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An ensemble framework for assessing solutions of interval programming problems

INFORMATION SCIENCES 2018年 436卷 146-161页

作者： Sun, Jing Gong, Dunwei Zeng, Xiaojun Geng, Na Huaihai Inst Technol Coll Sci Lianyungang 222005 Peoples R China China Univ Min & Technol Sch Informat & Control Engn Xuzhou 221116 Peoples R China Qingdao Univ Sci & Technol Sch Informat Sci & Technol Qingdao 266061 Peoples R China Univ Manchester Sch Comp Sci Manchester M13 9PL Lancs England Jiangsu Normal Univ Sch Elect Engn & Automat Xuzhou 221116 Peoples R China

interval programming is a commonly used technique in real-world situations. Its related theories and methods have been widely researched. There are a variety of approaches for assessing solutions of an interval programming problem due to the particularity of intervals. It is well-known that different assessing approaches may produce different optimal solution(s) for the same interval programming problem, and it is rather difficult to choose from these assessing approaches for users, especially for those who have little knowledge about interval arithmetic, which greatly restricts its extensive applications. In this paper, we develop an ensemble framework for assessing solutions of interval programming problems. At the start, interval dominance rules are defined, and their correlations are described via exclusion, inclusion and equivalence: then, a rule reduction strategy is developed through inspecting the impact of different rules on the sorting of solutions, and a novel ensemble dominance relation for interval programming is proposed to evaluate solutions;furthermore, their complexities are analyzed;finally, the experimental results empirically validate the correctness and effectiveness of the proposed framework. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Uncertain programming interval programming Numerical optimization Evolutionary algorithm Ensemble dominance

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A multiobjective interval programming model to explore the trade-offs among different aspects of job satisfaction under different scenarios

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SOCIO-ECONOMIC PLANNING SCIENCES 2019年 66卷 35-46页

作者： Henriques, C. O. Luque, M. Marcenaro-Gutierrez, O. D. Lopez-Agudo, L. A. Polytech Inst Coimbra ISCAC Business Sch P-3040316 Coimbra Portugal Univ Coimbra Polo II INESC Coimbra R Silvio Lima P-3030290 Coimbra Portugal Univ Malaga Dept Appl Econ Math C Ejido 6 E-29071 Malaga Spain Univ Malaga Dept Appl Econ Stat & Econometr C Ejido 6 E-29071 Malaga Spain Univ Malaga Econ & Business Malaga Spain

The need for greater concern about job quality/satisfaction seems clear, due to its potential link with workers' productivity, to the extent it affects employees' quitting behaviour, absenteeism, turnover, and firms' productivity. In order to guide managers and policy makers when making decisions related to future hiring of human resources, a multiobjective interval programming model, based on the results of an econometric estimation, is suggested where different (and conflicting) aspects of job satisfaction are considered. The modelling framework thus obtained allows assessing the trade-offs among the different aspects of job satisfaction under different scenarios herein given within interval ranges. Data obtained from Spain are used to carry out the model's instantiation. Possibly efficient solutions are then generated with the help of scalarizing problems relying on reference point-based methods. The solution approach herein proposed allows computing with a lower computational effort the closest "possibly" efficient solutions attainable regarding their corresponding interval ideal solutions. Overall, the results obtained highlight the trade-off between earnings and quality of life, particularly under a pessimistic scenario, with the maximization of earnings leading to the lowest value of the working times. Conversely, the lowest value obtainable for earnings is reached with the consideration of both scenarios when the maximization of the satisfaction of the quality of life seekers is attained. Finally, the trade-off between less prone to risk workers and quality of life seekers is also revealed, with the lowest job security levels found in the solution that maximizes working times.

关键词： Multiple objective programming Workers' satisfaction Econometric analysis interval programming

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Minimizing Impact of Bounded Uncertainty on McNaughton's Scheduling Algorithm via interval programming

Minimizing Impact of Bounded Uncertainty on McNaughton's Sch...

