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An η-approximation method in nonlinear vector optimization

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2005年第2期63卷 225-236页

作者： Antczak, T Univ Lodz Fac Math PL-90238 Lodz Poland

In this paper, a new approach for a solution of a nonlinear multiobjective programming problem is introduced. An equivalent eta-approximated vector optimization problem is constructed by a modification of the objective and the constraint functions in the original multiobjective programming problem. The connection between (weak) efficient points in the original multiobjective programming problem and its equivalent eta-approximated vector optimization problem is proved. In this way, optimality conditions for nonlinear constrained multiobjective programming problems having invex and/or generalized invex objective and constraint functions (with respect to the same functions eta) are obtained. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： multiobjective programming invex function with respect to eta eta-approximated vector optimization problem (weak) Pareto optimal point

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Effectiveness-Equity Models for Facility Location Problems on Tree Networks

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NETWORKS 2013年第4期62卷 243-254页

作者： Lejeune, Miguel A. Prasad, Srinivas Y. George Washington Univ Dept Decis Sci Sch Business Washington DC 20052 USA

We propose models to investigate effectiveness-equity tradeoffs in tree network facility location problems. We use the commonly used median objective as a measure of effectiveness, and the Gini index as a measure of (in)equity, and formulate bicriteria problems involving these objectives. We develop procedures to identify an efficient set of solutions to these problems, analyze the complexity of the proposed procedures, and finally illustrate the procedures with an *** (c) 2012 Wiley Periodicals, Inc. NETWORKS, Vol. 62(4), 243-254 2013

关键词： facility location equity quasiconvexity multiobjective programming tree network efficiency

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Solving Optimization Problems over the Weakly Efficient Set

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 2021年第2期42卷 180-210页

作者： Sadeghi, Javad Mohebi, Hossein Kerman Grad Univ Adv Technol Dept Math Kerman Iran Shahid Bahonar Univ Kerman Dept Math POB 76169133 Kerman *** Iran Shahid Bahonar Univ Kerman Mahani Math Res Ctr POB 76169133 Kerman *** Iran

In this paper, we study the optimization problem (PWE) of minimizing a convex function over the set of weakly efficient solutions of a convex multiobjective problem. This is done by using the fact that each lower semicontinuous convex function is an upper envelope of its affine minorants together with a generalized cutting plane method. We give necessary conditions for optimal solutions of the problem (PWE). Moreover, a novel algorithm for solving the problem (PWE) together with numerical results are presented. We also prove that the proposed algorithm terminates after a finite numbers of iterations, and the algorithm is coded in MATLAB language and evaluated by numerical examples.

关键词： Nonlinear programming multiobjective programming nonconvex programming weak-efficiency generalized cutting plane method

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multiobjective optimization of reliability-redundancy allocation problems for serial parallel-series systems based on importance measure

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART O-JOURNAL OF RISK AND RELIABILITY 2019年第5期233卷 881-897页

作者： Zhao, Jiangbin Si, Shubin Cai, Zhiqiang Su, Ming Wang, Wei Northwestern Polytech Univ Sch Mech Engn Dept Ind Engn Xian 710072 Shaanxi Peoples R China

For complex equipment, designers are challenged to reduce the expense while satisfying high requirements of system reliability. This article focuses on the multiobjective reliability-redundancy allocation problem for serial parallel-series systems to balance the conflicts between system reliability and design cost. The multiobjective reliability-redundancy allocation problem model for serial parallel-series systems is established with constraints on system reliability and design cost. An importance measure-based and harmony search-based multiobjective particle swarm optimization algorithm is proposed to solve the multiobjective model effectively based on the importance measure-based harmony search and multiobjective particle swarm optimization algorithm. The performance of the importance measure-based and harmony search-based multiobjective particle swarm optimization algorithm is verified by comparison with the nondominated sorting genetic algorithm and importance measure-based multiobjective particle swarm optimization algorithm. In Experiment 1, the performance of the importance measure-based and harmony search-based multiobjective particle swarm optimization algorithm is better than that of the nondominated sorting genetic algorithm and importance measure-based multiobjective particle swarm optimization, and the importance measure-based and harmony search-based multiobjective particle swarm optimization algorithm also can get the Pareto front with better uniformity. Compared to the nondominated sorting genetic algorithm, four cases with different constraints of system reliability and design cost are considered in Experiment 2, and the importance measure-based and harmony search-based multiobjective particle swarm optimization algorithm applies to the systems with the lower system reliability constraints and the higher design cost constraints.

