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fuzzy multi-objective optimization for optimum allocation in multivariate stratified sampling with quadratic cost and parabolic fuzzy numbers

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2017年第12期87卷 2372-2383页

作者： Gupta, Neha Bari, Abdul SGT Univ Fac Commerce & Management Gurgaon Haryana India Aligarh Muslim Univ Dept Stat & Operat Res Aligarh Uttar Pradesh India

This article deals with the uncertainties in a multivariate stratified sampling problem. The uncertain parameters of the problem, such as stratum standard deviations, measurement costs, travel costs and total budget of the survey, are considered as parabolic fuzzy numbers and the problem is formulated as a fuzzy multi-objective nonlinear programming problem with quadratic cost function. Using -cut, parabolic fuzzy numbers are defuzzified and then the compromise allocations of the problem are obtained by fuzzy programming for a prescribed value of . To demonstrate the utility of the proposed problem a numerical example is solved with the help of [LINGO User?s Guid. Lindo Systems Inc., 1415 North Dayton Street, Chicago,Illinois-60622, (USA), 2013] software and the derived compromise optimum allocation is compared with deterministic and proportional allocations.

关键词： fuzzy numbers fuzzy programming multi-objective programming compromise allocation stratified sampling travel cost 90C70 90C29 90C30 49M37

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A fuzzy long-term investment planning model for a GenCo in a hybrid electricity market considering climate change impacts

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INFORMATION SYSTEMS FRONTIERS 2017年第5期19卷 975-991页

作者： Sivrikaya, Berna Tektas Cebi, Ferhan Turan, Hasan Huseyin Kasap, Nihat Delen, Dursun Uludag Univ Dept MIS TR-16400 Inegol Bursa Turkey Istanbul Tech Univ Fac Management TR-34367 Istanbul Turkey Qatar Univ Dept Mech & Ind Engn Doha 2713 Qatar Sabanci Univ Sch Management TR-34956 Istanbul Turkey Oklahoma State Univ Spears Sch Business Stillwater OK 74078 USA

We study the long-term generation capacity investment problem of an independent power generation company (GenCo) that functions in an environment where GenCos perform business with both bilateral contracts (BC) and transactions in the day-ahead market (DAM). A fuzzy mixed integer linear programming model with a fuzzy objective and fuzzy constraints is developed to incorporate the impacts of imprecision/uncertainty in the economic environment on the calculation of the optimal value of the GenCo's objective function. In formulating the fuzzy objective function we also include the potential impacts of climate change on the energy output of hydroelectric power plants. In addition to formulating and solving the capacity planning/investment problem, we also performed scenario-based (sensitivity) analysis to explore how investment decisions of the GenCos change when fuzziness (tolerance) in the maximum energy output of hydroelectric units and/or drought expectation increases. The proposed model is novel and investigates the effects of factors like drought expectations of climate changes, hydroelectric power plant investments, and other power generation technology investment options.

关键词： Long-term capacity planning energy generation fuzzy programming bilateral contracts market day-ahead market climate change hydroelectric power

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An interactive optimization model for energy systems planning associated with clean-energy development under uncertainty

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INTERNATIONAL JOURNAL OF ENERGY RESEARCH 2017年第4期41卷 482-501页

作者： Jin, S. W. Li, Y. P. Huang, G. H. North China Elect Power Univ Sino Canada Energy & Environm Res Acad Beijing 102206 Peoples R China Beijing Normal Univ Sch Environm Beijing 100875 Peoples R China Univ Regina Inst Energy Environm & Sustainable Communities Regina SK S4S 7H9 Canada