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IEEE International Conference on Systems, Man, and Cybernetics (SMC)

作者： Hossny, Ahmad Nahavandi, Saeid Creighton, Douglas Deakin Univ Ctr Intelligent Syst Res Geelong Vic 3217 Australia

ISBN: (纸本)9781479906529

Uncertainty of data affects decision making process as it increases the risk and the costs of the decision. One of the challenges in minimizing the impact of the bounded uncertainty on any scheduling algorithm is the lack of information, as only the upper bound and the lower bound are provided without any known probability or membership function. On the contrary, probabilistic uncertainty can use probability distributions and fuzzy uncertainty can use the membership function. McNaughton's algorithm is used to find the optimum schedule that minimizes the makespan taking into consideration the preemption of tasks. The challenge here is the bounded inaccuracy of the input parameters for the algorithm, namely known as bounded uncertain data. This research uses interval programming to minimise the impact of bounded uncertainty of input parameters on McNaughton's algorithm, it minimises the uncertainty of the cost function estimate and increase its optimality. This research is based on the hypothesis that doing the calculations on interval values then approximate the end result will produce more accurate results than approximating each interval input then doing numerical calculations.

关键词： scheduling uncertainty interval programming interval arithmetic

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Analysis of interval programming in different environments and its application to fixed-charge transportation problem

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DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS 2017年第3期9卷

作者： Midya, Sudipta Roy, Sankar Kumar Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 W Bengal India

In this paper, we analyze the interval programming using interval and rough interval (RI). interval programming is one of the tools to tackle uncertainty in mathematical programming. In the real world situations, we often encounter the cases where the data cannot be determined with certainty. So, the value of the data is assessed using an interval. Here, we consider that the parameters of the Fixed-Charge Transportation Problem (FCTP) are imprecise. In our proposed problem, uncertainties are considered in terms of interval and RI. We present a study of the FCTP using the interval programming. An example of the FCTP is included to show the effectiveness and usefulness of our proposed study. Finally, concluding remarks and future scopes of our paper are discussed.

关键词： interval programming fuzzy programming rough interval fixed-charge transportation problem

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interval programming Model for Optimal Design of Returned Logistics Network

Interval Programming Model for Optimal Design of Returned Lo...

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第十五届工业工程与工程管理国际会议

作者： Di Weimin School of Management Engineering,Zhengzhou University,Zhengzhou,P.R.China,450001

The optimal design of Returned logistics network is an important part of returned logistics ***, the precise values of some parameters are difficult to obtain in practice,so it is reasonable to denote this type of problem as uncertain *** this paper,regarding both used products' volumes and processing capacities of logistics facilities as interval numbers,an interval programming model for the network's optimal design is developed,and then the model is transformed to a deterministic mixed integer programming model by converting its constraints with interval numbers to respective crisp equivalents with the help of constraints' *** is hereby believed that a good foundation is established for the model's further ***,a numerical example is given to show the application of proposed model indesign decision - making.

关键词： Returned Logistics Network interval programming Optimal Design

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Robust interval linear programming for environmental decision making under uncertainty

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ENGINEERING OPTIMIZATION 2012年第11期44卷 1321-1336页

作者： Fan, Y. R. Huang, G. H. Li, Y. P. N China Elect Power Univ SC Resources & Environm Res Acad MOE Key Lab Reg Energy Syst Optimizat Beijing 102206 Peoples R China

In this study, a robust interval linear programming (RILP) method is developed for dealing with uncertainties expressed as intervals with deterministic boundaries. An enhanced two-step method (ETSM) is also advanced to solve the RILP model. The developed RILP improves upon the conventional interval linear programming (ILP) method since it can generate solution intervals within a larger feasible zone. The decision space based on ETSM contains all feasible solutions, such that no useful information is neglected. Moreover, the RILP can guarantee the stability of the optimization model due to no violation for the best-case constraints. The results also suggest that the RILP is effective for practical environmental and engineering problems that involve uncertainties.

关键词： decision making enhanced two-step robust interval programming optimization uncertainty

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Minimizing Impact of Bounded Uncertainty on McNaughton's Scheduling Algorithm via interval programming

Minimizing Impact of Bounded Uncertainty on McNaughton's Sch...

