Article
Computer Science, Interdisciplinary Applications
Ozlem Karsu, Firdevs Ulus
Summary: This paper investigates split algorithms for partitioning the objective function space in multiobjective integer programming problems. A unified approach is proposed to allow different split strategies within the same algorithmic framework with minimal changes. The performance of these algorithms is compared in terms of exact computation and solution approaches under time restriction, with a focus on representativeness. Experimental results show that the (-1)-split structure is superior in computational time, while the-split structure has significant advantages in terms of representativeness under time/cardinality limited settings, especially with adaptive parameter setting and/or a suitable region exploration order.
COMPUTERS & OPERATIONS RESEARCH
(2022)
Article
Mathematics, Applied
N. Hoseinpoor, M. Ghaznavi
Summary: In this research, two scalarization techniques are proposed to solve multiobjective optimization problems (MOPs). These techniques utilize the generalized Tchebycheff norm and incorporate slack and surplus variables to provide scalarized approaches. By varying the range of parameters, we obtain results that elucidate the relationship between (weakly, properly) Pareto optimal solutions of the MOP and optimal solutions of the scalarized problems. Importantly, the theorems presented in this study do not require any convexity assumption for objective functions. The main advantage of the generalized Tchebycheff norm approach is that it eliminates the gap between necessary and sufficient conditions for (weak, proper) Pareto optimality and provides necessary and sufficient conditions for Pareto optimality in different results.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Mathematics
Narges Hoseinpoor, Mehrdad Ghaznavi
Summary: This article proposes a modified objective-constraint technique for solving multiobjective programming problems. By adding slack variables, easily checked conditions for Pareto optimality can be found. The suggested approach generates an almost even approximation of the efficient front.
HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS
(2022)
Article
Operations Research & Management Science
Jie Wang, Shengjie Li, Min Feng
Summary: This paper investigates nonconvex nonsmooth uncertain multiobjective optimization problems, where the decision variable is defined on a Banach space and uncertain parameters are defined on arbitrary nonempty sets. The Stone-Cech compactification of uncertainty sets and the upper semicontinuous regularization of original functions are employed to derive robust necessary optimality conditions for the local robust weakly efficient solution. Weak and strong KKT robust necessary conditions are also obtained based on the constraint qualification and the regularity condition. Several examples are provided to demonstrate the validity of the results.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2022)
Article
Operations Research & Management Science
J. W. Chen, R. Yang, E. Kobis, X. Ou
Summary: This paper investigates the robust optimality conditions and duality for a class of nonconvex multiobjective optimization problems with uncertain data. The Fermat principle for a locally Lipschitz function is presented using the upper semi-regular convexificator. Robust necessary optimality conditions of the Fritz-John type and KKT type are established for the uncertain nonconvex multiobjective optimization problems. Additionally, robust sufficient optimality conditions and saddle point conditions are derived under the generalized $ \hat {\partial }<^>{\ast } $ partial differential *-pseudoquasiconvexity and generalized convexity, respectively. The robust duality relations between the original problem and its mixed robust dual problem are obtained under a generalized pseudoconvexity assumption.
Article
Engineering, Multidisciplinary
Xiaoqing Ou, Suliman Al-Homidan, Qamrul Hasan Ansari, Jiawei Chen
Summary: The study introduces the establishment of C-robust efficient solutions and optimistic C-robust efficient solutions for uncertain multiobjective optimization problems, using image space analysis and uncertainty factors to apply robust optimality conditions and saddle point sufficient optimality conditions to problem solving.
JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION
(2021)
Article
Mathematics, Applied
Jie Wang, Sheng-Jie Li, Chun-Rong Chen, Ying-Rang Xu
Summary: This paper focuses on the robust duality relations for uncertain cone-constrained vector optimization problems in more general nonconvex settings. The authors introduce a new class of generalized Lagrange functions by combining the image space analysis method and scalarization technique, and formulate the Lagrange robust vector dual problem. The results of robust weak duality, strong duality, and converse duality are provided to characterize the vector dual relations between the primal worst and dual best problems.
APPLICABLE ANALYSIS
(2023)
Article
Computer Science, Artificial Intelligence
Hong Li, Li Zhang
Summary: An efficient solution strategy is proposed for bilevel multiobjective optimization problem with the lower-level MOP converted into a single-objective optimization problem. The Karush-Kuhn-Tucker optimality conditions are used to transform the original BLMOP into a single-level MOP with complementarity constraints. An effective smoothing technique is suggested to handle the complementarity constraints, and a decomposition-based constrained multiobjective differential evolution is developed for solving the transformed MOP. The experimental results demonstrate the proposed solution method's favorable convergence and diversity.
