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Optimality and Duality for multiobjective programming with Generalized Univexity

ENGINEERING LETTERS 2023年第4期31卷 1561页

作者： Zhang, Yonghong Wu, Xiaodi Xianyang Normal Univ Sch Math & Stat Xianyang 712000 Peoples R China Guangxi Univ Nationalities Fac Math & Phys Nanning 530006 Peoples R China

This paper presents the introduction of d-rho-(eta, theta)- univex functions, which are built upon the concepts of d-rho-(eta, theta)-invex functions and univex functions. By utilizing these concepts, the paper derives various optimality results for feasible solutions to be considered as efficient or weak efficient solutions. Additionally, the paper establishes several duality theorems for Mond-Weir and Wolf duality.

关键词： Generalized d-rho-(eta, theta)-univexity Duality Optimality multiobjective programming

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Social transfer policies and child poverty in European countries: Evaluating policy alternatives through a multiobjective programming model

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SOCIO-ECONOMIC PLANNING SCIENCES 2024年 93卷

作者： Gonzalez-Gallardo, Sandra Barcena-Martin, Elena Perez-Moreno, Salvador Luque, Mariano Univ Malaga Dept Appl Econ Math Campus El Ejido Malaga 29071 Spain Univ Malaga Dept Appl Econ Stat & Econometr Campus El Ejido Malaga 29071 Spain Univ Malaga Dept Appl Econ Econ Policy Campus El Ejido Malaga 29071 Spain

Child poverty remains a significant concern across Europe and citizens regard policy interventions that effectively address this issue to be of utmost importance. In this work, we analyse the potential of social transfer policy alternatives to alleviate child and overall poverty simultaneously in European countries. Using a logistic regression to define the objective functions and constraints, we rely on multiobjective programming to assess key features of national social transfer systems that can minimize child and overall poverty and tend to equal both levels downwards. Taking into account the starting levels of each country, the results underline the importance of finding an adequate combination of pro-child and pro-poor targeting of social transfer policies. For most European countries, an increase in the level of cash benefits for children is advisable - particularly universal benefits - except in Croatia, the Netherlands, and Norway. Nonetheless, in France, Greece, Italy, Ireland, the Netherlands, and Spain, the recommended proportion of GDP allocated to universal cash benefits is lower than the proportion allocated to means-tested benefits. In this regard, our research provides an innovative approach for policymakers to optimize poverty reduction strategies by contributing valuable insights for the design and implementation of effective social transfer policies to combat child and overall poverty in European countries.

关键词： multiobjective programming Econometric analysis Child poverty Social transfer policy

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HIGHER-ORDER SYMMETRIC DUALITY FOR multiobjective programming WITH CONE CONSTRAINTS

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2020年第4期16卷 1873-1884页

作者： Tang, Liping Yang, Xinmin Gao, Ying Chongqing Normal Univ Sch Math Sci Chongqing 401331 Peoples R China Southwest Univ Sch Math & Stat Chongqing 400715 Peoples R China Chongqing Technol & Business Univ Coll Math & Stat Chongqing 400067 Peoples R China

In this work, a pair of higher-order symmetric dual multiobjective optimization problems is formulated. Weak, strong and converse duality theorems are established under suitable assumptions. Some examples are also given to illustrate our main results. Furthermore, certain deficiencies in the formulations and the proof of the work of Kassem [Applied Mathematics and Computation, 209 (2009), 405-409] are pointed out.

关键词： multiobjective programming higher-order symmetric duality duality theorem

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Improving the min-max method for multiobjective programming

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OPERATIONS RESEARCH LETTERS 2020年第4期48卷 480-486页

作者： Salmei, Hossein Yaghoobi, Mohammad Ali Vali & Asr Univ Rafsanjan Dept Math Rafsanjan Iran Shahid Bahonar Univ Kerman Fac Math & Comp Dept Appl Math Kerman Iran

In this paper, a new version of the min-max method for solving multiobjective optimization problems is proposed. Using the new version, unlike the min-max method, we can prove results on (proper) efficiency of optimal solutions. Moreover, a special case of the model with flexible constraints is also studied. By considering approximate solutions, some relationships between epsilon 1-(weakly, properly) efficient solutions of a general multiobjective optimization problem and is an element of-optimal solutions of the introduced model are achieved. (C) 2020 Elsevier B.V. All rights reserved.

