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Integrating reference point, Kuhn-Tucker conditions and neural network approach for multi-objective and multi-level programming problems

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OPSEARCH 2017年第4期54卷 663-683页

作者： Rizk-Allah, R. M. Abo-Sinna, Mahmoud A. Menoufia Univ Dept Basic Engn Sci Fac Engn Shibin Al Kawm Egypt Princess Nora Bent AbdulRahman Univ Dept Math Sci Fac Sci Riyadh Saudi Arabia

In this paper, a neural network approach is constructed to solve multi-objective programming problem (MOPP) and multi-level programming problem (MLPP). The main idea is to convert the MOPP and the MLPP into an equivalent convex optimization problem. A neural network approach is then constructed for solving the obtained convex programming problem. Based on employing Lyapunov theory, the proposed neural network approach is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the MOPP and the MLPP. The simulation results also demonstrate that the proposed neural network is feasible and efficient.

关键词： Karush-Kuhn-Tucker conditions multi-level programming multi-objective programming Neural network Asymptotic stability

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A multi-level programming Model for Controlling the Operation Cost of a Complex Product System

A Multi-Level Programming Model for Controlling the Operatio...

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IEEE International Conference on Grey Systems and Intelligent Services (GSIS)

作者： Liu, Yuan Ying, Hongbing Hao, Jingjing Fang, Zhigeng Zhejiang Normal Univ Coll Econ & Management Jinhua Peoples R China Nanjing Univ Aeronaut and Astronaut Coll Econ & Management Nanjing Peoples R China

ISBN: (纸本)9781467352475;9781467352482

A novel analysis frame, house of cost control, is developed for a complex product system to manage the operation cost in a whole life circle. Specifically, the house of cost control and its components are designed to reflect the demands of cost control activities. Additionally, a multi-level programming model is constructed for the house of cost control to optimize the effect of cost improvement, which concerns the conflicts between several amelioration strategies. Finally, the case of a commercial aircraft production system is conducted to verify the effectiveness and practicality of the above method, which can furnish a new solution for the whole life cycle of cost management activities of a complex product system.

关键词： complex product house of cost control whole life circle multi-level programming

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Planning energy economy and eco-environment nexus system under uncertainty: A copula-based stochastic multi-level programming method

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APPLIED ENERGY 2022年 312卷 118736-118736页

作者： Lv, J. Li, Y. P. Huang, G. H. Ding, Y. K. Li, X. Li, Y. North China Elect Power Univ Sino Canada Energy & Environm Res Ctr Beijing 102206 Peoples R China Beijing Normal Univ Sch Environm State Key Joint Lab Environm Simulat & Pollut Con Beijing 100875 Peoples R China Univ Regina Inst Energy Environm & Sustainable Communities Regina SK S4S 0A2 Canada

Energy consumption, economic growth, and eco-environment protection of urban agglomeration is full of contradictions and continues to be challenges faced by decision makers. It is desired to develop effective methods to realize coordinated management of energy economy and eco-environment nexus (EEEN) system. In this study, a copula-based stochastic multi-level programming (CSMP) approach is first developed, where the conflicting objectives with multiple hierarchical levels and the uncertainty presented as random variables with different probability distributions can be tackled. CSMP can also reflect the complex interactions among random variables and examine the risk of violating joint-probabilistic constraints. The CSMP is then applied to planning EEEN system of Pearl River Delta (PRD) urban agglomeration (China) during the period of 2021-2035. Six scenarios based on joint and individual risk levels for violating energy consumption and GDP constraints are analyzed. Results reveal that the share of tertiary industry and high-tech industry would attain to 62.4% and 14.9% by 2035, the energy and CO2 intensity would decrease by 45.1% and 56.9%, and ecological land would expand to absorb more CO2, indicating that EEEN system would develop towards energy saving, economy and ecoenvironment friendly pattern. Results also disclose that decisions at high risk level would lead to high GDP, energy consumption and CO2 emissions, occupy ecological land and reduce CO2 absorption, and reduce the reliability of fulfilling system requirements.

