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Adaptive differential evolution algorithm for multiobjective optimization problems

APPLIED MATHEMATICS AND COMPUTATION 2008年第1-2期201卷 431-440页

作者： Qian, Weiyi Li, Ajun Bohai Univ Dept Math Jinzhou 121000 Liaoning Peoples R China

In this paper, a new adaptive differential evolution algorithm ( ADEA) is proposed for multiobjective optimization problems. In ADEA, the variable parameter F based on the number of the current Pareto-front and the diversity of the current solutions is given for adjusting search size in every generation to find Pareto solutions in mutation operator, and the select operator combines the advantages of DE with the mechanisms of Pareto-based ranking and crowding distance sorting. ADEA is implemented on five classical multiobjective problems, the results illustrate that ADEA efficiently achieves two goals of multiobjective optimization problems:find the solutions converge to the true Pareto-front and uniform spread along the front. (c) 2008 Elsevier Inc. All rights reserved.

关键词： multiobjective optimization problems differential evolution algorithm adaptive select operator

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A New Hybrid Metaheuristic Algorithm for multiobjective optimization problems

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2020年第1期13卷 920-940页

作者： Farag, M. A. El-Shorbagy, M. A. Mousa, A. A. El-Desoky, I. M. Menoufia Univ Fac Engn Dept Basic Engn Sci Shibin Al Kawm Egypt Prince Sattam Bin Abdulaziz Univ Coll Sci & Humanities Al Kharj Dept Math Al Kharj 11942 Saudi Arabia Taif Univ Fac Sci Math & Stat Dept At Taif Saudi Arabia

The elitist nondominated sorting genetic algorithm (NSGA-II) is hybridized with the sine-cos le algorithm (SCA) in this paper to solve multiobjective optimization problems. The proposed hybrid algorithm is named nondominated sorting sine-cosine genetic algorithm (NS-SCGA). The main idea of this algorithm is the following: NS-SCGA integrates the merits of exploitation capability of NSGA-II and exploration capability of SCA for a better search ability and speeds up the searching process. 'Elie performance of NS-SCGA is tested on the set of benchmark functions provided for CEC09. The NS-SCGA results are compared with other recently developed multiobjective algorithms in terms of convergence, spacing, and spread of the obtained nondominated solutions to the true Pareto front. The statistical analysis of the results obtained is performed by nonparametric Friedman and Wilcoxon signed-rank tests. The results prove that NS-SCGA is superior to or competitive with other multiobjective optimization algorithms considered in the comparison. Furthermore, the economic emission dispatch problem (EEDP) is solved by NS-SCGA. operating cost (fuel cost) and pollutant emission of the standard IEEE 30-bus network with six generating units are minimized simultaneously by the NS-SCGA considering the losses. The results show the superiority of NS-SCGA and confirm its ability in solving EEDE TOESIS technique is applied to choose the best compromise solution from the obtained Pareto-optimal solutions of EEDP according to the decision maker's preference. (C) 2020 The Authors. Publishedby Atlantis Press SARL.

关键词： Sine-cosine algorithm Nondominated sorting genetic algorithm multiobjective optimization problems The economic emission dispatch problem TOPSIS

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On constraint qualification in multiobjective optimization problems: Semidifferentiable case

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JOURNAL OF optimization THEORY AND APPLICATIONS 1999年第2期100卷 417-433页

作者： Preda, V Chitescu, I Univ Bucharest Fac Math Bucharest Romania

Some versions of constraint qualifications in the semidifferentiable case are considered for a multiobjective optimization problem with inequality constraints. A Maeda-type constraint qualification is given and Kuhn-Tucker-type necessary conditions for efficiency are obtained. In addition, some conditions that ensure the Maeda-type constraint qualification are stated.

关键词： multiobjective optimization problems constraint qualifications efficiency properly efficient solutions

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Weakly and properly nonessential objectives in multiobjective optimization problems

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OPERATIONS RESEARCH LETTERS 2008年第5期36卷 647-650页

作者： Malinowska, Agnieszka B. Bialystok Tech Univ Fac Comp Sci PL-15351 Bialystok Poland

In this work we characterize objective functions which do not change the set of efficient solutions (weakly efficient solutions, properly efficient solutions). Necessary and sufficient conditions for an objective function to be weakly nonessential (properly nonessential) are presented. We establish relations between weakly nonessential, properly nonessential and nonessential functions. (c) 2008 Elsevier B.V. All rights reserved.

关键词： multiobjective optimization problems Efficient (Pareto optimal) solutions Weakly efficient solutions Properly efficient solutions Nonessential objective functions

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Generalized trade-off directions in multiobjective optimization problems

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APPLIED MATHEMATICS LETTERS 1997年第1期10卷 119-122页

作者： Lee, GM Nakayama, H KONAN UNIV DEPT APPL MATHKOBE 658JAPAN

In this brief paper, we define the generalized trade-off directions for a multiobjective optimization problem (MP), by using the contingent cone, and characterize the set of generalized trade-off directions for the pr... 详细信息

关键词： generalized trade-off directions multiobjective optimization problems Pareto solutions contingent cones contingent derivatives

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Augmented Lagrangian cone method for multiobjective optimization problems with an application to an optimal control problem

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optimization AND ENGINEERING 2023年第3期24卷 1633-1665页

作者： Upadhayay, Ashutosh Ghosh, Debdas Ansari, Qamrul Hasan Jauny Banaras Hindu Univ Dept Math Sci Indian Inst Technol Varanasi 221005 Uttar Pradesh India Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India

