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interactive fuzzy programming based on a probability maximization model for two-level Stochastic linear programming problems

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 2006年第2期89卷 33-42页

作者： Kato, K Katagiri, H Sakawa, M Wang, JT Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan

In this paper, considering the two-level linear programming problem, which is a numerical model for the optimization of a hierarchical system by two decisionmakers, we focus on the situation where the coefficients are stochastic variables and reduce the formulated two-level stochastic linear programming problem to an ordinary two-level programming problem based on the probability maximization model in chance-constrained programming. Based on the assumption that motivation exists for cooperation between the high-level decisionmaker and the low-level decisionmaker in this resulting two-level programming problem, we consider interactive fuzzy programming that interactively derives a satisfactory solution of the high-level decisionmaker while considering the balance with the degree of satisfaction of the low-level decisionmaker. (c) 2005 Wiley Periodicals, Inc.

关键词： two-level stochastic linear programining problem chance constraint probability maximization model interactive fuzzy programming

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interactive fuzzy programming using partial information about preference for multiobjective two-level linear fractional programming problems

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ELECTRONICS AND COMMUNICATIONS IN JAPAN PART III-FUNDAMENTAL ELECTRONIC SCIENCE 2003年第9期86卷 54-62页

作者： Shen, YX Sakawa, M Nishizaki, I Hiroshima Univ Dept Artificial Complex Syst Engn Grad Sch Engn Higashi 7398527 Japan

This paper proposes an interactive fuzzy programming method for seeking a satisfactory solution for multiobjective two-level linear fractional programming problems in which the decision makers in the upper and lower levels have several objectives, by first setting up the fuzzy goals for several objectives of each decision maker and seeking a satisfactory solution for the degree of satisfaction of two decision makers in a cooperative manner. In the proposed method, the decision maker at the upper level sets the minimal satisfactory levels for each fuzzy goal and the decision maker at the lower level determines the aspiration levels. The minimal satisfactory levels are treated as a constraint and the solution closest to the aspiration levels of the decision maker at the lower level is computed. The ratio of the aggregative degrees of satisfaction of the decision makers in the upper and lower levels with the obtained solution is evaluated by using partial information on the preference of the decision makers. If the ratio of the degrees of satisfaction satisfies the given condition and the decision maker at the upper level is satisfied with this solution, then the interaction is complete. Otherwise, a satisfactory solution is sought by updating the minimal satisfactory and aspiration levels. (C) 2003 Wiley Periodicals, Inc.

关键词： multiobjective two-level linear fractional programming problem interactive fuzzy programming fuzzy goal partial information on preference

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Green road-rail intermodal routing problem with improved pickup and delivery services integrating truck departure time planning under uncertainty: an interactive fuzzy programming approach

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COMPLEX & INTELLIGENT SYSTEMS 2022年第2期8卷 1459-1486页

作者： Sun, Yan Yu, Nan Huang, Baoliang Shandong Univ Finance & Econ Sch Management Sci & Engn Jinan 250014 Shandong Peoples R China China Waterborne Transport Res Inst Beijing 100088 Peoples R China Shandong Univ Finance & Econ Sch Int Trade & Econ Jinan 250014 Shandong Peoples R China

This paper addresses the multi-objective optimization for the road-rail intermodal routing problem that aims to minimize the total costs and carbon dioxide emissions of the routes. To achieve high timeliness of the entire transportation process, pickup and delivery services are simultaneously improved based on the employment of fuzzy soft time windows to measure their service levels. The modeling of road-rail intermodal routing considers fixed schedules of rail and time flexibility of road to match the real-world transportation scenario, in which travel times and carbon dioxide emission factors of road services are considered to be time-varying. To improve the feasibility of the routing, uncertainty of travel times and carbon dioxide emission factors of road services and capacities of rail services are incorporated into the problem. By applying trapezoidal fuzzy numbers to formulate the uncertainty, we propose a fuzzy multi-objective nonlinear optimization model for the routing problem that integrates the truck departure time planning for road services. After processing the model with fuzzy chance-constrained programming and linearization, we obtain an auxiliary equivalent crisp linear model and solve it by designing an interactive fuzzy programming approach with the Bounded Objective Function method. Based on an empirical case study, we demonstrate the validity of the proposed approach and discuss the effects of improving the confidence levels and service levels on the optimization results. The case analysis reveals several managerial insights that help to realize an efficient transportation organization by making effective trade-offs among lowering costs, reducing emissions, improving service levels, and enhancing feasibility.

