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On approximate starshapedness in multiobjective optimization

optimization METHODS & SOFTWARE 2016年第2期31卷 290-304页

作者： Al-Shamary, Bader Mishra, S. K. Laha, Vivek Kuwait Univ Fac Sci Dept Math POB 5969 Safat 13060 Kuwait Banaras Hindu Univ Fac Sci Dept Math Varanasi 221005 Uttar Pradesh India

In this paper, we give the vector versions of the concepts of approximate starshapedness, equi-subdifferentiability and pseudo-equi-subdifferentiability and establish relationships among approximate vector starshapedness, vector-equi-subdifferentiability and vector-pseudo-equi-subdifferentiability. We extend the concept of epsilon-quasi-efficient solutions in the context of multiobjective optimization problems involving approximately starshaped functions and use approximate vector variational inequalities of Stampacchia and Minty type in terms of Frechet subdifferentials to characterize approximate efficient solutions.

关键词： multiobjective optimization problems approximate starshapedness Frechet subdifferentials vector variational inequalities approximate efficiency equi-subdifferentiability 90C26 90C29 90C30 49J40 49J50 49J52

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Preference clustering-based mediating group decision-making (PCM-GDM) method for infrastructure asset management

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EXPERT SYSTEMS WITH APPLICATIONS 2017年 83卷 206-214页

作者： Yoon, Yoojung Hastak, Makarand Cho, Kyuman West Virginia Univ Dept Civil & Environm Engn Morgantown WV 26506 USA Purdue Univ Div Construct Engn & Management W Lafayette IN 47907 USA Chosun Univ Dept Architectural Engn 309 Pilmun Daero Gwangju 61452 South Korea

The problem-solving decision-making process often requires involvement of a group of individuals who have differing interests and conflicting multiple evaluation criteria. Therefore, the greatest concern in multiobjective group decision-making problems is how to arrive at a best decision that is agreeable to all the members of the group. Many previous studies focused on handling this concern based on decision rules, such as the consensus or ranking selection approaches. Although many contributions to the literature were made by past studies on this issue, disagreement remains on finding an effective way to address the subjectivity issue in group decision-making. This paper introduces a new approach called the preference clustering-based mediating group decision-making (PCM-GDM) method for minimizing the subjectivity issue. The PCM-GDM method basically employs two concepts: (1) clustering the preferences of the group members in a decision and (2) utilizing a mediating agent as a final decision-making tool. The new approach was applied to a case study of sample concrete bridge decks in the state of Indiana. The results of this study confirm that the proposed approach can significantly improve the multicriteria group decision-making results by providing a way to exclude biased judgments by decision-makers that can interfere with the development of one best alternative. The proposed approach advanced the reliability of the conventional decision-making knowledge, which is dependent on a consensus or the ranking of approaches by human experts to reach one solution. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Group decision-making multiobjective optimization problems Mediating agent Infrastructure asset management

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multiobjective environmental adaptation method for solving environmental/economic dispatch problem

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EVOLUTIONARY INTELLIGENCE 2019年第2期12卷 305-319页

作者： Singh, Tribhuvan Mishra, Krishn Kumar Ranvijay Motilal Nehru Natl Inst Technol Allahabad Comp Sci & Engn Dept Allahabad Uttar Pradesh India

Environmental adaptation method is one of the evolutionary algorithms for solving single objective optimization problems. Although the algorithm converges very fast and produces diversified solutions, there are three weaknesses in it. In this paper, first we have given the solutions to resolve these weaknesses and then we have extended the modified method to deal with multiple conflicting objectives simultaneously. A permutation-based multiobjective environmental adaptation method (pMOEAM) has been suggested to solve the environmental/economic dispatch (EED) problem of the power system. In this paper, total generation cost and environmental emission have been taken as two objectives that need to be minimized simultaneously while meeting the load demand under equality and inequality constraints. Three test systems are considered to evaluate the performance of the proposed algorithm. The performance of the suggested algorithm is compared against five multiobjective algorithms. Extensive experimental results demonstrated that the pMOEAM method can obtain effective and feasible solutions for EED problem.

