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interval linear programming problem with interval valued decision variables

OPSEARCH 2025年 1-28页

作者： Karmakar, Jewel Karmakar, Samiran Mahato, Sanat Kumar Bankura Zilla Saradamani Mahila Mahavidyapith Dept Math Bankura 722101 West Bengal India Bankura Sammilani Coll Dept Math Bankura 722102 West Bengal India Sidho Kanho Birsha Univ Dept Math Purulia 723104 West Bengal India

In this article, we have proposed a new interval-oriented technique for full interval linear programming problems. This kind of problem not only involves interval-valued model parameters but also the decision variables are anticipated as interval-valued variables. Consideration of decision variables in interval form is much more realistic for decision-making in uncertain or inexact environments. At first, the interval variables are mathematically signified in the light of real-life problems. The problems are reduced to non-interval (crisp) Bi-objective linear programming problems which, normally, have uncountable many Pareto optimal solutions. The main goal lying behind this interval-oriented solution methodology is to achieve a Pareto optimal solution that is highly acceptable because of accuracy, elapsed time, and computational effort. Finally, the method is applied to a good number of test problems most of those are cited from the existing literature and the results are compared with the same.

关键词： interval linear programming interval decision variable Multi-objective optimization Compromised solutions

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Optimizing the selection of the secret parameters for public key cryptosystems by using interval linear programming and fully fuzzy linear programming

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2025年 144卷

作者： Bas, Esra Istanbul Tech Univ Dept Ind Engn TR-34367 Istanbul Turkiye

One of the basic tasks in public key cryptosystems is to determine the secret parameters. This paper proposes multi-objective interval linear programming and multi-objective fully fuzzy linear programming (FFLP) models to determine the optimum interval numbers and triangular fuzzy numbers (TFNs) of the secret parameters in the public key cryptosystems. The public and private (secret) objective function(s) and constraints can be considered such that the optimum interval numbers and optimum TFNs for the secret parameters can be obtained from which the random selection of the secret parameters can be made for each algorithm's execution. Adapting the general model to the Rivest, Shamir, Adleman (RSA) public key cryptosystem is also illustrated. In the interval programming model for the RSA, the linear combination method combines multiple objective functions into a single objective function, and nonlinear constraints are linearized using the Taylor series expansion method. No multiple objective functions are obtained in the FFLP model of the RSA, but the nonlinear constraints are again linearized using the Taylor series expansion method. The numerical application for the RSA public key cryptosystem is made for both models by considering five cases and twenty-four subcases, and the results are analyzed. To the best of our knowledge, there is no study in the literature that considers interval linear programming and/or FFLP to obtain the optimum interval numbers and TFNs for the secret parameters of the public key cryptosystems. The proposed methodology is systematic and generic and can also be adapted for other public key cryptosystems easily.

关键词： Public key cryptosystem Rivest Shamir Adleman public key cryptosystem interval linear programming Fully fuzzy linear programming Multi-objective optimization

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Some new results on rough interval linear programming problems and their application to scheduling and fixed-charge transportation problems

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RAIRO-OPERATIONS RESEARCH 2024年第5期58卷 3697-3714页

作者： Allahdadi, Mehdi Rivaz, Sanaz Univ Sistan & Baluchestan Math Fac Zahedan Iran Babol Noshirvani Univ Technol Fac Basic Sci Dept Math Babol Iran

This paper focuses on linear programming problems in a rough interval environment. By introducing four linear programming problems, an attempt is being made to propose some results on optimal value of a linear programming problem with rough interval parameters. To obtain optimal solutions of a linear programming problem with rough interval data, constraints of the four proposed linear problems are applied. In this regard, firstly, the largest and the smallest feasible spaces for a linear constraint set with rough interval coefficients and parameters are introduced. Then, a rough interval for optimal value of such problems is obtained. Further, an upper approximation interval and a lower approximation interval as the optimal solutions of linear programming problems with rough interval parameters are achieved. Moreover, two solution concepts, surely and possibly solutions, are defined. Some numerical examples demonstrate the validity of the results. In particular, a scheduling problem and a fixed-charge transportation problem (FCTP) under rough interval uncertainty are investigated.

