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A multi-objective nonlinear integer programming model for mixed runway operations within the TMAs

AERONAUTICAL JOURNAL 2024年第1320期128卷 340-370页

作者： Kaplan, Z. Cetek, C. Sarac, T. Eskisehir Tech Univ Air Traff Control Dept TR-26555 Iki Eylul Eskisehir Turkiye Eskisehir Osmangazi Univ Ind Engn Dept TR-26480 Meselik Eskisehir Turkiye

Global air traffic demand has shown rapid growth for the last three decades. This growth led to more delays and congestion within terminal manoeuvring areas (TMAs) around major airports. The efficient use of airport capacities through the careful planning of air traffic flows is imperative to overcome these problems. In this study, a mixed-integer nonlinear programming (MINLP) model with a multi-objective approach was developed to solve the aircraft sequencing and scheduling problem for mixed runway operations within the TMAs. The model contains fuel cost functions based on airspeed, altitude, bank angle, and the aerodynamic characteristics of the aircraft. The optimisation problem was solved by using the epsilon-constraint method where total delay and total fuel functions were simultaneously optimised. We tested the model with different scenarios generated based on the real traffic data of Istanbul Sabiha Gokcen Airport. The results revealed that the average total delay and average total fuel were reduced by 26.4% and 6.7%, respectively.

关键词： multi-objective programming Air traffic management Aircraft sequencing and scheduling problem Mixed-integer nonlinear programming

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Advantages, sensitivity and application efficiency of the new iterative method to solve multi-objective linear fractional programming problem

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2023年第3期31卷 751-767页

作者： Peric, Tunjo Matejas, Josip Babic, Zoran Univ Zagreb Fac Econ & Business Dept Math Trg J F Kennedya 6 Zagreb 10000 Croatia Univ Split Rudera Boskovica 31 Split 21000 Croatia

In the paper we consider advantages, sensitivity and application efficiency of the new method for solving multi-objective linear fractional programming problems. The proposed method is an iterative and numerically simple method that provides a unique solution in each iteration. The obtained solution is iteratively evaluated with the possibility of coarse and fine adjustment based on aspirations and cooperation among decision makers. Some relevant examples from the literature were used to present the stated properties and advantages of the proposed method in relation to the existing ones.

关键词： multi-objective programming Linear fractional programming Iterative method Sensitivity Efficient solution

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multi-objective Fuzzy Probabilistic programming Approach for Obtaining Optimum Crops Pattern with Water Replenishment

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International Journal of Applied and Computational Mathematics 2024年第4期10卷 1-21页

作者： Dutta, S. Sahoo, B.C. Bhanavi, S. Nethra, S. Department of Advanced Computing St. Joseph’s University Karnataka Bengaluru India Department of Soil and Water Conservation Engineering College of Agricultural Engineering and Technology Bhubaneswar India Department of Mathematics St. Joseph’s University Karnataka Bengaluru India

This research paper is concerned with the solution procedure of a multi-objective fuzzy probabilistic problem (MOFPP), taking different crop patterns as the objective functions and water requirements of crops as constraints, which is then solved using fuzzy programming technique. In order to handle fuzzy probabilistic constraints, a transformation technique is developed for fuzzy uniform distribution. As the study area receives less rainfall, the cultivation is mainly dependent on irrigation water. A continual use of underground water for irrigation led to a substantial decrease in the water level of the surrounding area. So, to uplift the underground water level, a proper selection of crops can play a vital role in the replenishment of underground water without compensating the farmer’s income. To illustrate the above technique, a case study is provided with the cultivated area of different crops as a decision variable. The two objective functions are taken as the yield of crops taken as fuzzy number and profit obtained by the farmers after selling the products. A comparison table is furnished in the result section for making better decisions. The study reveals that planting a combination of beans, bitter-gourd, and cabbages will yield maximum profit. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2024.

关键词： 60A86 60A86 97M40 Cropping pattern Fuzzy probabilistic programming multi-objective programming

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Uncertain programming model for designing multi-objective reverse logistics networks

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CLEANER LOGISTICS AND SUPPLY CHAIN 2024年 11卷

作者： Xia, Hanbing Chen, Zhiyuan Milisavljevic-Syed, Jelena Salonitis, Konstantinos Cranfield Univ Sustainable Mfg Syst Ctr Sch Aerosp Transport & Mfg Cranfield MK43 0AL England

Given the contradiction between the rapid growth of products and the modest recovery rate of end-of-life products, there is a pressing need to understand the societal significance of establishing a reverse logistics network for end-of-life products. This research constructs an open-loop five-tier reverse logistic network model encompassing customers, centres for collection, disassembly and inspection, remanufacturing, and disposal. A multi-objective mixed-integer nonlinear programming model under uncertainty has been developed. Unlike previous research, this model accounts for surrounding residents' disutility of facilities while simultaneously minimizing economic costs and environmental impact. Besides, uncertainty theory is introduced in solving the proposed model. More specifically, the formulated model converts all uncertain variables into uncertain distributions by implementing the uncertain multi-objective programming method. Furthermore, a customised non- dominated sorting genetic algorithm III (NSGA-III) is proposed and is employed for the first time to address facility selection and recycling volume distribution within the network. The model is then validated using a real- life case study focusing on end-of-life vehicles in Changchun, China. This research could assist decision-makers in both governmental and private sectors in achieving a balanced approach to the interests of the economy, environment, and local communities comprehensively when designing reverse supply chains.