关键词： multiobjective programming Scalarization Min-max method Properly efficient solutions Approximate solutions

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Economic planning of wind farms from a NBI-RSM-DEA multiobjective programming

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RENEWABLE ENERGY 2020年 158卷 628-641页

作者： Aquila, Giancarlo Souza Rocha, Luiz Celio Rotela Junior, Paulo Saab Junior, Joseph Youssif Brasil Lima, Joao de Sa Balestrassi, Pedro Paulo Univ Fed Itajuba Project 155507 2018 4 Itajuba MG Brazil Fed Inst Educ Sci & Technol Almenara MG Brazil Univ Fed Paraiba Dept Prod Engn Joao Pessoa Paraiba Brazil Maua Inst Technol Sao Caetano do Sul SP Brazil Univ Fed Itajuba Inst Prod Engn & Management Itajuba MG Brazil

One of the challenges of energy regulatory-agencies is to guide the agents decision-making process towards maximization of the overall welfare of the electricity sector. However, this is not a simple task since it requires meeting expectations of many stakeholders, from investors to consumers. This paper proposes an optimization methodology aimed at helping define the optimal combination of wind farm layout and type of equipment deployed, so that the electricity sector overall welfare is maximized in the process. The optimization objectives are (i) the energy density and (ii) the Net Present Value (NPV), and the parameters are (a) the power levels and (b) the selling price of the energy. The objective functions are modelled with the aid of a design-of-experiment technique known as Response Surface Methodology, relying on the multi-objective programming method of Normal Boundary Intersection for the optimization. The methodology is applied to four different scenarios arising from the combination of two different locations (Santa Vitoria do Palmar-RS and Macau-RN, both in Brazil), and two different wind turbine manufacturers (A and B). The final step comprises the application of the Data Envelopment Analysis technique in order to sort one from the set of optimal solutions identified by the four different scenarios. The results show that the proposed methodology is capable of supporting bidding processes and wind farms certification programs, in line with what should be expected by regulatory agencies, investors and electricity consumers alike. The deployment of the methodology proved discriminant and allowed selection of one final scenario (Macau-RN, brand A equipment) as overall optimal. It was also observed that equipment efficiency is dependent on siting location. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Energy planning Wind farms multiobjective programming Normal boundary intersection Response surface methodology

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BIOBJECTIVE OPTIMIZATION OVER THE EFFICIENT SET OF multiobjective INTEGER programming PROBLEM

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2021年第1期17卷 117-131页

作者： Cherfaoui, Yasmine Moula, Mustapha USTHB Dept Operat Res Bp 32 El Alia Algiers 16111 Algeria USTHB LaROMaD Lab Bp 32 El Alia Algiers 16111 Algeria

In this article, an exact method is proposed to optimize two preference functions over the efficient set of a multiobjective integer linear program (MOILP). This kind of problems arises whenever two associated decision-makers have to optimize their respective preference functions over many efficient solutions. For this purpose, we develop a branch-and-cut algorithm based on linear programming, for finding efficient solutions in terms of both preference functions and MOILP problem, without explicitly enumerating all efficient solutions of MOILP problem. The branch and bound process, strengthened by efficient cuts and tests, allows us to prune a large number of nodes in the tree to avoid many solutions. An illustrative example and an experimental study are reported.

关键词： multiobjective programming integer programming branch-and-cut

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A new mixed integer programming approach for optimization over the efficient set of a multiobjective linear programming problem

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OPTIMIZATION LETTERS 2020年第8期14卷 2323-2333页

作者： Lu, Kuan Mizuno, Shinji Shi, Jianming Tokyo Inst Technol 2 Chome-12-1 Ookayama Meguro Tokyo Japan Tokyo Univ Sci 1 Chome 3 Kagurazaka Shinjuku City Tokyo Japan

This paper concerns an optimization problem over the efficient set of a multiobjective linear programming problem. We propose and solve an equivalent mixed integer programming (MIP) problem to compute an optimal solution to the original problem. Compared with the previous MIP approach by Sun, the proposed approach relaxes a strong assumption and reduces the numbers of constraints and binary variables of the MIP problem. By conducting numerical experiments, we find that the proposed approach is more accurate and faster than the previous MIP approach. The proposed MIP problem can be efficiently solved with current state-of-the-art MIP solvers when the objective function is convex or linear.

