This paper is concerned with the solution procedure of a multi-objective transportation problem with fuzzy stochastic simulation based genetic algorithm. Supplies and demands are considered as a fuzzy random variables...
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This paper is concerned with the solution procedure of a multi-objective transportation problem with fuzzy stochastic simulation based genetic algorithm. Supplies and demands are considered as a fuzzy random variables with fuzzy means and fuzzy variances in proposed multi-objective fuzzy stochastic transportation problem. The first step in fuzzy simulation based genetic algorithm is to deal with aspiration level of the constraints with the help of alpha-cut technique to obtain multi-objective stochastic transportation problem. In next step, fuzzy probabilistic constraints (fuzzy chance constraints) are handled within fuzzy stochastic simulation based genetic algorithm to obtain a feasible region. The feasibilities of the chance constraints are checked by the stochastic programming with the genetic process without deriving the deterministic equivalents. The feasibility condition for the transportation problem is maintained through out the problem. Finally, multiple objective functions are considered in order to generate a Pareto optimal solutions for the fuzzy stochastic transportation problem using the proposed algorithm. The proposed procedure is illustrated by two numerical examples.
We study the downlink resource allocation problem for simultaneous wireless information and power transfer (SWIPT) in small cells underlaying a macrocell in a two-tier heterogeneous network. For SWIPT, we consider bot...
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We study the downlink resource allocation problem for simultaneous wireless information and power transfer (SWIPT) in small cells underlaying a macrocell in a two-tier heterogeneous network. For SWIPT, we consider both time-switching and power-splitting approaches. We determine downlink transmit power of small cell base stations along with time-switching/power-splitting variables for SWIPT to jointly optimize energy harvesting rate and achievable throughput of small cell users while ensuring minimum throughput of macrocell user. In the time-switching approach, the resource allocation problem is formulated as a mixed-integer non-linear programming (MINLP) problem. The formulated MINLP problem is solved by relaxing the binary integer constraint and then identifying the condition at which the obtained solution satisfies that constraint. In both the time-switching and power-splitting approaches, in the presence of non-negligible co-tier interference, the formulated problem is solved sub-optimally by iteratively maximizing the minorant of the non-convex objective function. A special case with negligible co-tier interference is considered in the time-switching approach and the optimal solution is obtained by using convex optimization techniques. Numerical results demonstrate significant gain in energy harvesting rate when macrocell users have flexible interference tolerance levels in time-switching approach, highlight the improvement in energy harvesting rate in the presence of co-tier interference signal, and reveal interesting trade-off in achievable throughput and energy harvesting rate.
The aim of this paper is to develop some new generalized aggregation operators for triangular intuitionistic fuzzy numbers (TIFNs) and apply to multi-attribute group decision making (MAGDM) problems. First, the weight...
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The aim of this paper is to develop some new generalized aggregation operators for triangular intuitionistic fuzzy numbers (TIFNs) and apply to multi-attribute group decision making (MAGDM) problems. First, the weighted possibility attitudinal expected values of TIFNs are defined and a new method is presented to rank TIFNs considering risk attitude of decision maker (DM). The sensitivity analyses on attitudinal character parameter are given. Then, the triangular intuitionistic fuzzy weighted averaging (TIFWA) operator, ordered weighted averaging (TIFOWA) operator, ordered weighted geometric (TIFOWG) operator and hybrid weighted averaging (TIFHWA) operator are defined. We further develop some new generalized aggregation operators for TIFNs, involving the triangular intuitionistic fuzzy generalized ordered weighted averaging (TIFGOWA) operator and generalized hybrid weighted averaging (TIFGHWA) operator. Some desirable properties for these operators are discussed in detail. Utilizing the TIFGHWA and TIFWA operators, we propose a new method for MAGDM with TIFNs and incomplete weight information. In this method, DMs' weights are determined by Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and the weights of attributes are objectively derived through constructing a multi-objective programming model which is transformed into a linear goal program to solve. Finally, the example analysis of an investment selection example verifies the effectiveness and practicability of the proposed method in this paper. (C) 2015 Elsevier Ltd. All rights reserved.
We consider a class of multi-objective probabilistically constrained programs (MOPCP) with a joint probabilistic constraint and a variable risk level. We consider two cases with only a random right-hand side vector or...
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We consider a class of multi-objective probabilistically constrained programs (MOPCP) with a joint probabilistic constraint and a variable risk level. We consider two cases with only a random right-hand side vector or a multi-row random technology matrix, and propose a Boolean modeling framework to derive new mixed-integer linear programs (MILP) that are either equivalent reformulations or inner approximations of MOPCP, respectively. Via testing randomly generated MOPCP instances, we demonstrate modeling insights pertaining to the most suitable MILP, to the trade-offs between conflicting objectives of cost/revenue and reliability, and to the parameter scalarization determining relative importance of each objective. We then focus on several MOPCP variants of a multi-portfolio financial optimization problem to implement a downside risk measure, which can be used in a centralized or decentralized investment context. We study the impact of modeling parameters on the portfolios, show, via a cross-validation study, robustness of MOPCP, and perform a comparative analysis of the optimal investment decisions. (C) 2016 Elsevier B.V. All rights reserved.
Owing to more vague concepts frequently represented in decision data, intuitionistic fuzzy sets (IFSs) are more fliexibly used to model real-life decision situations. At the same time, with ever increasing complexity ...