关键词： Copula EEEN Joint risk multi-level programming PRD urban agglomeration Uncertainty

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Interactive compensatory fuzzy programming for decentralized multi-level linear programming (DMLLP) problems

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FUZZY SETS AND SYSTEMS 2006年第23期157卷 3072-3090页

作者： Tiryaki, Fatma Yildiz Tech Univ Fac Arts & Sci Dept Math Istanbul Turkey

This paper presents interactive compensatory fuzzy programming for decentralized multi-level linear programming (DMLLP) problems. By adjusting the cooperative decision making process between the different levels and also between the decision makers of the same level;our aim is to obtain a preferred compensatory compromise Pareto-optimal solution for DMLLP. For this, the weights of objectives at each level are assigned by the next upper level decision maker (DM) by using analytic hierarchy process (AHP) or any other weighting methods. The weight of any objective for whole system is equal to the product of the weights on the path tying it to the top decision maker DM0. Using these weights, equivalence is established such that the satisfactory levels of all objectives are proportional to their own weights. Werners' compensatory "fuzzy and" operator is offered to solve DMLLP problem. The most important idea to be emphasized is that equivalence is established such that the satisfactory levels of all objectives are proportional to their own weights. Thanks to this equivalence, DMLLP problem has been transformed to the multi-objective linear programming (MOLP) problem at level 0, the equivalence is reflected to the compensatory model within the constraints, and the equivalence also enables all DMs to obtain proportional satisfactions with their weights as much as possible. So, in our compensatory model, a reduction on equivalent satisfactory level of one DM can be compensated for by an increase in the equivalent satisfactory level of another DM. Furthermore, being developed a finite interactive iterative procedure with maximum interaction step, a set of compensatory solutions which are also Pareto-optimal is obtained, depending on compensation parameter gamma. Giving a theorem, we will show that the solutions generated by Werners' compensatory "fuzzy and" operator do guarantee Pareto-optimality for our DMLLP problem. And comparing it with some other computational efficient

关键词： compensatory operators multi-level programming fuzzy mathematical programming fuzzy decision making

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An algorithm for non-linear multi-level integer programming problems

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INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS 2010年第3期3卷 211-225页

作者： Arora, Ritu Arora, S. R. Univ Delhi Keshav Mahavidyalaya Dept Math Delhi India Univ Delhi Hans Raj Coll Dept Math Delhi India

In this paper, an algorithm is proposed to solve a tri-level integer programming problem in which the objective function for the first level is an indefinite quadratic, the second one is linear and the third one is linear fractional. The feasible space of the decision variable is reduced at each level until a satisfactory point is obtained at the last level. The higher level decision-maker reduces the feasible space for the lower level decision maker to search for his optimum. A satisfactory solution of the bilevel decentralised programming problem can also be obtained by the method proposed above. This method is illustrated with the help of examples.

关键词： multi-level programming indefinite quadratic programming fractional programming integer programming satisfactory solution

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Location Model of Distribution Centers in Poverty-Stricken Areas Based on multi-level Fuzzy programming 13th

Location Model of Distribution Centers in Poverty-Stricken A...

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13th International Conference on Management Science and Engineering Management (ICMSEM)

作者： Hu, Zhineng Zheng, Shuangyi Feng, Qiong Tang, Dunzhe Sichuan Univ Sch Business Chengdu 610065 Peoples R China Tsinghua Univ Sch Econ & Management Beijing 100084 Peoples R China

ISBN: (纸本)9783030212483;9783030212476

This paper discusses the necessity of building agricultural product distribution centers in poverty-stricken areas in order to solve the deficiencies in current E-commerce Poverty Alleviation logistics and distribution. With consideration of existing site selection planning research, the hierarchical and alternative points of decision-making during the construction of the gathering center, the suitability of standby sites and uncertainty of agricultural products, we try to build a multi-level planning model and solve for the optimum solution through interactive fuzzy programming method. In addition, through specific case analysis, we verify the rationality and feasibility of our model. Consequently, our model is more reflective than the single-level model and the determined model, and allows us to achieve an aggregate welfare level that is closer to the optimal.