This paper proposes an augmented Lagrangian method to compute Pareto optimal sets of multiobjective optimization problems. The method neither requires a prior information about the locations of the Pareto surface nor the convexity of the objective and constraint functions. To generate Pareto optimal points, we convert a multiobjective optimization problem into a set of direction-based parametric scalar optimization problems by using the cone method. Subsequently, we apply the augmented Lagrangian method to the direction-based parametric problems to transform them into unconstrained problems. Transformed augmented Lagrangian subproblems are then solved by the steepest descent method with a max-type nonmonotone line search method. A step-wise algorithmic implementation of the proposed method is provided. We discuss the convergence property of the proposed algorithm with regard to a feasibility measure and the global Pareto optimality. Under a few common assumptions, we prove that any subsequential limit of the sequence generated by the proposed algorithm is the global minimizer of an infeasibility measure corresponding to each direction. In addition, the obtained limit is found to be a global minimizer when the feasible region of the given multiobjective optimization problem is nonempty. It is observed that the solution of the proposed method is not affected by variable scaling. The efficiency of the proposed algorithm is shown by solving standard test problems. As a realistic application, we employ the proposed method on a deterministic unemployment optimal control model with the implementation of government policies to create employment and vacancies as their controls.

关键词： Augmented Lagrangian method Pareto set Cone method multiobjective optimization problems Unemployment Mathematical model Optimal control

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Strong Kuhn-Tucker conditions and constraint qualifications in locally Lipschitz multiobjective optimization problems

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TOP 2009年第2期17卷 288-304页

作者： Giorgi, G. Jimenez, B. Novo, V. Univ Nacl Educ Distancia Dept Matemat Aplicada ETSI Ind E-28040 Madrid Spain Univ Pavia Dipartimento Ric Aziendali I-27100 Pavia Italy

We consider a Pareto multiobjective optimization problem with a feasible set defined by inequality and equality constraints and a set constraint, where the objective and inequality constraints are locally Lipschitz, and the equality constraints are Fr,chet differentiable. We study several constraint qualifications in the line of Maeda (J. Optim. Theory Appl. 80: 483-500, 1994) and, under the weakest ones, we establish strong Kuhn-Tucker necessary optimality conditions in terms of Clarke subdifferentials so that the multipliers of the objective functions are all positive.

关键词： multiobjective optimization problems Constraint qualification Necessary conditions for Pareto minimum Lagrange multipliers Clarke subdifferential

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Scalarizations for Approximate Quasi Efficient Solutions in multiobjective optimization problems

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Journal of the Operations Research Society of China 2015年第1期3卷 69-80页

作者： Rui-Xue Yue Ying Gao Department of Mathematics Chongqing Normal UniversityChongqing 400047China

In this paper,by reviewing two standard scalarization techniques,a new necessary and sufficient condition for characterizing(ε,.ε)-quasi(weakly)efficient solutions of multiobjective optimization problems is *** proposed procedure for the computation of(ε,.ε)-quasi efficient solutions is *** that all of the provided results are established without any convexity assumptions on the problem under *** our results extend several corresponding results in multiobjective optimization.

关键词： multiobjective optimization problems Approximate quasi efficeint solutions Nonlinear scalarizations

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MOP2P: Peer-to-Peer Platform applied to multiobjective optimization problems 42

MOP2P: Peer-to-Peer Platform applied to Multiobjective Optim...

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42nd Latin American Computing Conference (CLEI)

作者： Gonzalez, Fabio Paciello, Julio Univ Nacl Asuncion Fac Politecn Asuncion Paraguay

ISBN: (纸本)9781509016334

The resolution of multiobjective optimization problems (MOP) tipically requires a high demand of computational resources such as CPU and memory, finding candidate solutions at an acceptable response time, and with sufficient quality given a set of performance evaluation metrics. This paper presents a platform (denominated MOP2P) that allows the distributed execution of metaheuristic based algorithms for solving MOP using computers connected in a network in order to handle more computing power according to current demand. MOP2P implements Peer-to-Peer concepts to minimize the configuration effort and the management of a collection of computers. Also, a dynamic resource control mechanism is presented as a way to adapt the resource utilization levels intended for the optimization tasks executed on the different computers. Experimentally it was observed that the platform leverages the computing power available including desirable characteristics such as scalability, fault tolerance and non-intrusive use of computational resources.

关键词： multiobjective optimization problems Metaheuristics Artificial Intelligence Grid Computing Peer-to-Peer Systems Non-intrusive Computing

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Competitive Coevolutionary Genetic Algorithms for multiobjective optimization problems

Competitive Coevolutionary Genetic Algorithms for Multiobjec...

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International Conference on Artificial Intelligence and Computational Intelligence

作者： Liu, Jian-guo Congqing Bussiness & Technol Univ Coll Applicat Technol Chongqing Peoples R China

ISBN: (纸本)9780769538167

Enlightened by the knowledge of ecological environment and population competition, we proposed a Competitive Coevolutionary Genetic Algorithm (CCGA) based on ecological population competition mode for multiobjective optimization problems. In the algorithms, each objective corresponds to a population. At each generation, these populations compete among themselves. An ecological population density competition equation is used for reference to describe the relation between multiple objectives and to direct the adjustment over the relation at individual and population levels. The proposed approach store the Pareto optimal point obtained along the evolutionary process into external set, enforcing a more uniform distribution of such vectors along the Pareto front. The proposed approach was validated using typical test function taken from the specialized literature. Our comparative study showed that the proposed approach is competitive with respect three other algorithms that are representative of the state-of-the-art in evolutionary multiobjective optimization.

关键词： competitive coevolutionary genetic algorithm Pareto optimal point multiobjective optimization problems

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