In this study, an interactive fuzzy chance-constrained resolution (IFCR) method is developed for supporting energy systems planning (ESP) under uncertainty. IFCR can not only tackle multiple uncertainties presented as fuzzy membership functions and probability distributions using an interactive resolution method, but also enable decision makers to seek optimal solutions between satisfaction degree of objective and feasibility of constraints. Then, an IFCR-ESP model is formulated for energy systems of Bayingolin Mongol Autonomous Prefecture (abbreviated as Bazhou). Results provide decision makers with a complete view of the relationship between uncertain inputs and solutions. Policy-based solutions concerning energy consumption, electricity generation, capacity expansion, pollutant emission, and system cost are analyzed, which can help decision makers to identify desired strategies for ESP. Results indicate that transitioning from the conventional energy system to a sustainable one is associated to policy support, resources availability, energy supply security, and capital investment;clean energy policy (e.g. shift from coal to gas) is an effective way to facilitate the local energy system development in a sustainable manner;the solutions under different feasibility degrees can help decision makers to conduct in-depth analyses of tradeoffs between system cost and constraint-violation risk in an interactive way. Copyright (c) 2016 John Wiley & Sons, Ltd.

关键词： chance constrained energy systems fuzzy programming interactive resolution method sustainable development uncertainty

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fuzzy Modeling for Low-Carbon Dynamic Procurement Problem

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INTERNATIONAL JOURNAL OF fuzzy SYSTEMS 2017年第4期19卷 1238-1248页

作者： Kothyari, Akshat Singh, Surya Prakash Kaur, Harpreet Birla Inst Technol & Sci Pilani Rajasthan India Indian Inst Technol Delhi Dept Management Studies New Delhi India

The importance of effective and efficient procurement in the dynamic business environment cannot be neglected for overall performance of a firm. However, the parameters such as demand and availability of various resources are difficult to estimate with certainty. Thus, such uncertain parameters make it difficult to model lot-sizing procurement problem. Moreover, due to current environmental concerns the procurement problem must also address carbon emissions caused during procurement process. Therefore, this paper is an attempt to address the decision making for a low-carbon dynamic procurement problem for multi-products from multiple sources through multi-carriers in multi-period using fuzzy programming. In this paper, a fuzzy mixed integer linear program (FMILP) is proposed to obtain low-carbon optimal order allocation, supplier and carrier selection in the presence of fuzzy demand, fuzzy carrier and supplier capacities, and carbon emissions. The proposed FMILP is solved in LINGO 10. The working methodology of the proposed model is demonstrated using two illustrative examples.

关键词： fuzzy programming Low-carbon procurement Dynamic procurement Multi-sourcing Carrier selection

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fuzzy programming for mixed-integer optimization problems

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ARTIFICIAL LIFE AND ROBOTICS 2011年第2期16卷 174-177页

作者： Lin, Yung-Chin Lin, Yung-Chien Su, Kuo-Lan Lin, Wei-Cheng Chen, Tsing-Hua Natl Yunlin Univ Sci & Technol Grad Sch Engn Sci & Technol Touliu Yunlin Taiwan WuFeng Univ Dept Elect Engn Minhsiung Chiayi Taiwan Natl Yunlin Univ Sci & Technol Dept Elect Engn Touliu 64002 Yunlin Taiwan I Shou Univ Dept Elect Engn Kaohsiung Taiwan

Mixed-integer optimization problems belong to the group of NP-hard combinatorial problems. Therefore, they are difficult to search for global optimal solutions. Mixed-integer optimization problems are always described by precise mathematical programming models. However, many practical mixed-integer optimization problems have inherited a more or less imprecise nature. Under these circumstances, if we take into account the flexibility of the constraints and the fuzziness of the objectives, the original mixed-integer optimization problems can be formulated as fuzzy mixed-integer optimization problems. Mixed-integer hybrid differential evolution (MIHDE) is an evolutionary search algorithm which has been successfully applied to many complex mixed-integer optimization problems. In this article, a fuzzy mixed-integer mathematical programming model is developed to formulate the fuzzy mixed-integer optimization problem. In addition the MIHDE is introduced to solve the fuzzy mixed-integer programming problem. Finally, the illustrative example shows that satisfactory results can be obtained by the proposed method. This demonstrates that MIHDE can effectively handle fuzzy mixed-integer optimization problems.