关键词： Environmental/economic dispatch problem Environmental adaptation method multiobjective evolutionary algorithms multiobjective optimization problems

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On M-Stationary Conditions and Duality for multiobjective Mathematical Programs with Vanishing Constraints

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BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY 2022年第3期45卷 1315-1341页

作者： Hassan, Mohd Maurya, J. K. Mishra, S. K. Banaras Hindu Univ Inst Sci Dept Math Varanasi 221005 Uttar Pradesh India Kashi Naresh Govt Postgrad Coll Dept Math Bhadohi 221304 Uttar Pradesh India

Mathematical programs with vanishing constraints are the optimization problems that do not satisfy most of the constraint qualifications due to nonconvex feasible region. Hence, some weaker first-order conditions like M-stationary come into existence. In this paper, we establish necessary and sufficient M-stationary conditions for multiobjective mathematical problems with vanishing constraints. We formulate Wolfe and Mond-Weir type dual models for the treated problem and propose weak, strong and strict converse duality results for Wolfe and Mond-Wier dual models. Further, we provide some examples in the support of our theory.

关键词： Vanishing constraints multiobjective optimization problems Optimality conditions Duality Constraint qualifications

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Structure and Weak Sharp Minimum of the Pareto Solution Set for Piecewise Linear multiobjective optimization

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JOURNAL OF optimization THEORY AND APPLICATIONS 2010年第1期147卷 113-124页

作者： Yang, X. Q. Yen, N. D. Hong Kong Polytech Univ Dept Appl Math Hong Kong Hong Kong Peoples R China Vietnamese Acad Sci & Technol Inst Math Hanoi Vietnam

In this paper, the Pareto solution set of a piecewise linear multiobjective optimization problem in a normed space is shown to be the union of finitely many semiclosed polyhedra. If the problem is further assumed to b... 详细信息

关键词： Piecewise linear functions multiobjective optimization problems Pareto solution sets Global weak sharp minimum Image space analysis

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Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria optimization

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JOURNAL OF optimization THEORY AND APPLICATIONS 2008年第3期139卷 577-590页

作者： Malinowska, A. B. Torres, D. F. M. Bialystok Tech Univ Fac Comp Sci Bialystok Poland Univ Aveiro Dept Math P-3800 Aveiro Portugal

The question of obtaining well-defined criteria for multiple-criteria decision making problems is well known. One of the approaches dealing with this question is the concept of nonessential objective functions. A certain objective function is called nonessential if the set of efficient solutions is the same with or without that objective function. We present two methods for determining nonessential objective functions. A computational implementation is done using a computer algebra system.

关键词： multiobjective optimization problems Efficient (Pareto optimal) solutions Essential nonessential objective functions

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Changes of the solution set by adding objectives to multicriteria optimization problems

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8th International Conference on Fuzzy Logic and Intelligent Technologies in Nuclear Science

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

ISBN: (纸本)9789812799463

In this work we are interested in characterizing 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 nonessential (weakly nonessential, properly nonessential) are presented. We establish relations between: weakly nonessential, properly nonessential and nonessential functions.

关键词： multiobjective optimization problems efficient (Pareto optimal) solutions essential/nonessential objective functions

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A multiobjective Test Suite with Hexagon Pareto Fronts and Various Feasible Regions

A Multiobjective Test Suite with Hexagon Pareto Fronts and V...

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IEEE Congress on Evolutionary Computation (IEEE CEC)

作者： Matsumoto, Takashi Masuyama, Naoki Nojima, Yusuke Ishibuchi, Hisao Osaka Prefecture Univ Grad Sch Engn Dept Comp Sci & Intelligent Syst Sakai Osaka 5998531 Japan Southern Univ Sci & Technol Shenzhen Key Lab Computat Intelligence Univ Key Lab Evolving Intelligent Syst Guangdong Dept Comp Sci & Engn Shenzhen Guangdong Peoples R China