关键词： Reverse logistics network multi-objective programming Uncertainty theory End-of-life products Non-dominated sorting genetic algorithm III

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A class of multi-objective mathematical programming problems in a rough environment

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SCIENTIA IRANICA 2016年第1期23卷 301-315页

作者： Hamzehee, A. Yaghoobi, M. A. Mashinchi, M. Shahid Bahonar Univ Kerman Fac Math & Comp Dept Math Kerman Iran Shahid Bahonar Univ Kerman Fac Math & Comp Dept Stat Kerman Iran Islamic Azad Univ Kerman Branch Fac Basic Sci Dept Math Kerman Iran

This paper presents a set of multi-objective programming problems in a rough environment. These problems are classified into five classes according to the location of the roughness in the objective functions or the feasible set. We study the class in which all of the objective functions are crisp and the feasible region is a rough set and, in particular, discuss the properties of the complete and efficient (Pareto optimal) solutions of rough multi-objective programming problems. In order to obtain these solutions, we need certain theorems, which we derive. Finally, we illustrate our results by examples. (C) 2016 Sharif University of Technology. All rights reserved.

关键词： Rough set multi-objective programming Rough programming Complete-optimal solutions Efficient solutions

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An Application of Fully Intuitionistic Fuzzy multi-objective Linear Fractional programming Problem in E-education System

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INTERNATIONAL JOURNAL OF FUZZY SYSTEMS 2022年第8期24卷 3544-3563页

作者： Malik, Manisha Gupta, S. K. Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttar Pradesh India

This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.

关键词： multi-objective programming Triangular intuitionistic fuzzy number Goal programming Linear fractional programming problem Fuzzy mathematical programming

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A Novel Approach to Solve multi-objective Fuzzy Stochastic Bilevel programming Using Genetic Algorithm

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Operations Research Forum 2024年第1期5卷 11页

作者： Dutta, S. Acharya, S. Department of Advanced Computing St. Joseph’s University Bengaluru India Department of Mathematics School of Applied Sciences KIIT University Bhubaneswar India

A bilevel programming is a two-level optimization problem, namely, the upper level (leaders) and the lower level (followers). The two level’s decision variables are entwined with each other which increases the complexity to obtain the global solution for both the optimization problems. Each level aims to optimize their own objective function under the given constraints at both the levels. To reduce the complexity partial cooperation between the two levels has been exploited in obtaining the Pareto solution. A novel solution procedure is proposed for a multi-objective fuzzy stochastic bilevel programming (MOFSBLP) problem is studied and solved using genetic algorithm. In this paper, previous information of the lower level is used as a fuzzy stochastic constraints in the upper level along with its constraints. Then with the solution of the combine constraints, the lower level solution is evaluated. The proposed solution procedure is illustrated by a numerical example taken from Zheng et al., and results are compared. A simpler version is solved using GAMs software to analyze the result of the numerical example. The proposed method highlights the importance of partial cooperation in solving bilevel programming problem. The advantage of the proposed solution method is that it creates common constraint space which helps in convergence of the algorithm. © 2024, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

关键词： Bilevel programming problem Fuzzy stochastic programming Genetic algorithm multi-objective programming

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Computation of multi-objective two-stage fuzzy probabilistic programming problem

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SOFT COMPUTING 2022年第1期26卷 271-282页

作者： Ranarahu, Narmada Dash, J. K. Siksha O Anusandhan Deemed Univ Dept Math Inst Tech Educ & Res Khandagiri Sq Bhubaneswar Odisha India

This paper presents a mathematical model that combines the mathematical models of stochastic programming (SP), namely two-stage stochastic (TSS) programming and chance-constrained programming in fuzzy environment. The complexity of the proposed model is due to multiple objective functions and presence of fuzzy random variables. Since it is difficult to solve the proposed model directly, the mathematical model is converted into an equivalent multi-objective TSS programming crisp model using alpha-cut technique. Then, using the concept of epsilon-constraint method, multi-objective deterministic TSS programming problem is converted into single objective deterministic mathematical model. The transformed model is solved using the existing methodology. Lastly, a numerical example is provided for illustrating the methodology.

关键词： Stochastic programming multi-objective programming epsilon-Constraint method Fuzzy random variable Two-stage programming problem

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multi-objective programming and Time Optimal Algorithm Research

Multi-Objective Programming and Time Optimal Algorithm Resea...

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3rd International Conference on Materials Science and Engineering (ICMSE 2014)

作者： Yang, Chenghui Northwest Univ Nationalities Coll Elect Engn Lanzhou Peoples R China

ISBN: (纸本)9783037859520

As the elevator group control system of airport logistics has the characteristics of multi-objective, non-linearity, uncertainty, disturbances and incomplete information and so on, to improve the service quality and operational efficiency of elevator group control system, we created a more comprehensive performance evaluation index function. We used the algorithm called multi-objective optimization, which can reduce the time passengers waiting for the ladder, avoid crowding, and use less energy. According to different demands, select different optimal combination, to meet passengers' demands as possible as we can. With the use of computer simulation technology, we obtained the simulation results, and proof the feasibility and superiority of this algorithm.

关键词： airport logistics elevator group scheduling time optimal multi-objective programming computer simulation

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Robustness analysis in multi-objective Mathematical programming using Monte Carlo simulation

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第1期240卷 193-201页

作者： Mavrotas, George Pechak, Olena Siskos, Eleftherios Doukas, Hans Psarras, John Natl Tech Univ Athens Sch Chem Engn Lab Ind & Energy Econ Athens 15780 Greece Natl Tech Univ Athens Sch Elect & Comp Engn Decis Support Syst Lab EPU Athens 15780 Greece

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.

关键词： multi-objective programming Robustness analysis Monte Carlo simulation

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