关键词： Green routing Road-rail intermodal transportation Service level Carbon dioxide emissions Truck departure time planning Uncertainty Multi-objective optimization interactive fuzzy programming

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interactive fuzzy stochastic multi-level 0-1 programming using tabu search and probability maximization

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EXPERT SYSTEMS WITH APPLICATIONS 2014年第6期41卷 2957-2963页

作者： Sakawa, Masatoshi Matsui, Takeshi Hiroshima Univ Fac Engn Higashihiroshima 7398527 Japan

In this paper, we consider interactive fuzzy programming for multi-level 0-1 programming problems involving random variable coefficients both in objective functions and constraints. Following the probability maximization model together with the concept of chance constraints, the formulated stochastic multi-level 0-1 programming problems are transformed into deterministic ones. Taking into account vagueness of judgments of the decision makers, we present interactive fuzzy programming. In the proposed interactive method, after determining the fuzzy goals of the decision makers at all levels, a satisfactory solution is derived efficiently by updating satisfactory levels of the decision makers with considerations of overall satisfactory balance among all levels. For solving the transformed deterministic problems efficiently, we also introduce novel tabu search for general 0-1 programming problems. A numerical example for a three-level 0-1 programming problem is provided to illustrate the proposed method. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Multi-level programming Random variables interactive fuzzy programming Probability maximization Tabu search 0-1 programming

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interactive fuzzy stochastic two-level linear programming with simple recourse

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INFORMATION SCIENCES 2014年 278卷 67-75页

作者： Sakawa, Masatoshi Katagiri, Hideki Matsui, Takeshi Hiroshima Univ Fac Engn Dept Syst Cybernet Higashihiroshima 7398527 Japan

In this paper, assuming cooperative behavior of the decision makers, two-level linear programming problems involving random variables in constraints are considered. Using the concept of simple recourse, the formulated stochastic two-level simple recourse problems are transformed into deterministic two-level programming ones. Taking into account vagueness of judgments of the decision makers, interactive fuzzy programming is presented. In the proposed interactive method, after determining the fuzzy goals of the decision makers at both levels, a satisfactory solution is derived efficiently by updating the satisfactory degree of the decision maker at the upper level with considerations of overall satisfactory balance between both levels. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Two-level linear programming Random variable Simple recourse interactive fuzzy programming

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interactive fuzzy stochastic two-level integer programming through fractile criterion optimization

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OPERATIONAL RESEARCH 2012年第2期12卷 209-227页

作者： Sakawa, Masatoshi Katagiri, Hideki Matsui, Takeshi Hiroshima Univ Fac Engn Higashihiroshima 7398527 Japan

In this paper, we focus on stochastic two-level integer programming problems with cooperative decision makers. Using the fractile criterion optimization model in chance constrained programming, the formulated stochastic two-level integer programming problems are transformed into deterministic ones. Taking into account vagueness of judgments of the decision makers, we present an interactive fuzzy programming method to derive a satisfactory solution through interactions with the upper-level decision maker in consideration of the cooperative relation to the lower-level decision maker. For solving transformed deterministic problems efficiently, we also introduce genetic algorithms with double strings for nonlinear integer programming problems. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.

关键词： Two-level integer programming Stochastic programming interactive fuzzy programming Chance constraints Fractile criterion optimization Genetic algorithms Double strings

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interactive fuzzy-Boundary Interval programming for Water Resources Management of the Hetao Basin, China

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JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING 2016年第12期142卷 016056-1-016056-13页

作者： Niu, G. Li, Y. P. Huang, G. H. Liu, J. Chen, M. North China Elect Power Univ Sino Canada Resources & Environm Res Acad Beijing 102206 Peoples R China Beijing Normal Univ Sch Environm Beijing 100875 Peoples R China Univ Regina Fac Engn & Appl Sci Environm Syst Engn Program Regina SK S4S 0A2 Canada

In this study, an interactive fuzzy-boundary interval programming (IFBIP) method is developed to plan water resources management under uncertain conditions. IFBIP is capable of addressing dual uncertainties expressed as fuzzy-boundary intervals, as well as analyzing the reliability of satisfying (or the risk of violating) various constraints. The IFBIP method is then applied to the water resources management of the Hetao Basin (located in Inner Mongolia, China), one of the largest irrigation areas and the main food-producing region in the Yellow River Basin, where water scarcity is a major constraint for socioeconomic development. Results of water-allocation pattern and system benefit have been obtained under different feasibility degrees. Results reveal that agricultural irrigation is still the largest water consumer, compared with the other users such as industry, municipality, and livestock;meanwhile, irrigation water in each subarea is mainly from the Yellow River over the planning horizon. Moreover, water-saving technology and irrigation regime are relative backward, leading to more inefficient water usage. The findings can facilitate local managers in generating desired decisions of water-related activities with maximized system benefit and minimized water shortage. (C) 2016 American Society of Civil Engineers.