关键词： Global optimization multiobjective programming Efficient set Linear complementarity conditions Mixed integer programming

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Proposed method for contracting of wind-photovoltaic projects connected to the Brazilian electric system using multiobjective programming

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RENEWABLE & SUSTAINABLE ENERGY REVIEWS 2018年第Dec.期97卷 377-389页

作者： Aquila, Giancarlo Souza Rocha, Luiz Celio Pamplona, Edson de Oliveira de Queiroz, Anderson Rodrigo Rotela Junior, Paulo Balestrassi, Pedro Paulo Fonseca, Marcelo Nunes Univ Fed Itajuba Inst Prod Engn & Management Itajuba MG Brazil Fed Inst Educ Sci & Technol Almenara MG Brazil North Carolina Cent Univ Sch Business Dept Decis Sci Durham NC 27707 USA Univ Fed Paraiba Dept Prod Engn Joao Pessoa PB Brazil Univ Fed Goias Dept Prod Engn Aparecida De Goiania Go Brazil

Owing to the wind and photovoltaic (PV) potential in Brazil, the country has recently seen increased exploration into the construction of wind-PV hybrid plants. However, as specific criteria for contracting this type of project have not yet been developed, this paper presents a model to assist the government in contracting projects that maximize the socioeconomic well-being of the Brazilian electricity sector. For this, multiobjective programming is used to simultaneously handle two objective functions-maximally reducing emission density and minimizing the levelized cost of electricity (LCOE)-with the aid of the mixture arrangement technique. In this respect, the optimization method called normal boundary intersection (NBI) is applied to solve the multiobjective problem and construct the Pareto frontier. Additionally, a metric based on the ratio between entropy and the global percentage error (GPE) is used to identify the optimal Pareto solution. The model was applied to determine optimal configurations for wind-PV powerplants in twelve Brazilian cities, and the results obtained reveal the capacity of the model to indicate the optimum configuration according to the wind and PV potential of each city.

关键词： Renewable energy sources multiobjective programming Normal boundary intersection Brazilian electricity system Wind-PV farms

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Vector Exponential Penalty Function Method for Nondifferentiable multiobjective programming Problems

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BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY 2018年第2期41卷 657-686页

作者： Antczak, Tadeusz Univ Lodz Fac Math & Comp Sci Banacha 22 PL-90238 Lodz Poland

In this paper, a new vector exponential penalty function method for nondifferentiable multiobjective programming problems with inequality constraints is introduced. First, the case when a sequence of vector penalized optimization problems with vector exponential penalty function constructed for the original multiobjective programming problem is considered, and the convergence of this method is established. Further, the exactness property of a vector exact penalty function method is defined and analyzed in the context of the introduced vector exponential penalty function method. Conditions are given guaranteeing the equivalence of the sets of (weak) Pareto solutions of the considered nondifferentiable multiobjective programming problem and the associated vector penalized optimization problem with the vector exact exponential penalty function. This equivalence is established for nondifferentiable vector optimization problems with inequality constraints in which involving functions are r-invex.

关键词： multiobjective programming (weak) Pareto solution Vector exact exponential penalty function Penalized vector optimization problem r-Invex function

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Solution of multiobjective linear programming problems in interval-valued intuitionistic fuzzy environment

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SOFT COMPUTING 2019年第1期23卷 77-84页

作者： Bharati, S. K. Singh, S. R. Univ Delhi Kamala Nehru Coll Dept Math Delhi 110049 India Banaras Hindu Univ Inst Sci Dept Math Varanasi 221005 Uttar Pradesh India

The present paper gives a new computational algorithm for the solution of multiobjective linear programming (MOLP) problem in interval-valued intuitionistic fuzzy (IV-IF) environment. In MOLP problem which occurs in agricultural production planning, industrial planning and waste management. The parameters involved in real-life MOLP problems are impure, and several pioneer works have been done based on fuzzy or intuitionistic fuzzy sets for its compromise solutions. But many times the degree of membership and non-membership for certain element is not defined in exact numbers, so we observe another important kind of uncertainty. Thus fixed values of membership and non-membership cannot handle such uncertainty involved in real-life MOLP problem. Atanassov and Gargov first identified it and presented concept of IV-IF sets which is characterized by sub-intervals of unit interval. In this paper, we study IV-IF sets and develop a new computational method for the solution of real-life MOLP problems based on IV-IF sets. Further, the developed method has been presented in the form of a computational algorithm and implemented on a production problem, and solutions are compared with other existing methods.

关键词： multiobjective programming Interval-valued intuitionistic fuzzy sets Positive deal solution Pareto optimal solution

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