关键词： multi-level programming Interactive fuzzy programming Method Poverty-stricken areas Distribution center Location

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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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A modified fuzzy approach for the fully fuzzy multi-objective and multi-level integer quadratic programming problems based on a decomposition technique

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2019年第2期37卷 2727-2739页

作者： Fathy, E. Helwan Univ Fac Sci Dept Math Cairo Egypt

This paper focuses on extending and applying a fuzzy approach for utilization with the fully fuzzy multi-objective and multi-level integer quadratic programming (FFMMQP) problems. First, the decomposition technique is used to convert the fuzzy problem for each level into three crisp multi-objective integer quadratic (MQP) problems namely, Middle-MQP, Upper-MQP and Lower-MQP problem. Each crisp problem has its own variables. Furthermore, the functions of each problem have several quadratic functions. Then by considering the individual solution of each objective function, the middle, upper and lower membership functions are constructed. Second, the concept of the tolerance membership function and multi-objective optimization in the decomposition form is used to establish decomposed Tchebycheff problems to achieve the Pareto optimal fuzzy solution for the FFMMQP problems. An example is provided to prove the theoretical results.

关键词： Fully fuzzy programming multi-level programming multi-objective programming quadratic programming fuzzy approach

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Solving multi-level multi-objective Fractional programming Problems with Fuzzy Demands via FGP Approach

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International Journal of Applied and Computational Mathematics 2018年第1期4卷 1-24页

作者： Osman, M.S. Emam, O.E. El Sayed, M.A. Mathematics and Operations Research El Asher University El Asher City Egypt Department of Information Systems Faculty of Computers and Information Helwan University P.O. Box 11795 Greater Cairo Egypt Department of Basic Engineering Sciences Faculty of Engineering Benha University Benha ElQalyoubia Egypt

This paper presents a fuzzy goal programming approach for solving multi-level multi-objective fractional programming problem with fuzzy demands. It makes an extension work of Pal et al. (Fuzzy Sets Syst 139(2):395–405, 2003). Firstly, the concept of α-cut is applied to transform the fuzzy mathematical problem into a common deterministic one. Then, the membership functions for the defined fuzzy goals are developed. Also, in the proposed approach, linearization of membership goals of the objective functions is presented. Secondly, the highest degree of each of these membership goals is achieved by minimizing the sum of the negative deviational variables. Moreover, the final model is simplified by eliminating solution preferences by the decision makers at each level, thereby avoiding decision deadlock situations. Finally, an illustrative numerical examples and comparisons with the existing methods are used to demonstrate the applicability and performance of the proposed approach. © 2017, Springer (India) Private Ltd., part of Springer Nature.

关键词： Fractional programming Fuzzy goal programming Fuzzy sets multi-level programming multi-objective programming

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Stochastic Fuzzy multi-level multi-objective Fractional programming Problem: A FGP Approach

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OPSEARCH 2017年第4期54卷 816-840页

作者： Osman, M. S. Emam, O. E. El Sayed, M. A. El Asher Univ El Asher City Egypt Helwan Univ Fac Comp & Informat Dept Informat Syst POB 11795 Helwan Egypt Benha Univ Dept Basic Engn Sci Fac Engn Elqalyoubia Egypt

In this paper, a fuzzy goal programming (FGP) approach is considered for solving stochastic fuzzy multi-level multi-objective fractional programming (ML-MOFP) problem. In the developed stochastic fuzzy ML-MOFP model the fractional objective function coefficients and scalars are represented by fuzzy parameters. Moreover, in the constraints, the right-hand sides are independent random variable with known distribution function while both the left-hand side coefficients and the tolerance measures are considered to be fuzzy parameters. Therefore, the chance-constrained approach with dominance possibility criteria and the alpha-cut approach are utilized to transform the stochastic fuzzy ML-MOFP problem to its equivalent deterministic-crisp problem. Then, the membership functions for the defined fuzzy goals are setup. Also, in the proposed FGP model, a linearization procedures for the membership goals of the objective functions is developed. Hence, the FGP approach is used to achieve the highest degree of each of the membership goals by minimizing the sum of the negative deviational variables. Finally, an algorithm to clarify the developed FGP approach, as well as Illustrative numerical example, are presented.

关键词： multi-level programming Fractional programming Chance-constrained approach Fuzzy sets Fuzzy goal programming

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