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Interactive Fuzzy Goal programming Based on Taylor Series to Solve multiobjective nonlinear programming Problems With Interval Type-2 Fuzzy Numbers

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2018年第4期26卷 2434-2449页

作者： Dalman, Hasan Bayram, Mustafa Istanbul Gelisim Univ Dept Comp Engn TR-34310 Istanbul Turkey

This paper presents an interactive fuzzy goal programming (FGP) approach for solving multiobjective nonlinear programming problems (MONLPP) with interval type-2 fuzzy numbers (IT2 FNs). The cost and time of the objective functions, the resources, and the requirements of each kind of resources are taken to be trapezoidal IT2 FNs. Here, the considered problem is first transformed into an equivalent crisp MONLPP, and then the transformed MONLPP is converted into an equivalent multiobjective linear programming problem. By using a procedure based on Taylor series, this problem is reduced into a single objective linear programming problem that can be easily solved by Maple 2017 optimization toolbox. Finally, the proposed solution procedure is illustrated by two numerical examples.

关键词： Fuzzy goal programming (FGP) interactive approach interval type-2 (IT2) fuzzy sets multiobjective nonlinear programming Taylor series

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Second-order necessary and sufficient optimality conditions for multiobjective interval-valued nonlinear programming

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APPLICABLE ANALYSIS 2025年第4期104卷 691-718页

作者： Tung, Le Thanh Can Tho Univ Coll Nat Sci Dept Math Can Tho Vietnam

In this article, the second-order optimality conditions for nonlinear programming with multiple interval-valued objective functions (in brief, NPMIOF) are studied. In the first part, the second- and first-order necessary optimality conditions for some types of efficient solutions of NPMIOF are established under of Abadie second- and first-order constraint qualifications. In the next part, we investigate both primal and dual second-order sufficient optimality conditions. Our second-order necessary conditions enhance the previous results. The second-order sufficient optimality conditions are new.

关键词： multiobjective nonlinear programming interval-valued objective functions second-order necessary and sufficient optimality conditions second-order Abadie constraint qualifications

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Optimization of Bridging Bus Timetable and Vehicle Scheduling under URT Disruption

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JOURNAL OF TRANSPORTATION ENGINEERING PART A-SYSTEMS 2023年第8期149卷

作者： Song, Liying Shao, Lihua Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China

After the occurrence of a disruptive event in an urban rail transit (URT) network, passengers' travel is affected, and a large number of passengers are stranded in the stations. These stranded passengers have to be evacuated urgently. With its flexible deployment, a bus bridging service has become an effective solution to evacuate stranded passengers. In order to avoid large passenger flow at stations, in addition to evacuating the static passenger flow stranded at the disrupted stations, the bridging buses need to focus on the dynamic passenger flow arriving at the turnover stations along the short-turning trains. In this paper, we propose a mathematical model to optimize the timetable and vehicle scheduling of bridging buses considering the adjustment of rail transit operations. The model aims to minimize passenger waiting time, the number of lost passengers, and the amount of bridging buses used. The model makes buses operate flexibly on different routes, taking the bus capacity and number of buses into account. By creating an improved e-constraint method, the Pareto front of the problem is solved using the model with a commercial solver. Finally, the accuracy and validity of the model is verified by applying an example based on China's Hangzhou rail transit line 4. The results show that the bridging bus timetable and scheduling plan generated by the model effectively solved the problem of large passenger flow at turnover stations. In addition, compared with bridging buses with an even headway timetable, the results demonstrate that bridging buses with an uneven headway timetable, which considers coordination with rail transit, could reduce the passenger waiting time and the number of lost passengers. The model has better performance with an uneven headway timetable in the face of large passenger demand. The computational experiment shows that the total passenger waiting time and the number of bridging buses was reduced when the bus capacity was increased. Howeve

关键词： Urban rail transit (URT) disruption Bridging bus timetable Vehicle scheduling multiobjective nonlinear programming Dynamic passenger flow

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Study on multi-objective nonlinear programming problem with rough parameters