Article
Operations Research & Management Science
Jiawei Chen, Suliman Al-Homidan, Qamrul Hasan Ansari, Jun Li, Yibing Lv
Summary: This paper studies robust necessary optimality conditions for a nondifferentiable complex fractional programming with uncertain data, introducing a robust counterpart and the concept of a robust optimal solution. An equivalence between the optimal solutions of the robust counterpart and a minimax nonfractional parametric programming is given, and Fritz John-type and Karush-Kuhn-Tucker-type robust necessary optimality conditions are established under suitable conditions.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2021)
Article
Operations Research & Management Science
Ellen H. Fukuda, L. M. Grana Drummond, Ariane M. Masuda
Summary: The proposed extension of the real-valued conjugate directions method is used for unconstrained quadratic multiobjective problems, aiming to find weak Pareto and Pareto optima through specific steps and calculations in each iteration.
Article
Management
Patrick Groetzner, Ralf Werner
Summary: The article explores robust optimization methods and extends the concept of regret from single-objective to multiobjective decision problems, providing a proper definition of multivariate regret. The approach separates the modeling of multiobjective regret from its numerical solution, allowing for tractable computations in various scenarios.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2022)
Article
Operations Research & Management Science
Nguyen Minh Tung, Mai Van Duy
Summary: This paper investigates a robust nonsmooth semi-infinite objective optimization problem associated with data uncertainty. It proposes some constraint qualifications and derives sufficient conditions for them. Necessary and sufficient conditions for robust weak Pareto, Pareto, and Benson proper solutions are established under these conditions. The paper also addresses the Wolfe and Mond-Weir duality schemes and presents conditions for linear programming using the obtained results.
4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH
(2023)
Article
Mathematics, Applied
Tadeusz Antczak
Summary: This paper develops a methodology to solve uncertain multiobjective fractional programming problems, using a robust optimization approach to find e-efficient solutions. It establishes necessary and sufficient optimality conditions for feasible solutions to be e over bar-efficient solutions of the parametric robust vector optimization problem. The relationship between e-efficiency of the robust multiobjective fractional programming problem and e over bar-efficiency of its corresponding parametric robust vector optimization problem is also proven.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Operations Research & Management Science
Cagin Ararat, Firdevs Ulus, Muhammad Umer
Summary: We propose an algorithm to generate inner and outer polyhedral approximations to the upper image of a bounded convex vector optimization problem. The algorithm is free of direction-biasedness as it does not involve a direction parameter. We also prove for the first time the finiteness of an algorithm for convex vector optimization by introducing a suitable compact subset of the upper image. The computational performance of the algorithm shows promising results compared to a similar algorithm based on Pascoletti-Serafini scalarization.
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
(2022)
Article
Computer Science, Artificial Intelligence
Jinlong Zhou, Juan Zou, Jinhua Zheng, Shengxiang Yang, Dunwei Gong, Tingrui Pei
Summary: This paper proposes an infeasible solutions diversity maintenance strategy for solutions with constraint violations degree greater than epsilon. Experimental results demonstrate that our proposed algorithm is highly competitive with other state-of-the-art algorithms for constrained multiobjective optimization problems.
Article
Computer Science, Theory & Methods
Yan-Kuen Wu, Yung-Yih Lur, Ching-Feng Wen, Shie-Jue Lee
Summary: This paper focuses on the classical problem of computing max-min inverse fuzzy relation and proposes a simple analytical method for finding exact or approximate solutions. The resolution for this problem is useful for solving well-known problems in fuzzy abductive/backward reasoning.
FUZZY SETS AND SYSTEMS
(2022)
Article
Operations Research & Management Science
N. Tuyen, C-F Wen, T. Q. Son
Summary: This paper proposes an approach to characterize epsilon-solution sets of convex programs with a given epsilon > 0, divided into two parts. The first part establishes the expressions of epsilon-solution sets of a class of convex infinite programs, while the second part focuses on some special cases, such as the epsilon-solution sets of convex programs with set constraints. The results are validated through several examples.
Article
Computer Science, Artificial Intelligence
Jiali He, Liangdong Qu, Zhihong Wang, Yiying Chen, Damei Luo, Ching-Feng Wen
Summary: This paper investigates attribute reduction in an incomplete categorical decision information system (ICDIS) based on fuzzy rough sets. An attribute reduction algorithm is proposed and experiments show that it outperforms existing algorithms.
ARTIFICIAL INTELLIGENCE REVIEW
(2022)
Article
Computer Science, Artificial Intelligence
Yan-Kuen Wu, Ching-Feng Wen, Yuan-Teng Hsu, Ming-Xian Wang
Summary: This study proposes a minimal-maximal programming problem based on fuzzy relational inequalities to study the stability of peer-to-peer file sharing systems and network congestion. By adjusting constraint variables meticulously, the minimal optimal solution obtained can minimize the maximum transmission level and achieve balanced data download amounts.
FUZZY OPTIMIZATION AND DECISION MAKING
(2022)
Article
Computer Science, Artificial Intelligence
Yan-Kuen Wu, Ching-Feng Wen, Yuan-Teng Hsu, Ming-Xian Wang
Summary: This paper studies the properties of minimal solutions in an addition-min fuzzy relational inequalities system and proposes an iterative algorithm to find these minimal solutions. The proposed algorithm not only efficiently finds the minimal solutions, but also discovers multiple minimal solutions in different iterative sequences of variables.