ISBN: (纸本)9781728121536

The performance of a multiobjective Evolutionary Algorithm (MOEA) for many-objective optimization is often evaluated by multiobjective scalable test problems like DTLZ and WFG problems. This is because the scalable test problems are quite useful for an MOEA analysis. However, the scalable test problems do not have enough diversity of the shapes of the Pareto front and the feasible region to evaluate the capability of MOEAs. Previous studies showed that these shapes have a great impact on the performance of MOEAs. Thus, MOEAs should be evaluated on more test problems with different shapes of the Pareto front and the feasible region. In this study, the shapes of the Pareto front in the existing scalable test problems are examined from some viewpoints such as the distribution of optimal or worst solutions for each objective and the degree of the correspondence with the distribution of the weight vectors. The shape of the feasible region is also examined from the viewpoint of the spread of an initial population and the existence of dominance resistant solutions. According to the observations, we propose new shapes of the Pareto front and the feasible region to design a new scalable test suite. Experimental results show that the proposed test suite has totally different properties from the existing test problems.

关键词： multiobjective optimization problems scalable test suites many-objective optimization evolutionary multiobjective optimization algorithms

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Coevolutionary optimization Algorithm: With Ecological Competition Model

Coevolutionary Optimization Algorithm: With Ecological Compe...

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3rd International Conference on Artificial Intelligence and Computational Intelligence (AICI 2011)

作者： Liu, Jianguo Wu, Weiping Congqing Business & Technol Univ Chongqing 400067 Peoples R China

ISBN: (纸本)9783642242816

Premature convergence and low converging speed are the distinct weaknesses of the genetic algorithms, a new algorithm called ECCA (ecological competition coevolutionary algorithm) is proposed for multiobjective optimization problems, in which the competition is considered to be in important position. 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 experiment results show the high efficiency of the improved Genetic Algorithms based on this model in solving premature convergence and accelerating the convergence.

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

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Policy Gradient Approaches for Multi-Objective Sequential Decision Making: A Comparison

Policy Gradient Approaches for Multi-Objective Sequential De...

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IEEE Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL)

作者： Parisi, Simone Pirotta, Matteo Smacchia, Nicola Bascetta, Luca Restelli, Marcello Politecn Milan Dept Elect Informat & Bioengn Piazza Leonardo da Vinci 32 I-20133 Milan Italy

ISBN: (纸本)9781479945528

This paper investigates the use of policy gradient techniques to approximate the Pareto frontier in Multi-Objective Markov Decision Processes (MOMDPs). Despite the popularity of policy-gradient algorithms and the fact that gradient-ascent algorithms have been already proposed to numerically solve multi-objective optimization problems, especially in combination with multi-objective evolutionary algorithms, so far little attention has been paid to the use of gradient information to face multi-objective sequential decision problems. Three different Multi-Objective Reinforcement-Learning (MORL) approaches are here presented. The first two, called radial and Pareto following, start from an initial policy and perform gradient-based policy-search procedures aimed at finding a set of non-dominated policies. Differently, the third approach performs a single gradient-ascent run that, at each step, generates an improved continuous approximation of the Pareto frontier. The parameters of a function that defines a manifold in the policy parameter space are updated following the gradient of some performance criterion so that the sequence of candidate solutions gets as close as possible to the Pareto front. Besides reviewing the three different approaches and discussing their main properties, we empirically compare them with other MORL algorithms on two interesting MOMDPs.

关键词： Pareto optimisation approximation theory decision making evolutionary computation gradient methods learning (artificial intelligence) MOMDPs MORL approaches Pareto following Pareto frontier approximation gradient-ascent algorithms gradient-based policy-search procedures multiobjective Markov decision processes multiobjective evolutionary algorithms multiobjective optimization problems multiobjective reinforcement-learning approaches multiobjective sequential decision making nondominated policies performance criterion policy gradient approaches policy-gradient algorithms radial following Algorithm design and analysis Approximation algorithms Approximation methods Manifolds Measurement optimization Water resources evolutionary algorithm Performance metrics Pareto optimisation Algorithm design and analysis Manifolds Approximation method gradient methods Approximation Theory Approximation algorithms Water Resources Policies decision making

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