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022年第4期42卷 3591-3604页

作者： Garg, Harish Alodhaibi, Sultan S. Khalifa, Hamiden Abd El-Wahed Deemed Univ Sch Math Thapar Inst Engn & Technol Patiala 147004 Punjab India Qassim Univ Coll Sci & Arts Dept Math Arrass Saudi Arabia Cairo Univ Giza Fac Grad Studies Stat Res Dept Operat Res Giza Egypt Qassim Univ Coll Sci & Arts Dept Math Al Badayaa Saudi Arabia

Rough set theory, introduced by Pawlak in 1981, is one of the important theories to express the vagueness not by means of membership but employing a boundary region of a set, i.e., an object is approximately determined based on some knowledge. In our real-life, there exists several parameters which impact simultaneously on each other and hence dealing with such different parameters and their conflictness create a multi-objective nonlinear programming problem (MONLPP). The objective of the paper is to deal with a MONLPP with rough parameters in the constraint set. The considered MONLPP with rough parameters are converted into the two-single objective problems namely, lower and upper approximate problems by using the weighted averaging and the epsilon-constraints methods and hence discussed their efficient solutions. The Karush-Kuhn-Tucker's optimality conditions are applied to solve these two lower and upper approximate problems. In addition, the rough weights and the rough parameters are determined by the lower and upper the approximations corresponding each efficient solution. Finally, two numerical examples are considered to demonstrate the stated approach and discuss their advantages over the existing ones.

关键词： multiobjective nonlinear programming rough set lower approximation programming problem upper approximation programming problem weighting method epsilon-constraints method parametric analysis

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Best Strategy for Gold Bitcoin Investment based on Bollinger Bands and Multi-objective Optimization Model

Frontiers in Economics and Management

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Frontiers in Economics and Management 2022年第4期3卷 89-105页

作者： Rongding He Zonghai Li Jinghua Guo Chaofan Luo Jing Xu

With the economic development and the change of people's investment consciousness, asset investment has become an important part of modern life. The purpose of this paper aims to help market traders make full use of the gold coins and bitcoins to maximize their total profits. Therefore, we test the correlation between the gold and bitcoin value streams. The results show that they vary between positive and negative correlation. Based on the changing trend of the comprehensive value of gold and bitcoin, this paper puts forward four trading scenarios, that is, bottom, peak, hedge and stable, and gives the corresponding optimal trading strategies. On the basis of the above classification model, we set up a multi-objective nonlinear programming model to ensure the optimal quantitative investment strategy under the constraints of each transaction scenario. The results shows that our model is the best in terms of the number of transactions and annualized rate of return, and the winning rate is second only to MACD.

关键词： ARIMA Quantitative Investment multiobjective nonlinear programming Bollinger Band

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Interactive goal programming algorithm with Taylor series and interval type 2 fuzzy numbers

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2019年第6期10卷 1563-1579页

作者： Dalman, Hasan Bayram, Mustafa Istanbul Gelisim Univ Dept Comp Engn Istanbul Turkey

This paper presents an interactive fuzzy goal programming (FGP) approach for solving multiobjective nonlinear programming Problems (MONLPP) with interval type 2 fuzzy numbers (IT2 FNs). The cost and time of the objective functions, and the requirements of each kind of resources are taken to be trapezoidal IT2 FNs. Here, the considered fuzzy problem is first transformed into an equivalent crisp MONLPP, and then the MONLPP is converted into an equivalent multiobjective linear programming problem (MOLPP). By using an algorithm based on Taylor series, this problem is also reduced into a single objective linear programming problem (LPP) which can be easily solved by Maple 2017 optimization toolbox. Finally, the proposed solution procedure is illustrated by a numerical example.

