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Steepest descent method for uncertain multiobjective optimization problems under finite uncertainty set

APPLICABLE ANALYSIS 2025年第7期104卷 1163-1184页

作者： Kumar, Shubham Ansary, Md Abu T. Mahato, Nihar Kumar Ghosh, Debdas PDPM IIITDMJ Discipline Nat Sci Jabalpur India IIT Jodhpur Dept Math Sci Jodhpur India Indian Inst Technol BHU Dept Math Sci Varanasi India

In this paper, a steepest descent method is developed for the robust counterpart of uncertain multiobjective optimization problems under finite uncertainty. The robust counterpart under consideration is the minimum of objective wise worst case, which is a nonsmooth deterministic multiobjective optimization problem. To solve this robust counterpart with the help of the steepest descent method, a subproblem is constructed and solved to find a descent direction. An Armijo-type inexact line search technique is employed to find a suitable step length. With the help of the descent direction and step length, a sequence is generated. The convergence of the proposed method is justified under some common assumptions. Finally, the algorithm is verified and compared with one existing method with the help of some numerical problems.

关键词： multiobjective optimization problem uncertainty robust optimization robust efficiency steepest descent method line search techniques

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Linear Complementarity problem and multiobjective optimization

Linear Complementarity Problem and Multiobjective Optimizati...

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2nd International Conference on Engineering Design and optimization (ICEDO 2011)

作者： Yong, Longquan Shaanxi Univ Technol Hanzhong 723001 Shaanxi Provinc Peoples R China

ISBN: (纸本)9783037852590

A new method is proposed for the linear complementarity problem (LCP). Firstly we formulate the LCP into a multiobjective optimization problem (MOP), and study the relations between the efficient solution of MOP and optimal solution of LCP. Based on the efficient solution of MOP, we define zero-efficient solution. Then we indicate that zero-efficient solution of the MOP is also the solution to the LCP. Finally some standard LCP examples are respectively transformed into MOP and solved by minimax method. Numerical results indicate that the proposed method is effective.

关键词： Linear complementarity problem multiobjective optimization problem Zero-efficient solution Minimax method

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multiobjective optimization Method for Solving Nonlinear Complementarity problem

Multiobjective Optimization Method for Solving Nonlinear Com...

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23rd Chinese Control and Decision Conference

作者： Yong, Longquan Shaanxi Univ Technol Dept Math Hanzhong 723001 Shaanxi Peoples R China

ISBN: (纸本)9781424487363

In last decades, there has been much effort on the solution and the analysis of the nonlinear complementarity problem (NCP) by reformulating NCP as an unconstrained minimization. In this paper, we propose a new method for the NCP under the condition that the solution exists. We formulate the NCP into a multiobjective optimization problem (MOP), and define zero-efficient solution of MOP. Then we indicate that zero-efficient solution of the MOP is also the solution to the NCP. Finally we use minimax method for the MOP. Numerical results indicate that the proposed method is promising.

关键词： Nonlinear complementarity problem multiobjective optimization problem Zero-efficient solution Minimax method

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Real-Time Scheduling Framework for Multiagent Cooperative Logistics With Dynamic Supply Demands

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2025年第4期21卷 3007-3016页

作者： Guan, Yuxiang Chen, Yuning Liu, Yi Zhang, Hongda Zhou, Ziqing Ding, Wenchao Zou, Zhuo Xu, Lida Ouyang, Chun Gan, Zhongxue Fudan Univ Acad Engn & Technol Shanghai 200433 Peoples R China Fudan Univ Sch Informat Sci & Technol Shanghai 200433 Peoples R China Old Dominion Univ Dept Informat Technol Norfolk VA USA

In logistics systems with multiagent collaboration, one of the prevailing focus lies on modeling as the dynamic multiperiod vehicle routing problem (DMPVRP). This work introduces modifications to DMPVRP to align with the requirements of real factory operations, particularly with dynamic supply demands. A self-established multiagent dynamic scheduling framework has been proposed to adapt to dynamic environmental changes and make timely adjustments, which consists of two modules: dynamic path planning and machine assignment. The first module utilizes a self-designed multioperator two-stage evolutionary algorithm to dynamically update the routes for vehicles. The second module maintains the workload balance among vehicles in real time. Experimental results demonstrate that the proposed algorithm achieves optimal outcomes compared to three state-of-the-art algorithms, surpassing others by 20% in machine output and exhibiting 5% lower transportation costs. In addition, a case study from a steel cord manufacturing factory is conducted, demonstrating its capability to promptly enhance efficiency.

关键词： Dynamic supply task multiagent logistics multiobjective optimization problem multiobjective optimization problem multiobjective optimization problem

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The multiobjective traveling salesman-repairman problem with profits: design and implementation of a variable neighborhood descent algorithm for a real scenario

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INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2025年第1期32卷 221-243页

作者： Morante-Gonzalez, R. Lopez-Sanchez, A. D. Sanchez-Oro, J. Hernandez-Diaz, A. G. Univ Rey Juan Carlos Tulipán S-N Madrid 28933 Spain Univ Pablo Olavide Ctra Utrera Km 1 Seville 41013 Spain

This paper introduces a problem that can be seen as a combination of the traveling salesman problem with profits and the traveling repairman problem with profits, coined as the multi-objective traveling salesman-repairman problem with profits (Mo-TSRPP). The objective of the Mo-TSRPP is to simultaneously optimize three objectives: the total cost, total latency, and total profit. Indirectly, the number of nodes visited is also considered although not as an objective itself since it is determined by the size of every efficient solution in the Pareto front. The Mo-TSRPP emerges as a real-world problem in which a freelancer, which repairs appliances, wants to plan the daily route. Moreover, the daily plan does not require to visit all customers. To solve the problem, first, a greedy randomized adaptive procedure is designed to generate a set of high-quality nondominated solutions and then, a variable neighborhood descent algorithm is applied for further improving the initial set. This procedure allows us to attain a good approximation of the Pareto front. To prove the performance of the proposal a comparison is done against three well-known evolutionary algorithms: NSGA-II, SPEA-2, and MOEA/D. Finally, a realistic problem is shown and solved to illustrate the potential of the algorithm.

