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Two modified Pascoletti-Serafini methods for solving multiobjective optimization problems and multiplicative programming problems

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SOFT COMPUTING 2023年第21期27卷 15675-15697页

作者： Dolatnezhadsomarin, Azam Khorram, Esmaile Yousefikhoshbakht, Majid Amirkabir Univ Technol Dept Math & Comp Sci 424 Hafez Ave Tehran 15914 Iran Bu Ali Sina Univ Fac Sci Dept Math Hamadan Iran

In this paper, a modified Pascoletti-Serafini scalarization approach, called MOP_MPS, is proposed to generate approximations of a Pareto front of bounded multi-objective optimization problems (MOPs). The objective is obtaining some points with an almost even distribution overall Pareto front. This algorithm is applied to six test problems with convex, non-convex, connected, and dis-connected Pareto fronts, and its results are compared with results of some famous algorithms. The results emphasize that MOP_MPS is effective and competitive in comparing with the other considered algorithms. In addition, it is shown that an optimal solution of a multiplicative programming problem is a properly Pareto optimal solution of an MOP. By considering this relation between MOPs and multiplicative programming problems (MPPs), another algorithm based on MOP_MPS, called MPP_MPS, is suggested for approximately solving non-linear MPPs in which functions multiplied are continuous and bounded from below. The computational results on seven problems of convex MPPs demonstrate that the algorithm is much better than a cut and bound algorithm presented by Shao and Ehrgott in terms of CPU time.

关键词： multiobjective optimization problem Multiplicative programming problem Pareto optimal solution Global optimal Pascoletti-Serafini approach

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Equivalence and existence of weak Pareto optima for multiobjective optimization problems with cone constraints

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APPLIED MATHEMATICS LETTERS 2008年第6期21卷 599-606页

作者： Li, Lun Li, Jun China W Normal Univ Sch Math & Informat Nanchong 637002 Sichuan Peoples R China

In this work, a differentiable multiobjective optimization problem with generalized cone constraints is considered, and the equivalence of weak Pareto solutions for the problem and for its eta-approximated problem is established under suitable conditions. Two existence theorems for weak Pareto solutions for this kind of multiobjective optimization problem are proved by using a Karush-Kuhn-Tucker type optimality condition and the F-KKM theorem. (C) 2007 Elsevier Ltd. All rights reserved.

关键词： multiobjective optimization problem q-invex q-convexlike weak Pareto solution (KKT) condition KKM-mapping

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Game model based co-evolutionary solution for multiobjective optimization problems

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2004年第2期2卷 247-255页

作者： Sim, KB Kim, JY Lee, DW Chung Ang Univ Sch Elect & Elect Engn Seoul 156756 South Korea

The majority of real-world problems encountered by engineers involve simultaneous optimization of competing objectives. In this case instead of single optima, there is a set of alternative trade-offs, generally known as Pareto-optimal solutions. The use of evolutionary algorithms Pareto GA, which was first introduced by Goldberg in 1989, has now become a sort of standard in solving multiobjective optimization problems (MOPs). Though this approach was further developed leading to numerous applications, these applications are based on Pareto ranking and employ the use of the fitness sharing function to maintain diversity. Another scheme for solving MOPs has been presented by J. Nash to solve MOPs originated from Game Theory and Economics. Sefrioui introduced the Nash Genetic Algorithm in 1998. This approach combines genetic algorithms with Nash's idea. Another central achievement of Game Theory is the introduction of an Evolutionary Stable Strategy, introduced by Maynard Smith in 1982. In this paper, we will try to find ESS as a solution of MOPs using our game model based co-evolutionary algorithm. First, we will investigate the validity of our co-evolutionary approach to solve MOPs. That is, we will demonstrate how the evolutionary game can be embodied using co-evolutionary algorithms and also confirm whether it can reach the optimal equilibrium point of a MOP. Second, we will evaluate the effectiveness of our approach, comparing it with other methods through rigorous experiments on several mops.