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Owing to more vague concepts frequently represented in decision data, intuitionistic fuzzy sets (IFSs) are more fliexibly used to model real-life decision situations. At the same time, with ever increasing complexity in many decision situations in reality, there are often some challenges for a decision maker to provide complete attribute preference information, i.e., the weights may be completely unknown or partially known. The aim of this paper is to develop an effiective method for solving intuitionistic fuzzy multi-attribute decision making (MADM) problems with incomplete weight information. In this method, ratings of alternatives on attributes are expressed with IFSs. The multi-objective programming models are established to calculate unknown weights by using weight information partially known a priori. The derived minimum weighted Minkowski distance power models are used to determine the unknown weights and to generate the ranking order of the alternatives simultaneously. The proposed models are easily extended to intuitionistic fuzzy MADM problems with different weight information structures. An example of the supplier selection problem is examined to demonstrate applicability and flexibility of the proposed models and method.
This paper presents an integrated decision support methodology for locating bank branches. The methodology is composed of two stages: problem structuring, and modeling. In the first stage, initially, a number of crite...
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This paper presents an integrated decision support methodology for locating bank branches. The methodology is composed of two stages: problem structuring, and modeling. In the first stage, initially, a number of criteria are selected with the help of a detailed literature review and expert opinions. Subsequently, importance weights of these criteria for different types of bank branches are identified based on judgments of experts for pairwise comparison questions. At the modeling stage, considering the characteristics and importance of the criteria, a novel multiobjective mathematical programming model is proposed to find specific locations of bank branches. The proposed methodology is applied in locating branches of a Turkish bank. In order to test the validity of the results and robustness, a sensitivity analysis is conducted and the solutions are found to be robust.
This paper is concerned with multi-objective fuzzy stochastic model for determination of optimum cropping patterns with water balance for the next crop season. The objective functions of the model is to study the effe...
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This paper is concerned with multi-objective fuzzy stochastic model for determination of optimum cropping patterns with water balance for the next crop season. The objective functions of the model is to study the effect of various cropping patterns on crop production subject to total water supply in a small farm. The decision variables are the cultivated area of different crops at the farm. The water requirement of the crops follows fuzzy uniform distribution and yields in the objective functions are taken as a fuzzy numbers. The model is solved by using fuzzy stochastic simulation based genetic algorithm without deriving the deterministic equivalents.
We introduce in this paper a new definition for the overall system efficiency in network DEA, which is inspired by the "weak link" notion in supply chains and the maximum-flow/minimum- cut problem in network...
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We introduce in this paper a new definition for the overall system efficiency in network DEA, which is inspired by the "weak link" notion in supply chains and the maximum-flow/minimum- cut problem in networks. We use a two-phase max-min optimization technique in a multi-objective programming framework to estimate the individual stage efficiencies and the overall system efficiency in two-stage processes of varying complexity. This enables us to estimate unique and unbiased efficiency scores and, if required, to drive the efficiency assessments effectively in line with specific priorities given to the stages. A comparison with the multiplicative decomposition approach on data drawn from the literature brings into light the advantages of our method. (C) 2016 Elsevier B.V. All rights reserved.
Water quality management is a significant item in the sustainable development of wetland system, since the environmental influences from the economic development are becoming more and more obvious. In this study, an i...
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Water quality management is a significant item in the sustainable development of wetland system, since the environmental influences from the economic development are becoming more and more obvious. In this study, an inexact left-hand-side chance-constrained fuzzy multi-objective programming (ILCFMOP) approach was proposed and applied to water quality management in a wetland system to analyze the tradeoffs among multiple objectives of total net benefit, water quality, water resource utilization and water treatment cost. The ILCFMOP integrates interval programming, left-hand-side chance-constrained programming, and fuzzy multi-objective programming within an optimization framework. It can both handle multiple objectives and quantify multiple uncertainties, including fuzziness (aspiration level of objectives), randomness (pollutant release limitation), and interval parameters (e. g. water resources, and wastewater treatment costs). A representative water pollution control case study in a wetland system is employed for demonstration. The optimal schemes were analyzed under scenarios at different probabilities (pi, denotes the admissible probability of violating the constraint i). The optimal solutions indicated that, most of the objectives would decrease with increasing probability levels from scenarios 1 to 3, since a higher constraint satisfaction probability would lead to stricter decision scopes. This study is the first application of the ILCFMOP model to water quality management in a wetland system, which indicates that it is applicable to other environmental problems under uncertainties.
This study proposed a multi-objective environmental reservoir operation methodology (MOEROM) and applied the new methodology to the Three Gorges Reservoir (TGR) in China. The MOEROM directly incorporated the statistic...
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This study proposed a multi-objective environmental reservoir operation methodology (MOEROM) and applied the new methodology to the Three Gorges Reservoir (TGR) in China. The MOEROM directly incorporated the statistical water quality models in the objective functions to reflect the response relationships between reservoir operations and water quality in three tributaries (the Xiangxi River, the Daning River and the Xiaojing River). A real-coded genetic algorithm with self-adaptive crossover operators was employed to solve the environmental reservoir operation model. And four different MCDA approaches (AHP, TOPSIS, Fuzzy AHP, and Fuzzy TOPSIS) were proposed to evaluate the optimal operational schemes. The results showed that TOPSIS and AHP were more suitable for selecting the schemes than the others because of the larger fluctuations. To demonstrate the advantage of MOEROM, the environmental operation schemes were compared with traditional and practical operation schemes in 2013. The advantages of the environmental operation scheme over the others were that it would help reach a compromise between economic benefit, flood control and water quality improvement. In the future, more water quality indices, uncertainties in water environmental information, and more efficient algorithms would be further considered and researched.
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