In most multi-objective optimization problems we aim at selecting the most preferred among the generated Pareto optimal solutions (a subjective selection among objectively determined solutions). In this paper we consi...
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In most multi-objective optimization problems we aim at selecting the most preferred among the generated Pareto optimal solutions (a subjective selection among objectively determined solutions). In this paper we consider the robustness of the selected Pareto optimal solution in relation to perturbations within weights of the objective functions. For this task we design an integrated approach that can be used in multi-objective discrete and continuous problems using a combination of Monte Carlo simulation and optimization. In the proposed method we introduce measures of robustness for Pareto optimal solutions. In this way we can compare them according to their robustness, introducing one more characteristic for the Pareto optimal solution quality. In addition, especially in multi-objective discrete problems, we can detect the most robust Pareto optimal solution among neighboring ones. A computational experiment is designed in order to illustrate the method and its advantages. It is noteworthy that the Augmented Weighted Tchebycheff proved to be much more reliable than the conventional weighted sum method in discrete problems, due to the existence of unsupported Pareto optimal solutions. (C) 2014 Elsevier B.V. All rights reserved.
Generally, in project time, cost and quality trade-off problems, the decision maker (DM) has to take different conflicting objectives into account in order to find an optimal solution. In project management literature...
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Generally, in project time, cost and quality trade-off problems, the decision maker (DM) has to take different conflicting objectives into account in order to find an optimal solution. In project management literature, many models have been developed for project crashing and project time-cost trade-off, but only a few of them consider quality as an objective. This article employs a chance constrained compromise programming approach (CCCP) to solve the time, cost and quality trade-off problem (TCQTP). The purpose of this paper is to present and test a new model for the project time, cost and quality problem. In fact, we try to find the optimal decrease in cost and duration of activities while maximizing quality under uncertainty conditions. In order to expect more realistic outcomes for the problem of uncertainties in project activities, time should be taken into account. Therefore, we assume the activity duration as a random and normally distributed parameter. An example of a project network, consisting of 6 nodes and 7 activities, is analyzed under different uncertainty levels.
Crisp multi-objective programming has been applied successfully in many fields. But in real applications, the decision environment often exists randomness and the objectives are fuzzy. So it is significant and valuabl...
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ISBN:
(纸本)9781510803084
Crisp multi-objective programming has been applied successfully in many fields. But in real applications, the decision environment often exists randomness and the objectives are fuzzy. So it is significant and valuable to establish a fuzzy multi-objective programming model under random environment. In this paper, we use fuzzy number to represent the fuzzy events and fuzzy objectives. Firstly, the general formula of effect probability based on continuous distributions is given combined with effect theory, and a special one based on normal distribution is further given. Secondly, an effect probability-based fuzzy multi-objective programming(abbreviated as FMO-EP) model is proposed by regarding fuzzy objectives as fuzzy events. Finally, the effectiveness and interpretability of FMO-EP is proved through a case.
This paper presents a new fuzzy clustering approach based on an efficient fuzzy distance measurement and multi-objective mathematical programming. As the human intuitions implies, it is not rational to measure the dis...
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This paper presents a new fuzzy clustering approach based on an efficient fuzzy distance measurement and multi-objective mathematical programming. As the human intuitions implies, it is not rational to measure the distance between two fuzzy clusters by a crisp measurement. Unfortunately, most of the existing fuzzy clustering approaches, consider the distance between two fuzzy clusters as a crisp value. This will yield a rounding error and is assumed a pitfall. In this paper, an efficient fuzzy distance measurement is developed in order to measure distance between multi-dimensional fuzzy clusters as a fuzzy measure. The triangle fuzzy numbers (TFNs) are used to develop the applicable fuzzy clustering approach. Then, multi-objective mathematical programming is utilized to optimize the center, and left and right spreads of fuzzy clusters which are calculated as TFNs. More formally, the advantages of proposed fuzzy clustering in comparison with existing procedure is (a) developing an efficient fuzzy distance measurement, and (b) optimizing the center and spread of the fuzzy clusters using multi-objective mathematical programming. An illustrative random simulated instance is supplied in order to present the mechanism and calculations of the proposed fuzzy clustering approach. The performance of proposed fuzzy clustering approach is compared with an existing Fuzzy C-means approach in the literature on several benchmark instances. Then, the Error Ratio is defined to compare the performance of both methods and comprehensive statistical analysis and hypothesis test are accomplished to test the performance of both methods. Finally, a real case study, called group decision making multi-possibility multi-choice investment partitioning problem, is discussed in order to illustrate the efficacy and applicability of the proposed approach in real world problems. The proposed approach is straightforward, its quality is as well as existing approach in the literature and its results ar
From perspective of energy security, this study focuses on oil-importing optimal decision based on multi-objective programming approach. Different from other models, country risk is considered as the main objective to...
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From perspective of energy security, this study focuses on oil-importing optimal decision based on multi-objective programming approach. Different from other models, country risk is considered as the main objective to minimize risk exposure of importing disruption. What is more, this model connects emergency management with programming, and optimal decisions are solved under different scenarios of emergency, where one given kind of extreme events break out and impact exporting regions to different degrees. Specifically, two main steps are involved in the proposed methodology, including impact analysis of the extreme events and optimization programming under scenarios of emergency. The first step is to statistically analyze whether and to what extent the given extreme events impact country risk of oil-exporting sources. Secondly, a multi-objective programming model is formulated, and optimal decision is simulated under different scenarios with extreme events. For illustration, China's oil-importing optimization is performed to verify the practicability of the novel methodology. The experimental results suggest that wars in Middle East may significantly enhance country risk of Middle East;and China's oil-importing optimal plan should be changed correspondingly. This further indicates that the proposed methodology can be utilized as an effective tool to adjust oil-importing plan according to certain extreme events. (C) 2011 Elsevier Ltd. All rights reserved.