关键词： co-evolutionary algorithm evolutionary game theory multiobjective optimization problem nash genetic algorithm pareto optimal set

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Robust neutrosophic programming approach for solving intuitionistic fuzzy multiobjective optimization problems

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COMPLEX & INTELLIGENT SYSTEMS 2021年第4期7卷 1935-1954页

作者： Ahmad, Firoz Aligarh Muslim Univ Dept Stat & Operat Res Aligarh Uttar Pradesh India Indian Stat Inst SQC & Unit 203 BT Rd Kolkata 700108 India

This study presents the modeling of the multiobjective optimization problem in an intuitionistic fuzzy environment. The uncertain parameters are depicted as intuitionistic fuzzy numbers, and the crisp version is obtained using the ranking function method. Also, we have developed a novel interactive neutrosophic programming approach to solve multiobjective optimization problems. The proposed method involves neutral thoughts while making decisions. Furthermore, various sorts of membership functions are also depicted for the marginal evaluation of each objective simultaneously. The different numerical examples are presented to show the performances of the proposed solution approach. A case study of the cloud computing pricing problem is also addressed to reveal the real-life applications. The practical implication of the current study is also discussed efficiently. Finally, conclusions and future research scope are suggested based on the proposed work.

关键词： Intuitionistic fuzzy parameters Robust neutrosophic programming approach multiobjective optimization problem Cloud computing pricing problem

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Equivalence of Weak Pareto Optima for multiobjective optimization problems with Cone Constrains

Equivalence of Weak Pareto Optima for Multiobjective Optimiz...

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5th International Conference on Digital Image Processing (ICDIP)

作者： Mei, Cao Xue, Zhao Beihua Univ Coll Comp Beijing 132021 Jilin Peoples R China Beihua Univ Coll Math Beijing 132013 Peoples R China

In this paper, a differentiable multiobjective optimization problem with generalized cone constrains is considered, and the equivalence of weak Pareto solutions for the problem and for its (eta)-approximated problem i... 详细信息

ISBN: (纸本)9780819493057

关键词： multiobjective optimization problem weakly pareto solution invex

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Necessary and sufficient conditions for multiobjective optimization problems

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optimization 1996年第2期36卷 97-104页

作者： Taa, A. Dept. de Mathématiques Fac. des Sci. et Techniques Gueliz-Marrakech B.P. 618 Morocco

We consider the following multiobjective optimization problem (P) Minimize F(χ) subject to χ ∈ X where F is a set-valued map between two Banach X and Y. When the set-valued map F is upper semidifferentiable and compact Luc [2] gives necessary and sufficient optimality conditions for (P) in terms of contingent derivatives. In this paper we study the same problem under weaker notion of set-valued derivatives and without neither compactness nor upper semidifferentiability assumptions.

关键词： Compact base Contingent derivative multiobjective optimization problem Pareto minimal point S-derivative Set-valued map

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NEWTON'S METHOD FOR UNCERTAIN multiobjective optimization problemS UNDER FINITE UNCERTAINTY SETS

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS

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JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS 2023年第5期7卷 785-809页

作者： Kumar, Shubham Ansary, Md Abu Talhamainuddin Mahato, Nihar Kumar Ghosh, Debdas Shehu, Yekini Pandit Dwarka Prasad Mishra Indian Inst Informat T Jabalpur India Indian Inst Technol Jodhpur Dept Math Jodhpur India Indian Inst Technol BHU Varanasi Dept Math Sci Varanasi India Zhejiang Normal Univ Sch Math Sci Jinhua 321004 Peoples R China

In this paper, we develop Newton's method for robust counterpart of an uncertain multiobjective optimization problem under an arbitrary finite uncertainty nonempty set. Here the robust counterpart of an uncertain multiobjective optimization problem is the minimum of objective wise worst case, which is the nonsmooth deterministic multiobjective optimization problem. To solve this robust counterpart with the help of Newton's method, a suproblem is constructed and solved to find a descent direction for robust counterpart. An Armijo type inexact line search technique is developed to find a suitable step length. With the help of the descent direction and step length, we present the Newton's algorithm for the robust counterpart. The convergence of the Newton's algorithm for the robust counterpart is obtained under some usual assumptions. We also prove that the algorithm converges with super linear and quadratic rate under different assumptions. Finally, we verify the algorithm and compare with the weighted sum method via some numerical problems.