关键词： interval linear programming rough interval optimal solution optimal value

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A novel interval linear programming based on probabilistic dominance

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FUZZY SETS AND SYSTEMS 2022年 434卷 20-47页

作者： Qiu, Zhiping Xia, Haijun Beihang Univ Sch Aeronaut Sci & Engn Inst Solid Mech Beijing 100083 Peoples R China

This study investigates a novel interval linear programming based on probabilistic dominance. Firstly, the definition of interval linear programming is briefly reviewed. Then a new interval linear programming model is presented based on probabilistic domi-nance. The probabilistic dominance index treats the intervals as uniformly distributed variables and the interval inequality relation is further defined by probability. To deal with non-linearity in probabilistic dominance index, sequential quadratic programming is used to solve the problem and the performance measure approach is proposed to overcome the convergence difficulties. The deter-mination and sensitivity analysis of the target performance measure are discussed to assess the sequential quadratic programming algorithm. Meanwhile, the extension of the proposed method to fuzzy interval linear programming is discussed. Furthermore, the proposed method is applied to the design of the plane truss structure with interval parameters. Finally, the effectiveness and ratio-nality of the developed method are demonstrated by two mathematical examples and one interval parametric plane truss structure optimization example.(c) 2021 Elsevier B.V. All rights reserved.

关键词： interval linear programming Probabilistic dominance Sequential quadratic programming algorithm Performance measure approach interval parametric plane truss structure optimization

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An Analysis to Treat the Degeneracy of a Basic Feasible Solution in interval linear programming 9th

An Analysis to Treat the Degeneracy of a Basic Feasible Solu...

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9th International Symposium on Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM)

作者： Gao, Zhenzhong Inuiguchi, Masahiro Osaka Univ Toyonaka Osaka 5608531 Japan

ISBN: (纸本)9783030980184;9783030980177

When coefficients in the objective function cannot be precisely determined, the optimal solution is fluctuated by the realisation of coefficients. Therefore, analysing the stability of an optimal solution becomes essential. Although the robustness analysis of an optimal basic solution has been developed successfully so far, it becomes complex when the solution contains degeneracy. This study is devoted to overcoming the difficulty caused by the degeneracy in a linear programming problem with interval objective coefficients. We focus on the tangent cone of a degenerate basic feasible solution since the belongingness of the objective coefficient vector to its associated normal cone assures the solution's optimality. We decompose the normal cone by its associated tangent cone to a direct union of subspaces. Several propositions related to the proposed approach are given. To demonstrate the significance of the decomposition, we consider the case where the dimension of the subspace is one. We examine the obtained propositions by numerical examples with comparisons to the conventional techniques.

关键词： interval linear programming Degeneracy Polyhedral convex cone Tangent cone Basic space

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Optimal allocation of photovoltaic energy storage in DC distribution network based on interval linear programming

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JOURNAL OF ENERGY STORAGE 2024年 85卷

作者： Yu, Dan Tang, Ren Pan, Lezhen Zhejiang Huayun Elect Power Engn Design Consulting Hangzhou 310000 Zhejiang Peoples R China State Grid Wenzhou Power Supply Co Wenzhou 325000 Zhejiang Peoples R China

In order to improve the capacity of optimal allocation of photovoltaic energy storage in DC (Direct Current) distribution network, an optimal allocation method of photovoltaic energy storage in DC distribution network based on interval linear programming is proposed. Taking into account the operational life loss of energy storage and aiming at the minimum operating income of energy storage investment, the fluctuation relationship and constraint variable relationship model are built in the storage and allocation of photovoltaic energy in the DC distribution network, and the comprehensive cost concept distribution set is established based on the network loss cost and the cost of energy storage and allocation, and the optimization detection in the process of energy storage and allocation of photovoltaic energy in the DC distribution network is realized through interval linear programming scheduling. The configuration model is built taking into account the voltage offset index, and the balanced dispatching and fast response model analysis of photovoltaic energy storage in the DC distribution network are realized through the zoning dispatching and power density spectrum analysis. According to the analysis of suppressing the fluctuation of distributed energy, the hybrid energy storage is used to suppress. A twolevel configuration model is constructed. The upper layer is the hybrid energy storage capacity and power planning layer, while the lower layer is the power distribution layer, which is to reduce the battery charging and discharging power to reduce the life loss of photovoltaic power supply in the DC distribution network, and realize the configuration of photovoltaic energy storage in the DC distribution network through interval planning. The test shows that this method has good balance and large gain in the configuration of photovoltaic energy storage in the DC distribution network, which improves the output efficiency of the distribution network. The maximum outpu

关键词： interval linear programming DC distribution network Including photovoltaic energy Energy storage configuration

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Weak optimal inverse problems of interval linear programming based on KKT conditions

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Applied Mathematics(A Journal of Chinese Universities) 2021年第3期36卷 462-474页

作者： LIU Xiao JIANG Tao LI Hao-hao School of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China Hangzhou College of Commerce Zhejiang Gongshang UniversityHangzhou 310018China School of Data Sciences Zhejiang University of Finance and EconomicsHangzhou 310018China.

