Article
Mathematics, Applied
Liu Xiao, Jiang Tao, Li Hao-hao
Summary: This paper explores weak optimal inverse problems of interval linear programming based on KKT conditions. It defines the problem precisely and shows that adjusting the minimum change of the current cost coefficient can convert a weak solution to an optimal one. An equivalent characterization of weak optimal inverse IvLP problems is obtained, and the problem is simplified without adjusting the cost coefficient of null variable.
APPLIED MATHEMATICS-A JOURNAL OF CHINESE UNIVERSITIES SERIES B
(2021)
Article
Operations Research & Management Science
Tran Hung Cuong, Yongdo Lim, Nguyen Dong Yen
Summary: This study investigates the properties of the Proximal Difference-of-Convex functions decomposition algorithm in indefinite quadratic programming with linear constraints. It is found that the algorithm can converge to a Karush-Kuhn-Tucker point at a root linear rate, provided that the problem has a solution. Moreover, when the initial points are chosen from a suitable neighborhood, the algorithm can converge to a locally unique solution. Through numerical tests, the influence of the decomposition parameter on the convergence rate is analyzed, and the performance of the Proximal Difference-of-Convex functions decomposition algorithm is compared with that of the Projection Difference-of-Convex functions decomposition algorithm. Additionally, the performances of these algorithms and the Gurobi software are compared in solving randomly generated nonconvex quadratic programs.
Article
Mathematics, Applied
Fatemeh Salary Pour Sharif Abad, Mehdi Allahdadi, Hasan Mishmast Nehi
Summary: This paper introduces three algorithms to obtain the optimal solution set for interval linear fractional programming models. One algorithm obtains the OS set by solving two sub-models, while the other two algorithms only obtain a single feasible OS.
Article
Computer Science, Artificial Intelligence
Sapan Kumar Das, S. A. Edalatpanah
Summary: This paper extends linear fractional programming problems to neutrosophic sets and proposes a new algorithm based on aggregation ranking function and arithmetic operations of triangular neutrosophic sets. Numerical models and a case study are employed to demonstrate the effectiveness and superiority of the novel techniques over current strategies.
Article
Computer Science, Artificial Intelligence
Ehsan Korani, Alireza Eydi
Summary: The paper introduces a bi-level programming model to solve hub location problems in production and distribution systems. The research aims to reduce costs of establishing hub networks in the first level and service loss in the second level. Through analysis and algorithms, a feasible solution is proposed and improved.
EXPERT SYSTEMS WITH APPLICATIONS
(2021)
Article
Energy & Fuels
Jian Pan, Tingzhang Liu
Summary: With the integration of electric vehicles and renewable energy sources into power systems, the unit commitment problem has become increasingly complex. The study of optimal scheduling for thermal, wind, solar, and EV power units is of great academic and practical significance.
Article
Engineering, Electrical & Electronic
Sezen Ece Kayacik, Burak Kocuk
Summary: In this letter, an alternative mixed-integer non-linear programming formulation of the reactive optimal power flow (ROPF) problem is proposed, utilizing a mixed-integer second-order cone programming (MISOCP) based approach to find global optimal solutions. The MISOCP relaxation is improved using convex envelopes and cutting planes, showing promising results in computational experiments on challenging test cases compared to a semidefinite programming based approach from the literature.
IEEE TRANSACTIONS ON POWER SYSTEMS
(2021)
Article
Mathematics
Kin Keung Lai, Shashi Kant Mishra, Sanjeev Kumar Singh, Mohd Hassan
Summary: This paper investigates the solution sets of interval-valued mathematical programming problems with switching constraints. It introduces weak, Mordukhovich, and strong stationary conditions to characterize the problems and derives the corresponding solution sets.
Article
Automation & Control Systems
Alex Parkinson
Summary: This paper focuses on a discrete time periodic optimal control problem. Linear programming based optimality conditions are established, and a method for constructing near optimal controls is presented. A numerical example is included to demonstrate the results.
SYSTEMS & CONTROL LETTERS
(2022)
Article
Mathematics, Applied
Phantipa Thipwiwatpotjana, Artur Gorka, Worrawate Leela-apiradee
Summary: This study introduces six types of solutions for equations and four types of solutions for inequalities, with necessary and sufficient conditions for their solvabilities depending on the sign of variables. A standard linear programming approach can be used to solve an interval linear programming problem with nonnegative variables and two-sided interval linear constraints.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Management
Daniel De Wolf, Yves Smeers
Summary: The article presents a characterization of the Clarke subdifferential of the optimal value function of a linear program in terms of matrix coefficients. It generalizes the result of Freund (1985) to situations where derivatives may not be defined due to the presence of multiple primal or dual solutions.
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
(2021)
Article
Computer Science, Artificial Intelligence
Mijanur R. Seikh, Shibaji Dutta, Deng-Feng Li
Summary: The paper explores matrix games with Rough Interval (RI) pay-offs and investigates two different solution methodologies. The first approach constructs auxiliary linear programming problems with RI coefficients and converts them into classical linear programming problems (LPPs). The second approach uses the expected value technique for RI to transform auxiliary mathematical programming models to crisp LPP. The applicability of these approaches is demonstrated through a case study on the telecom market share problem.
INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS
(2021)
Article
Chemistry, Multidisciplinary
Andrzej Piegat, Marcin Plucinski
Summary: Determining the tolerance solution of interval linear systems has been a long-standing task, yet remains unsolved. This article presents a new method using multidimensional interval arithmetic to find the optimal tolerance solution for a basic equation, and showcases its applications with examples.
APPLIED SCIENCES-BASEL
(2022)
Article
Engineering, Industrial
Yiyong Xiao, Yue Zhang, Sadan Kulturel-Konak, Abdullah Konak, Yuchun Xu, Shenghan Zhou
Summary: This paper investigates the problem of aperiodic facility layout in dynamic manufacturing environments, decomposing it into a master problem and a set of static facility layout problems. With the use of mixed-integer linear programming models, solutions can be efficiently obtained for small-sized problems. Computational experiments show promising results for solving the AFLP and new best solutions were found for benchmark problems with the improved problem evolution algorithm.
INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH
(2021)
Article
Environmental Sciences
Qiangqiang Rong, Jingni Zeng, Meirong Su, Wencong Yue, Yanpeng Cai
Summary: This research introduces an integrated land-use prediction and optimization model that can predict future land-use patterns and nonpoint-source pollution loads, and optimize the patterns under different pollution reduction scenarios. The study finds that land-use changes greatly impact nonpoint-source pollution, and regional land-use patterns should be optimized to mitigate such pollution.
JOURNAL OF ENVIRONMENTAL MANAGEMENT
(2022)