关键词： Fuzzy goals Taylor series Interval type 2 fuzzy sets multiobjective nonlinear programming Interactive mechanism

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An implicit filtering algorithm for derivative-free multiobjective optimization with box constraints

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2018年第2期69卷 267-296页

作者： Cocchi, G. Liuzzi, G. Papini, A. Sciandrone, M. Univ Firenze Dipartimento Ingn Informaz Via Santa Marta 3 I-50139 Florence Italy CNR Ist Anal Sistemi & Informat Via Taurini 19 I-00185 Rome Italy Univ Firenze Dipartimento Ingn Ind Viale Morgagni 40-44 I-50134 Florence Italy

This paper is concerned with the definition of new derivative-free methods for box constrained multiobjective optimization. The method that we propose is a non-trivial extension of the well-known implicit filtering algorithm to the multiobjective case. Global convergence results are stated under smooth assumptions on the objective functions. We also show how the proposed method can be used as a tool to enhance the performance of the Direct MultiSearch (DMS) algorithm. Numerical results on a set of test problems show the efficiency of the implicit filtering algorithm when used to find a single Pareto solution of the problem. Furthermore, we also show through numerical experience that the proposed algorithm improves the performance of DMS alone when used to reconstruct the entire Pareto front.

关键词： multiobjective nonlinear programming Derivative-free optimization Implicit filtering

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Integer compromise allocation in multivariate stratified surveys

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ANNALS OF OPERATIONS RESEARCH 2015年第1期226卷 659-668页

作者： Varshney, Rahul Khan, M. G. M. Fatima, Ummatul Ahsan, M. J. Amity Univ Dept Stat Noida India Univ S Pacific Sch Comp Informat & Math Sci Suva Fiji Aligarh Muslim Univ Dept Stat & Operat Res Aligarh Uttar Pradesh India

In multivariate stratified sampling more than one characteristic are defined on every unit of the population. An optimum allocation which is optimum for one characteristic will generally be far from optimum for others. To resolve this problem, a compromise criterion is needed to work out a usable allocation. In this manuscript, a compromise criterion is discussed and integer compromise allocations are obtained by using goal programming technique. A numerical example is presented to illustrate the computational details, which reveals that the proposed criterion is suitable for working out a usable compromise allocation for multivariate stratified surveys.

关键词： Compromise allocation Goal programming multiobjective nonlinear programming Multivariate stratified sampling

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Stability achievement scalarization function for multiobjective nonlinear programming problems

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APPLIED MATHEMATICAL MODELLING 2008年第6期32卷 1044-1055页

作者： Kassem, Mohamed Abd El-Hady Tanta Univ Fac Sci Dept Math Tanta Egypt

In this paper, we present a method to determine the stability of nondominated criterion vectors using a modified weighted achievement scalarization metric. This method is based on the application of a particular objective function which scalarizes and parameterizes the original multiobjective nonlinear programming problem. Also, we show that this modified weighted achievement metric coincides with the metric introduced by Choo and Atkins [E.-U. Choo, D.R. Atkins, Proper efficiency in nonconvex multicriteria programming, Math. Oper. Res. 8 (1983) 467-470] and Kaliszewski [L Kaliszewski, A modified weighted Tchebycheff metric for multiple objective programming, Comput. Oper. Res. 14 (1987) 315-323] in cases when sets of all criterion vectors are finite or polyhedral. (c) 2007 Elsevier Inc. All rights reserved.

关键词： multiobjective nonlinear programming achievement scalarization function nondominated solutions stability

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Interactive stability cutting-plane algorithm for multiobjective nonlinear programming problems

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APPLIED MATHEMATICS AND COMPUTATION 2007年第2期192卷 446-456页

作者： Kassem, Mohamed Abd El-Hady Tanta Univ Fac Sci Dept Math Tanta Egypt

In this paper, we introduce an interactive stability cutting-plane algorithm for determining a best-compromise solution to a multiobjective nonlinear programming problems in situations with an implicitly defined utility function. The method is called "interactive stability cutting-plane compromise programming (ISCPCP)". The cutting-planes which I am going to derive, are based on suitable pairwise trade-offs between the objective functions, as prescribed by the decision maker (DM) at each iterate generated by the algorithm. This algorithm requires no line searches, and generates iterates that are all contained in the efficient frontier. This feature facilitates the preference judgment of the decision maker, and permits an analyst to terminate short of optimality with an efficient near-optimal solution. Also, we investigate the stability of its efficient solutions which are obtained by using this algorithm. An illustrating example is presented to clarify this algorithm. (C) 2007 Elsevier Inc. All rights reserved.

关键词： cutting-plane algorithm multiobjective nonlinear programming trade-off method best-compromise solution stability

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