关键词： . Line search techniques multiobjective optimization problem Newton's method Robust efficiency Uncertainty Robust optimization

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The Exact Solution of the Environmental/Economic Dispatch problem

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IEEE TRANSACTIONS ON POWER SYSTEMS 2012年第2期27卷 723-731页

作者： Bayon, Luis Grau, Jose M. Ruiz, Maria M. Suarez, Pedro M. Univ Oviedo Dept Math Gijon Spain

In this paper, the exact analytical solution for the environmental/economic dispatch (EED) optimization problem is presented for the first time. The EED, which simultaneously satisfies multiple contradictory criteria, is stated as a multiobjective optimization problem (MOP). Our paper has improved several aspects of a previous analytical approach. First, we take into account the unit capacity constraints in the exact formulae. Second, we obtain the set of compromise solutions known as Pareto optimal solutions and, third, our treatment of transmission losses satisfies the power balance constraint. In contrast with the known heuristic methods used in the literature, which only provide a reasonable solution (suboptimal, nearly global optimal), our method provides the global solution. Moreover, our method can obtain the Pareto optimal set under different loading conditions. The performance of the proposed technique is validated using a standard test system.

关键词： Environmental/economic dispatch multiobjective optimization problem Pareto optimal set transmission losses

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multiobjective problems: Enhanced Necessary Conditions and New Constraint Qualifications through Convexificators

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NUMERICAL FUNCTIONAL ANALYSIS AND optimization 2018年第1期39卷 11-37页

作者： Hejazi, Mansoureh Alavi Movahedian, Nooshin Nobakhtian, Soghra Univ Isfahan Dept Math Esfahan *** Iran Inst Res Fundamental Sci IPM Sch Math Tehran 193955746 Iran

In this paper, we study necessary optimality conditions for local Pareto and weak Pareto solutions of multiobjective problems involving inequality and equality constraints in terms of convexificators. We develop the enhanced Karush-Kuhn-Tucker conditions and introduce the associated pseudonormality and quasinormality conditions. We also introduce several other new constraint qualifications which entirely depend on the feasible set. Then a connecting link between these constraint qualifications is presented. Moreover, we provide several examples that clarify the interrelations between the different results that we have established.

关键词： Constraint qualification convexificator multiobjective optimization problem necessary optimality condition nonsmooth analysis pseudo-differential

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A Big Data-Enabled Consolidated Framework for Energy Efficient Software Defined Data Centers in IoT Setups

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2020年第4期16卷 2687-2697页

作者： Kaur, Kuljeet Garg, Sahil Kaddoum, Georges Bou-Harb, Elias Choo, Kim-Kwang Raymond Univ Quebec Ecole Technol Super Dept Elect Engn Montreal PQ H3C 1K3 Canada Florida Atlantic Univ 777 Glades Rd Boca Raton FL 33431 USA Univ Texas San Antonio Dept Informat Syst & Cyber Secur San Antonio TX 78249 USA Univ Texas San Antonio Dept Elect & Comp Engn San Antonio TX 78249 USA

The rapidly evolving industry standards and transformative advances in the field of Internet of Things are expected to create a tsunami of Big Data shortly. This, in turn, will demand real-time data analysis and processing from cloud computing platforms. A substantial part of the computing infrastructure is supported by large-scale and geographically distributed data centers (DCs). Nevertheless, these DCs impose a substantial cost in terms of rapidly growing energy consumption, which in turn adversely affects the environment. In this context, efficient resource utilization is seen as a potential candidate to enhance energy efficiency and minimize the load on the power sector. Nevertheless, in the majority of the public clouds, the resources are idle most of the time (i.e., under-utilized) as the load of the servers is unpredictable;thereby leading to a lofty increase in the energy utilization index and wastage of resources. Thus, it is highly essential to devise a precise and efficient resource management technique. Therefore, in this article, we leverage the advantages of software defined data centers (SDDCs) to minimize energy utilization levels. Precisely, SDDC refers to the process of programmatically abstracting the logical computing, network, and storage resources;and configuring them in real-time based on workload demands. In detail, we demonstrate the possibility of 1) designing a consolidated SDDC-based model to jointly optimize the process of virtual machine (VM) deployment and network bandwidth allocation for reduced energy consumption and guaranteed quality of service (QoS), particularly for heterogeneous computing infrastructures;2) formulating a multiobjective optimization problem to deduce the optimal allocation of resources for both critical and noncritical applications;and 3) designing an efficient scheme based on heuristics to provide suboptimal results for the formulated multiobjective optimization problem. The proposed article presents a suboptim

关键词： Quality of service Switches Data centers Cloud computing Software Virtual machining Internet of Things Big Data cloud computing energy minimization Internet of Things multiobjective optimization problem prioritized scheduling software defined data centers and virtual machines

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