关键词： fuzzy programming Mixed-integer optimization Evolutionary algorithm

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Multi-Objective Fixed-Charge Transportation Problem with Random Rough Variables

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INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 2018年第6期26卷 971-996页

作者： Roy, Sankar Kumar Midya, Sudipta Yu, Vincent F. Vidyasagar Univ Dept Appl Math Oceanol & Comp Programming Midnapore 721102 W Bengal India Natl Taiwan Univ Sci & Technol Dept Ind Management 43Sect 4Keelung Rd Taipei 10607 Taiwan

This paper considers a multi-objective fixed-charge transportation problem (MOFCTP) in which the parameters of the objective functions are random rough variables, while the supply and the demand parameters are rough variables. In real-life situations, the parameters of a multi-objective fixed-charge transportation problem may not be defined precisely, because of globalization of the market, uncontrollable factors, etc. As such, the multi-objective fixed-charge transportation problem is proposed under rough and random rough environments. To tackle uncertain (rough and random rough) parameters, the proposed model employs an expected value operator. Furthermore, a procedure is developed for converting the uncertain multi-objective fixed-charge transportation problem into a deterministic form and then solving the deterministic model. Three different methods, namely, the fuzzy programming, global criterion, and epsilon-constrained methods, are used to derive the optimal compromise solutions of the suggested model. To provide the preferable optimal solution of the formulated problem, a comparison is drawn among the optimal solutions that are extracted from different methods. Herein, the epsilon-constrained method derives a set of optimal solutions and generates an exact Pareto-front. Finally, in order to show the applicability and feasibility of the proposed model, the paper includes a real-life example of a multi-objective fixed-charge transportation problem. The main contribution of the paper is that it. deals with MOFCTP using two types of uncertainties, thus making the decision making process more flexible.

关键词： Fixed-charge transportation problem rough and random rough variables rough programming fuzzy programming global criterion method epsilon-constrained method

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Facing equity in transportation Network Design Problem: A flexible constraints based model

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TRANSPORT POLICY 2017年 55卷 9-17页

作者： Caggiani, Leonardo Camporeale, Rosalia Ottomanelli, Michele DICATECh Dept Civil Environm & Bldg Engn & Chem Politecnico BariViale Orabona4 I-70125 Bari Italy

In transportation planning, solutions designed to meet objectives of equity and social inclusion have to be achieved. From this standpoint, most of Network Design Problem (NDP) models aim at identifying the optimal layout of transportation networks by deterministic bi-level problems formulation to reflect the different goals of at least two decision makers (the network users and the planner). Considering the societal function of transport systems, the NDP, even at operational level, should be addressed also to the research of solutions in which the outcomes of the design (costs and/or benefits) are distributed as much as possible among the potential users or classes of users. Traditional approaches often neglect equity goals that, conversely, should play an important role or define some flows rebalancing problem. In this paper an Equity Based NDP is proposed, where the optimal layout of a road network is determined by minimizing the total system cost under flexible constraints, (jointly with rigid thresholds) by solving a single programming problem. It considers both horizontal and vertical equity criteria in the form of an equity constraint specified for uncertain variables or approximate reasoning environment: this results in a multi-objective fuzzy programming model that aims at maximizing user satisfaction according to all constraints, while taking into account the route choice behaviour of network users. A sensitivity analysis has been performed on a test network, and a comparison with a literature equity based model has been carried out;then, the proposed method has been applied to a real sized network, where an application of equity network design optimization is presented and the results discussed.

关键词： Equity in transportation fuzzy programming Network Design Problem Uncertainty Flexible constraints

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A fuzzy Goal programming Approach for fuzzy Multiobjective Stochastic programming through Expectation Model

A Fuzzy Goal Programming Approach for Fuzzy Multiobjective S...