FUZZY OPTIMIZATION AND DECISION MAKING
(2022)
Article
Mathematics
Lu-Chuan Ceng, Ching-Feng Wen, Yeong-Cheng Liou
Summary: This paper investigates the properties of K-preinvex set-valued maps using the normal subdifferential and equilibrium-like function. It establishes sufficient conditions for the existence of super minimal points of a K-preinvex set-valued map and provides necessary optimality terms for a general type of super efficiency.
Article
Mathematics
Tzu-Chien Yin, Yan-Kuen Wu, Ching-Feng Wen
Summary: In this paper, we investigate a common problem of the fixed point problem and the quasimonotone variational inequality problem in Hilbert spaces. We propose an iterative algorithm to find a common element of the solution of a quasimonotone variational inequality and the fixed point of a pseudocontractive operator. Convergence theorems are proven under certain mild conditions, and several corollaries are obtained.
JOURNAL OF MATHEMATICS
(2022)
Article
Operations Research & Management Science
N. T. T. Huong, C. -F. Wen, J. -C. Yao, N. D. Yen
Summary: This paper investigates the properness of efficient solutions in the sense of Geoffrion for linear fractional vector optimization problems with unbounded constraint sets. Sufficient conditions for an efficient solution to be Geoffrion's properly efficient solution are obtained via Benson's characterization.
Article
Mathematics, Applied
Yongjian Liu, Zhenhai Liu, Sisi Peng, Ching-Feng Wen
Summary: This paper investigates optimal feedback control problems derived from a class of Riemann-Liouville fractional evolution equations with history-dependent operators in separable reflexive Banach spaces. The existence and uniqueness of mild solutions are proved, feasible pairs and optimal control pairs are demonstrated to exist for optimal feedback control systems with history-dependent operators using a feedback iterative technique and Filippov theorem, and some applications are provided to illustrate the main results.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2022)
Correction
Mathematical & Computational Biology
Zhaowen Li, Qinli Zhang, Pei Wang, Fang Liu, Yan Song, Ching-Feng Wen
INTERDISCIPLINARY SCIENCES-COMPUTATIONAL LIFE SCIENCES
(2022)
Article
Mathematics
Lu-Chuan Ceng, Ching-Feng Wen, Yeong-Cheng Liou, Jen-Chih Yao
Summary: In this paper, two strengthened inertial-type subgradient extragradient rules are proposed for solving the VIP and CFPP problems, with adaptive step sizes. The strong convergence of these rules to a common solution of the VIP and CFPP, which is the unique solution of a hierarchical variational inequality (HVI), is proved with suitable restrictions.
Article
Mathematics
Arvind Kumar Rajpoot, Rais Ahmad, Mohd Ishtyak, Ching-Feng Wen
Summary: We investigate a mixed variational inequality problem involving the generalized Yosida approximation operator in q-uniformly smooth Banach space and establish its equivalence to a fixed-point equation. Based on this formulation, we propose an algorithm to solve the problem and discuss convergence criteria. We provide an example with Matlab program, computation table, and convergence graphs to verify the effectiveness of the problem and its fixed-point formulation.
JOURNAL OF MATHEMATICS
(2022)
Article
Computer Science, Artificial Intelligence
Zhaowen Li, Qinli Zhang, Pei Wang, Yan Song, Ching-Feng Wen
Summary: This paper studies the uncertainty measurement of gene space based on the class-consistent technology and discusses its application in gene selection from the perspective of GrC. The class-consistent relation between cells in a gene space is established, and the information granules are obtained. Two metrics to measure the uncertainty of gene space are defined, and their effectiveness is verified through numerical experiments and statistical tests. Furthermore, two gene selection algorithms are proposed and shown to outperform state-of-the-art feature selection algorithms in clustering experiments.
APPLIED INTELLIGENCE
(2023)
Article
Mathematics, Applied
Donghui Fang, Jiaolang Wang, Xianyun Wang, Ching-Feng Wen
Summary: This paper is focused on the approximate optimality condition and mixed type duality for DC composite optimization problems in locally convex Hausdorff topological vector spaces. A new constraint qualification is introduced based on the properties of the Fre acute accent chet subdifferential. Under this constraint qualification, approximate optimality conditions for the quasi (alpha, epsilon)-optimal solution and associated mixed type duality theorems are established, which improve and extend the previous results.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2023)
Article
Mathematics, Applied
Lu-Chuan Ceng, Nan-Jing Huang, Ching-Feng Wen
Summary: In this paper, we investigate a class of generalized global fractional-order composite dynamical systems involving set-valued perturbations in real separable Hilbert spaces. First, we prove that the solution set of the systems is nonempty and closed under some suitable conditions. Second, we show that the solution set is continuous with respect to the initial value in the sense of the Hausdorff metric. Last, an example is provided to illustrate the applicability of the main results.
JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS
(2022)
