from 37.8 to 79 MCM/year for the total period. Conversely, there was a significant increase in flow during August and September due to hydroelectric power generation in the summer, with quantities of 20.6 and 15.5 MCM/year, respectively. Additionally, applying the non-linear optimization model to the last 2 years (2019-2020) and (2020-2021) revealed an increase in hydroelectric power production (220 and 180 MW, respectively) compared to actual hydropower generated (2067 and 2155 MW, respectively), as management did not realize the impact of Ilisu Dam on inflows. At the same time, the hydropower created during these 2 years fell short of the average hydropower generated throughout the entire period, which was 3367 MW. Also, the strength and efficiency of the non-linear optimization model and the possibility of employing it in identifying the operational policy when inflow is relatively low were proved.
In this paper, we propose an algorithm for solving non-linearnon-convex programming problems, which is based on the interior point approach. Main theoretical results concern direction determination and step-length se...
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In this paper, we propose an algorithm for solving non-linearnon-convex programming problems, which is based on the interior point approach. Main theoretical results concern direction determination and step-length selection. We split inequality constraints into active and inactive to overcome problems with stability. Inactive constraints are eliminated directly while active constraints are used to define symmetric indefinite linear system. Inexact solution of this system is obtained iteratively using indefinitely preconditioned conjugate gradient method. Theorems confirming efficiency of several indefinite preconditioners are proved. Furthermore, new merit function is defined, which includes effect of possible regularization. This regularization can be used to overcome problems with near linear dependence of active constraints. The algorithm was implemented in the interactive system for universal functional optimization UFO. Results of extensive numerical experiments are reported. Copyright (C) 2004 John Wiley Sons, Ltd.
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