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2nd International Conference of Mathematical Modelling and Scientific Computation (ICMMSC 2012)

作者： Biswas, Animesh Modak, Nilkanta Univ Kalyani Dept Math Kalyani 741235 W Bengal India

ISBN: (纸本)9783642289255

In this paper a fuzzy goal programming method for modeling and solving multiobjective stochastic decision making problem involving fuzzy random variables associated with the parameters of the objectives as well as system constraints is developed. In the proposed approach. an expectation model is generated on the basis of the mean of the fuzzy random variables involved with the objectives of the problem. Then the problem is converted into an equivalent fuzzy programming model by considering the fuzzily defined chance constraints. Afterwards, the model is decomposed on the basis of the tolerance ranges of the fuzzy numbers associated with the fuzzy parameters of the problem. Now to construct the membership goals of the decomposed objectives under the extended feasible region defined by the decomposed system constraints, the individual optimal values of each objective is calculated in isolation. Then the membership functions are constructed to measure the degree of satisfaction of each decomposed objectives in the decision making environment. The membership functions are then converted into membership goals by assigning unity as the aspiration level of the membership goals. Then a fuzzy goal programming model is developed by minimizing the under deviational variables and thereby obtaining the optimal solution in the decision making environment.

关键词： Stochastic programming Chance constrained programming Expectation model fuzzy random variables fuzzy numbers fuzzy programming fuzzy goal programming

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fuzzy programming for Mixed-Integer Optimization Problems

Fuzzy Programming for Mixed-Integer Optimization Problems

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16th International Symposium on Artificial Life and Robotics (AROB 16th '11)

作者： Lin, Yung-Chin Lin, Yung-Chien Su, Kuo-Lan Lin, Wei-Cheng Chen, Tsing-Hua Natl Yunlin Univ Sci & Technol Dept Elect Engn Yunlin Taiwan WuFeng Univ Dept Elect Engn Chiayi Taiwan I Shou Univ Dept Elect Engn Kaohsiung Taiwan

ISBN: (纸本)9784990288051

Mixed-integer optimization problems belong to NP-hard combinatorial problems. Therefore, they are difficult to search for the global optimal solutions. The mixed-integer optimization problems are always described by precise mathematical programming models. However, many practical mixed-integer optimization problems inherit more or less imprecise nature. Under this circumstance, if we take into account the flexibility of constraints and the fuzziness of objectives, the original mixed-integer optimization problems can be formulated as fuzzy mixed-integer optimization problems. Mixed-integer differential evolution (MIME) is an evolutionary search algorithm, and has been successfully applied to many complex mixed-integer optimization problems. In this paper, a fuzzy mixed-integer mathematical programming model is developed to formulate the fuzzy mixed-integer optimization problem. And then the MIHDE is introduced to solve this fuzzy mixed-integer programming problem. Finally, the illustrative example shows that satisfactory results can be obtained by the proposed method. This demonstrates that the MIHDE can effectively handle the fuzzy mixed-integer optimization problems.

关键词： fuzzy programming mixed-integer optimization evolutionary algorithm

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Multi-objective Solid Transportation Problem in Uncertain Environment

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IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE 2017年第A2期41卷 505-514页

作者： Dalman, Hasan Sivri, Mustafa Gelisim Univ Dept Comp Engn TR-34310 Istanbul Turkey Yildiz Tech Univ Dept Math Engn TR-34210 Istanbul Turkey

Although new information technologies decrease information and transaction costs, transportation problem of physical goods is still relevant. Globalization of trade increased the uncertainty that companies are facing, it also increased the importance of supply chain management in world economies drastically. Because transportation systems are crucial for operation management, the problem of finding efficient and sustainable solutions under such uncertain environments needs to be studied. Thus, this paper focuses on "multi-objective solid transportation problem (STP) in uncertain environment'' and presents some approaches to find the compromised optimal solution of multi-objective STP. Then, compatible with uncertainty, fuzzy programming and some techniques of the fuzzy set theory are implemented to solve the problem by using Maple 17.02. A numerical example is executed and presented here to illustrate suggested procedures.

关键词： Multi-objective solid transportation Interval numbers Goal programming fuzzy programming Global criteria

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