In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT ***,the problem is precisely ***,by adjusting the minimum change of the current cost coefficient,a given weak solution can become ***,an equivalent characterization of weak optimal inverse IvLP problems is ***,the problem is simplified without adjusting the cost coefficient of null variable.

关键词： interval linear programming inverse problems KKT conditions weak optimal solution

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A Copula-based interval linear programming model for water resources allocation under uncertainty

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JOURNAL OF ENVIRONMENTAL MANAGEMENT 2022年 317卷 115318页

作者： Yue, Wencong Yu, Shujie Xu, Meng Rong, Qiangqiang Xu, Chao Su, Meirong Dongguan Univ Technol Res Ctr Ecoenvironm Engn Dongguan 523808 Peoples R China Guangdong Prov Key Lab Water Qual Improvement & Ec Guangzhou 510006 Peoples R China Zhejiang Univ Finance & Econ Sch Publ Adm Hangzhou 310018 Peoples R China

Water scarcity tends to be aggravated by increase in water demand with the trend of socio-economic development. Thus, non-stationary characteristics of water demand should be identified in water resources allocation (WRA) to alleviate the potential influences from water shortages. In this study, a Copula-based interval linear programming model was established for regional WRA. Through combining correlation analysis and an interval linear programming model, this model can: 1) identify interactions between water demand and socio-economic development levels based on Copula functions, 2) explore variations in water shortage with consideration of multiple risk tolerance levels of decision-makers based on Copula sampling, and 3) obtain desired strategies for WRA through an interval linear programming model. Also, Dalian City in China was selected as a case study area to verify the effectiveness of the model for WRA to five water users (i.e., agricultural sector, industrial sector, public service sector, domestic residents, and ecological environment). Considering multiple tolerance levels of decision-makers to water shortage risk, three scenarios (i.e., S1 to S3), indicating 20%, 40%, and 60% of their low, medium, and high tolerance levels, were proposed. The results showed that the correlation between the amount of water demand and indicators of socio-economic development can be described by Clayton and Gaussian Copula functions. The total water supply of Dalian in 2030 would increase by 2.06%-2.65%, compared with the one in 2025. The allocation of water resources across districts was influenced by varied water demand, energy consumption, and risk tolerance levels. Compared with the amount of water allocation in 2025, the contribution of transferred water sources would increase by 6.71% and 7.04% under S1 and S2 in 2030, respectively, and decrease by 14.31% under S3. With the increase of risk tolerance levels of decision-makers, the amount of water supply in Dalian City

关键词： Water resources allocation Copula functions interval linear programming Water shortage risk Dalian city

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Optimization of electric-heat-gas model based on interval linear programming 33

Optimization of electric-heat-gas model based on interval li...

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33rd Chinese Control and Decision Conference (CCDC)

作者： Li Mingtong Wang Lidi Zhu Sitong Miao Yilin Wang Xinyao Shenyang Agr Univ Shenyang 110866 Peoples R China

ISBN: (纸本)9781665440899

In order to improve the coupling relationship between energy sources and improve the energy utilization rate, this paper controls the parameter variables of energy storage equipment and renewable energy power generation technology, compiles the corresponding optimization program, obtains the optimal combination of different energy types distribution work, and realizes the economic optimization goal. The program analysis shows that: the existence of renewable energy power generation technology will greatly reduce the wind energy abandonment rate and make the wind energy output regulation within the controllable range;the existence of energy storage equipment will reduce the overall economic consumption of the system;the joint output of different energy sources can not only meet the energy demand, but also improve the efficiency of the whole system, so the system has flexible energy regulation ability, At the same time, the economic budget is within the controllable range and has practical value.

关键词： interval linear programming Combined power heating and gas Renewable energy Optimal design

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On the new solution to interval linear fractional programming problems

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EVOLUTIONARY INTELLIGENCE 2024年第5-6期17卷 4001-4005页

作者： Khastan, A. Jimenez, B. Hernandez Moreno, A. Beato Inst Adv Studies Basic Sci Dept Math Zanjan Iran Univ Pablo Olavide Dept Econ Metodos Cuantitat & Hist Econ Seville Spain Univ Seville Dept Estadist & Invest Operat Seville Spain

In this paper, we study the interval linear fractional programming problems using the concept of g-division. We transform the problem into a new linear fractional programming problem and obtain a nondominated solution to the interval linear fractional programming problem. We show that the new solution dominates the previous nondominated objective value presented in the literature. Finally, some examples are provided to illustrate our results.

关键词： interval linear fractional programming g-division interval linear programming interval arithmetic

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