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IEEE International Conference on Systems, Man, and Cybernetics

作者： Ahmad Hossny Saeid Nahavandi Douglas Creighton Centre for Intelligent Systems Research Deakin University Australia

ISBN: (纸本)9781479906505

关键词： scheduling uncertainty interval programming interval arithmetic interval arithmetic input parameter Bounded Uncertainty Membership functions algorithms decision making process programming

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A multi-stage interval-stochastic programming model for planning end-of-life vehicles allocation

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JOURNAL OF CLEANER PRODUCTION 2016年 115卷 366-381页

作者： Simic, Vladimir Univ Belgrade Fac Transport & Traff Engn Vojvode Stepe 305 Belgrade 11000 Serbia

The amount of material entering end-of-life vehicles (ELVs) management systems all over the EU has been reduced due to increased export of used vehicles to non-EU countries. According to the latest data, only 6.23 million ELVs were processed in 2012 (e.g., 8.37 million ELVs were processed in 2009). Considering that currently 342 active vehicle recycling factories exist in the EU, as well as that in the last ten years the total processing capacity has been increased several times, it is clear that there is a serious conflict. This paper proposes a multi-stage interval-stochastic programming model for planning end-of life vehicles allocation. The developed model is able to reflect dynamics in terms of decisions for ELV allocation from a multi-region waste management system to multiple vehicle recycling factories within a multi-period context. It is capable of incorporating multiple policies within the optimization framework. Uncertainties expressed as probability distributions and discrete intervals are effectively handled, based on a multi-layered scenario tree with a finite set of scenarios. A semi-hypothetical case study is conducted in order to demonstrate the potentials and applicability of the proposed model. Influences of parameter uncertainty on model solutions are thoroughly examined. Comprehensive analyses of various policy situations, associated with different levels of economic penalties and system failure risks, are presented. The proposed model is effective for solving difficult ELV allocation problems with uncertainties included as part of the formulation. It can help quantify the relationships between ELV management system profit and disruption risk of the vehicle recycling factories, and thus provide optimal ELV allocation schemes. (C) 2015 Elsevier Ltd. All rights reserved.

关键词： End-of-life vehicle Management Multi-stage Stochastic interval programming Uncertainty

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An integrated interval programming and input–output knowledge model for risk and resiliency management

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Decision Analytics Journal 2023年 9卷

作者： Pamucar, Dragan Sarkar, Bishal Dey Shardeo, Vipulesh Soni, Tarun Kumar Dwivedi, Ashish Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon University of Belgrade Faculty of Organizational Sciences Department of Operations Research and Statistics Belgrade Serbia Symbiosis Institute of Operations Management Symbiosis International (Deemed University) Pune India FORE School of Management New Delhi India Jindal Global Business School OP Jindal Global University Sonipat India

The COVID-19 pandemic has devastated nearly every sector of the global economy. The research seeks to examine the COVID-19 pandemic's effects on economy and its interdependencies, specifically on mining and minerals, energy, and agriculture sectors. We propose a mathematical model by combining interval programming with input–output knowledge modeling. The input–output model illustrates how pandemic-induced perturbations in one sector spread to others. According to how susceptible they are to disturbances coming from the primary sector (e.g., mining and minerals, agriculture, or energy), a ranking of the impacted sectors can serve as an essential input for risk and resiliency management. The study also determines which sectors are anticipated to suffer significant financial losses due to the pandemic, allowing decision-makers to prioritize their investment plans in light of system-level uncertainty. We further develop four distinct scenarios and analyze the influence of the three most influential sectors on others. © 2023 The Author(s)

关键词： Input–output knowledge modeling interval programming Pandemic Resiliency modeling Risk assessment

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interval Goal programming for Economic-Environmental Power Generation - Dispatch Problems

Interval Goal Programming for Economic-Environmental Power G...

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IEEE International Conference on Fuzzy Systems (FUZZ)

作者： Pal, Bijay Baran Kumar, Mousumui Univ Kalyani Dept Math Kalyani 741235 W Bengal India Alipurduar Coll Dept Math Sobhaganj 736122 W Bengal India

ISBN: (纸本)9781479900206

This paper presents a linear goal programming method to solve thermal power generation and dispatch problems with interval data uncertainty. In the proposed approach, the nonlinear objectives inherently involved to a problem are first transformed into their linear equivalents in the decision situation. Then, target intervals for achieving objectives are defined in power generation planning horizon. In the model formulation, the objectives with target intervals are converted into standard form of goals in goal programming methodology. In goal achievement function, both the modeling aspects of goal programming, minsum and minimax formulations, are addressed for achieving objective values within target intervals specified in the decision environment. To illustrate the potential use of the approach, the model is tested on the standard IEEE 6-Generator 30-Bus System.

关键词： economic-environmental power generation-dispatch goal programming interval programming target interval Taylor Series approximation

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