A copula-measure Me based interval multi-objectivemulti-stage stochastic chance-constrained programming (CMIMOMSP) model is proposed for water consumption optimization. It can conduct water allocation amid multiple u...
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A copula-measure Me based interval multi-objectivemulti-stage stochastic chance-constrained programming (CMIMOMSP) model is proposed for water consumption optimization. It can conduct water allocation amid multiple users and multiple stages, and deal with the uncertainties presented as interval numbers, random fuzzy interval numbers, and stochastic variables. It improves upon multi-stage stochastic chance-constrained programming by introducing the multi-objective programming, and it can tradeoff the relationships amid economic benefit, full usage of water resources, and economic loss. It enhances the accuracy of copula function and conditional distribution function through proposing the interval functions. Besides, it can deal with the impact of the decision attitudes of managers on water allocation by formulating the function equation between water demand and the optimistic-pessimistic factor. The CMIMOMSP model is applied to a case study of the Heihe River Basin to verify its application. The results indicate that: (1) the optimistic-pessimistic factors have different degrees of positive influences on water allocation for industrial, domestic and ecological sectors;(2) the joint violated probability and optimistic-pessimistic factor have various range of impacts on agricultural water allocation;(3) tthe objective function values have different variation tendencies with the rise of joint violated probabilities and optimistic-pessimistic factors. Its robustness is enhanced by comparing it with the three single-objectiveprogramming models. The CMIMOMSP model can provide various water allocation schemes for managers with different risk attitudes in semi-arid and arid districts.
This paper discusses a new algorithm for generating the Pareto frontier for bi-level multi-objective rough nonlinear programming problem (BL-MRNPP). In this algorithm, the uncertainty exists in constraints which are m...
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This paper discusses a new algorithm for generating the Pareto frontier for bi-level multi-objective rough nonlinear programming problem (BL-MRNPP). In this algorithm, the uncertainty exists in constraints which are modeled as a rough set. Initially, BL-MRNPP is transformed into four deterministic models. The weighted method and the Karush-Kuhn-Tucker optimality condition are combined to obtain the Pareto front of each model. The nature of the problem solutions is characterized according to newly proposed definitions. The location of efficient solutions depending on the lower/upper approximation set is discussed. The aim of the proposed solution procedure for the BL-MRNPP is to avoid solving four problems. A numerical example is solved to indicate the applicability of the proposed algorithm. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Ain Shams University.
multi-objective programming with uncertain information has been widely applied in modeling of industrial produce and logistic distribution problems. Usually the expectation value model and chance-constrained model as ...
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multi-objective programming with uncertain information has been widely applied in modeling of industrial produce and logistic distribution problems. Usually the expectation value model and chance-constrained model as solution models are used to deal with such uncertain programming. In this paper, we consider the uncertain programming problem which contains random information and rough information and is hard to be solved. A new solution model, called stochastic rough multi-objective synthesis effect (MOSE) model, is developed to deal with a class of multi-objective programming problems with random rough coefficients. The MOSE model contains expectation value model and chance-constrained model by choosing different synthesis effect functions and can be considered as an extension of crisp multi-objective programming model. Combined with genetic algorithm, the optimal solution of the MOSE model can be obtained. It shows that the solutions of the MOSE model are better than that of other solution models. Finally, an illustrative example is provided to show the effectiveness of the proposed method.
This study proposes the multi-objective programming (MOP) method for solving network DEA (NDEA) models. In the proposed method, the divisional efficiencies (within an organization) and the overall efficiency of the or...
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This study proposes the multi-objective programming (MOP) method for solving network DEA (NDEA) models. In the proposed method, the divisional efficiencies (within an organization) and the overall efficiency of the organization are formulated as separate objective functions in the multi-objective programming model. Compared with conventional DEA where the intermediate processes and products are ignored, this work measures the organization's overall efficiency without neglecting the efficiencies of its subunits. Two case studies demonstrate the proposed NDEA-MOP's utility in measuring the efficiencies of an organization with concerning interactive internal process. (C) 2014 Elsevier B.V. All rights reserved.
In this study, a fuzzy dependent-chance interval multi-objective stochastic expected value programming model is developed for irrigation water resources management under uncertainties. It incorporates fuzzy dependent-...
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In this study, a fuzzy dependent-chance interval multi-objective stochastic expected value programming model is developed for irrigation water resources management under uncertainties. It incorporates fuzzy dependent-chance programming, stochastic expected value programming, interval programming into multi-objective programming. Compared with conventional programming methods, it can quantify the relationship between the expected values of stochastic variables and the fuzzy goals of expected values set by decision-makers through the satisfactory degrees, and trade-off the relationship amid multiple satisfactory degrees selected as objective functions. Besides, it can cope with uncertainties expressed as interval numbers, fuzzy numbers, and stochastic variables. Moreover, the fairness of water allocation constraints formulated by the GINI coefficient can achieve the interactions between fair water allocation and satisfactory degrees. The model is applied to a real case study of irrigation water resources management of different water types (i.e., surface water and groundwater) under different water flow levels (high, medium, and low flow levels) in the midstream region of the Heihe River basin, northwest China. The results reveal that: (1) maximum water demands of wheat and economic crop are satisfied while that of corn is not met under three flow levels;(2) the expected economic benefit and water shortages of crops have positive relationships with water allocation while the expected canal water loss has a negative relationship with water allocation;(3) the bigger expected economic benefit results in the higher satisfactory degree of the expected economic benefit while the lower expected water shortage and canal water loss lead to higher satisfactory degrees of expected water shortage and canal water loss. It shows that the developed model can overcome the disadvantages of the single-objectiveprogramming of putting attention to the satisfactory degree of a kind of ex
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