关键词： Agricultural irrigation Dual uncertainties fuzzy-boundary interval interactive fuzzy programming Management Water resources

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interactive fuzzy Boundary Interval programming for Air Quality Management Under Uncertainty

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WATER AIR AND SOIL POLLUTION 2013年第5期224卷 1574-1574页

作者： Wang, S. Huang, G. H. Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada

This paper presents an interactive fuzzy boundary interval programming (IFBIP) approach for addressing dual uncertainties that exist in the objective function and the left-and right-hand sides of constraints. IFBIP permits an interactive participation of the decision maker (DM) in all steps of the decision process through expressing his/her preferences in linguistic terms. A regional air quality management problem is studied to illustrate the proposed approach. The results indicate that a number of decision alternatives can be obtained under different feasibility degrees of constraints. They can help quantify the relationship between the total operating cost and the constraint violation risk, which is meaningful not only for supporting an in-depth analysis of the tradeoff between the economic objective and the system safety but also for the DM to identify a desired compromise between two conflicting concerns: the satisfaction degree of the goal and the feasibility degree of constraints.

关键词： Air quality management Dual uncertainties fuzzy boundary interval interactive fuzzy programming Interval

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Solving Tea Blending Problems Using interactive fuzzy Multi-Objective Linear programming

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PROCESSES 2023年第1期11卷 49-49页

作者： Jarernsuk, Saran Phruksaphanrat, Busaba Thammasat Univ Fac Engn Thammasat Sch Engn Res Unit Ind Stat & Operat ResInd Engn Dept Pathum Thani 12121 Thailand

Blending is a classical and well-known optimization problem that has been applied in the food, steel, and composite material industries. However, tea blending is more complicated than general problems due to the variety of products, processes, and sources of raw materials and semi-products. So, in this research, a fuzzy multi-objective model for the tea blending problem was proposed to minimize the total production cost and the deviation of quality target score;it provides a more robust and flexible method than existing models for complex real-world problems. Existing research works of a blending problem consider only raw material cost, but semi-product cost and processing cost are included in the proposed model that matches the actual case. Losses that occur during production are also incorporated. The selection of appropriate raw materials and semi-product sources can be obtained with the preferred levels of cost and quality by the proposed algorithm. The interactive fuzzy multi-objective programming to solve the problem has advantages over existing interactive programming methods. It is easy to manipulate interactively to obtain more efficient solutions than existing methods and both balanced and unbalanced solutions can be selected. The comparison of the results of an existing approach and the interactive fuzzy multi-objective programming algorithm for the tea industry is illustrated.

关键词： blending problem tea industry interactive fuzzy programming multi-objective decision making fuzzy-efficient solution

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Bilevel Optimization of Regional Water Resources Allocation Problem under fuzzy Random Environment

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JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT 2013年第3期139卷 246-264页

作者： Xu, Jiuping Tu, Yan Zeng, Ziqiang Sichuan Univ State Key Lab Hydraul & Mt River Engn Chengdu 610064 Peoples R China Sichuan Univ Uncertainty Decis Making Lab Chengdu 610064 Peoples R China

The allocation of water resources has long been recognized as a critical optimization problem. In this study, a bilevel programming model with fuzzy random variables is developed for tackling a regional water resources allocation problem on the basis of water rights distribution in a river basin. The bilevel programming model takes the optimal total benefit of the society and the optimal economic benefit of each subarea as the upper and lower targets, respectively. In contrast to previous studies, the balance of the satisfactory degree between the upper and lower decision makers is considered in the bilevel optimization for ensuring the equity of the water resource allocation. To deal with inherent uncertainties, the fuzzy random variables are first transformed into trapezoidal fuzzy numbers, and by taking advantage of the expected value operation, the trapezoidal fuzzy numbers are subsequently defuzzified. For solving the complex and nonlinear bilevel programming model, an interactive fuzzy programming technique and an entropy-Boltzmann selection-based genetic algorithm are designed as a combined solution method. Finally, the results and comparisons analysis of a case study are presented to demonstrate the practicality and efficiency of the optimization method. DOI: 10.1061/(ASCE)WR.1943-5452.0000248. (C) 2013 American Society of Civil Engineers.

关键词： Regional water resources allocation Water rights Bilevel optimization fuzzy random interactive fuzzy programming Algorithms

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