关键词： traveling salesman problem traveling repairman problem profit multiobjective optimization problem greedy randomized adaptive search procedure variable neighborhood descent

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BackCom-Aided NOMA Systems: A Simultaneous Process of Covertness and Information at Tag

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IEEE WIRELESS COMMUNICATIONS LETTERS 2025年第1期14卷 83-87页

作者： Hai, Ngo Thanh Khoa, Dang Le VNUHCM Univ Sci Fac Elect & Telecommun Dept Telecommun & Networks Ho Chi Minh City 70000 Vietnam

In this letter, we achieve a simultaneous process of covertness and information by using the backscatter node (Tag) in uplink non-orthogonal multiple access (NOMA) systems. To reach this goal, we employ the best antenna pair scheme for decoding and formulate the multiobjective optimization problem for both the covert user's effective covertness rate and Tag's effective transmission rate. As a result, Tag is capable of both transmitting information and performing a covertness function. Adopting Tag for covertness presents outstanding performance in comparison to using an energy harvesting jammer. Under the Tag scheme, the use of a large number of antennas for legal decoding is an efficient way to enhance covertness performance. In addition, the public user plays an active role in covert communications by increasing the transmit power in a controlled manner.

关键词： NOMA Backscatter Uplink Wireless networks Radiometry optimization Fading channels Decoding Transmitting antennas Telecommunications Covert communication backscatter communication multiobjective optimization problem

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multiobjective optimization Method for Solving Nonlinear Complementarity problem

Multiobjective Optimization Method for Solving Nonlinear Com...

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2011 China Control and Decision Conference(2011中国控制与决策会议 CCDC)

作者： Longquan Yong Department of Mathematics Shaanxi University of Technology Hanzhong 723001 China

关键词： Nonlinear complementarity problem multiobjective optimization problem Zero-efficient solution Minimax method

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multiobjective optimization problems with modified objective functions and cone constraints and applications

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JOURNAL OF GLOBAL optimization 2011年第1期49卷 137-147页

作者： Chen, Jia Wei Cho, Yeol Je Kim, Jong Kyu Li, Jun Gyeongsang Natl Univ Dept Math Educ Chinju 660701 South Korea Gyeongsang Natl Univ RINS Coll Educ Chinju 660701 South Korea China W Normal Univ Sch Math & Informat Nanchong 637002 Sichuan Peoples R China Kyungnam Univ Dept Math Masan 631701 South Korea

In this paper, we consider a differentiable multiobjective optimization problem with generalized cone constraints (for short, MOP). We investigate the relationship between weakly efficient solutions for (MOP) and for the multiobjective optimization problem with the modified objective function and cone constraints [for short, (MOP) (eta) (x)] and saddle points for the Lagrange function of (MOP) (eta) (x) involving cone invex functions under some suitable assumptions. We also prove the existence of weakly efficient solutions for (MOP) and saddle points for Lagrange function of (MOP) (eta) (x) by using the Karush-Kuhn-Tucker type optimality conditions under generalized convexity functions. As an application, we investigate a multiobjective fractional programming problem by using the modified objective function method.

关键词： multiobjective optimization problem Q-(pseudo)invex Q-convexlike Weakly efficient solution Saddlepoint KKT condition Weak (strong, converse) duality Lagrange function

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multiobjective optimization problems on Jet Bundles

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FRONTIERS IN PHYSICS 2022年 10卷

作者： Pitea, Ariana Univ Politehn Bucuresti Dept Math & Informat Bucharest Romania

The aim of this work is to study constrained optimization problems by means of (phi, rho)-convexity. We provide some sufficient conditions of optimality for a class of vectors of cuvilinear integrals by means of an adequate generalized convexity. Dual problems associated with this one are stated and developed, in terms of weak, strong, and converse duality results. The framework chosen here is one specific to the Riemannian geometry, namely that of first order jet bundles.

关键词： Riemannian mainfold jet bundle multiobjective optimization problem efficiency duality generalized convexity

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Convergence analysis of Tikhonov-type regularization algorithms for multiobjective optimization problems

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APPLIED MATHEMATICS AND COMPUTATION 2009年第1期211卷 167-172页

作者： Chen, Zhe Xiang, Changhe Zhao, Kequan Liu, Xuewen Chongqing Normal Univ Dept Math & Comp Sci Chongqing 400047 Peoples R China Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

In this paper, we introduce a vector-valued Tikhonov-type regularization algorithm for an extended-valued multiobjective optimization problem. Under some mild conditions, we prove that any sequence generated by this algorithm converges to a weak Pareto optimal solution of the multiobjective optimization problem. Our results improve and generalize some known results. (C) 2009 Elsevier Inc. All rights reserved.

关键词： multiobjective optimization problem Tikhonov-type regularization algorithm Asymptotic cone Asymptotic function Weak Pareto optimal solution

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