关键词： multiobjective programming reliability-redundancy allocation problem particle swarm optimization harmony search importance measure Pareto front

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Objective prioritization sing lexicographic minimizers for MPC of sewer networks

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IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 2008年第1期16卷 113-121页

作者： Ocampo-Martinez, Carlos Ingimundarson, Ari Puig, Vicenc Quevedo, Joseba Tech Univ Catalonia UPC Dept Automat Control Terrassa 08222 Spain

In this brief, objective prioritization of multiobjective cost functions using the lexicographic approach is applied in the model predictive control (MPC) framework of sewer networks. Using the lexicographic approach, the control problem solution can be obtained by solving a sequence of single objective, constrained, convex programming problems. This brief demonstrates with an elaborated case study treating a portion of the Barcelona sewer network, that important improvements can be achieved in performance using lexicographic optimization. At the same time, costly commissioning and implementation efforts related to the traditional weight based approach for implementation of priorities are avoided.

关键词： convex optimization lexicographic programming model predictive control (MPS) multiobjective programming sewer networks urban drainage

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multiobjective expected value model for portfolio selection in fuzzy environment

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OPTIMIZATION LETTERS 2013年第8期7卷 1765-1791页

作者： Gupta, Pankaj Mittal, Garima Mehlawat, Mukesh Kumar Univ Delhi Dept Operat Res Delhi 110007 India Apeejay Sch Management Dept Decis Sci New Delhi India

In this paper, we propose a credibilistic framework for portfolio selection problem using an expected value multiobjective model with fuzzy parameters. We consider short term return, long term return, risk and liquidity as key financial criteria. A solution procedure comprising fuzzy goal programming and fuzzy simulation based real-coded genetic algorithm is developed to solve the model. The proposed solution approach is considered advantageous particularly for the cases where the fuzzy parameters of the problem may assume any general functional form. An empirical study is included to illustrate the usefulness of the proposed model and solution approach in real-world applications of portfolio selection.

关键词： Fuzzy portfolio selection Expected value model multiobjective programming Real-coded genetic algorithm Fuzzy simulation

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An interval fuzzy multiobjective watershed management model for the Lake Qionghai watershed, China

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WATER RESOURCES MANAGEMENT 2006年第5期20卷 701-721页

作者： Wang, Lijing Meng, Wei Guo, Huaicheng Zhang, Zhenxing Liu, Yong Fan, Yingying Peking Univ Coll Environm Sci Beijing 100871 Peoples R China Chinese Res Inst Environm Sci Beijing 100012 Peoples R China SUNY Syracuse Coll Environm Sci & Forestry Syracuse NY 13210 USA

Integrated watershed management is required to ensure the reasonable use of resources and reconcile interactions among natural and human systems. In the present study, an interval fuzzy multiobjective programming (IFMOP) method was used to solve an integrated watershed management problem. Based on system analysis, an IFMOP model suitable for a lake watershed system {IFMOPLWS} was developed and applied to the Lake Qionghai watershed in China. Scenario analysis and an interactive approach were used in the solution process. In this manner, various system components were incorporated into one framework for holistic consideration and optimization. Integrality and uncertainty, as well as the multiobjective and dynamic characteristics of the watershed system, were well addressed. Using two scenarios, two planning schemes were generated. Agriculture, tourism, macroeconomics, cropland use, water supply, forest coverage, soil erosion, and water pollution were fully interpreted and compared to identify a preferable planning alternative for local agencies. This study showed that the IFMOPLWS is a powerful tool for integrated watershed management planning and can provide a solid base for sustainable watershed management.

关键词： fuzzy interval Lake Qionghai watershed multiobjective programming scenario analysis uncertainty watershed management

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Efficiency in forest management: A multiobjective harvest scheduling model

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JOURNAL OF FOREST ECONOMICS 2014年第3期20卷 236-251页

作者： Hernandez, M. Gomez, T. Molina, J. Leon, M. A. Caballero, R. Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain Univ Pinar del Rio Dept Math Pinar Del Rio Cuba

This paper presents a new forest harvest scheduling model taking into account four conflicting objectives. The economic factor of timber production is considered and also aspects related to environmental protection. We also incorporate adjacency constraints to limit the maximum contiguous area where clear-cutting can be applied. The model proposed is applied to a timber production plantation in Cuba located in the region of Pinar del Rio. One factor to be taken into account in Cuban plantations is that the forest has a highly unbalanced age distribution. Therefore, in addition to the classical objectives of forest planning, we have the objective of rebalancing age distribution by the end of the planning horizon. Explicitly, the four objectives considered in the model are: (a) obtaining a balance-aged forest;(b) minimizing the area with trees older than the rotation age;(c) maximizing the NPV of the forest over the planning horizon;and (d) maximizing total carbon sequestration over the whole planning horizon. The solution to the proposed model provides a set of efficient management plans that are of assistance in analysing the tradeoffs between the economic and ecological objectives. The model is also applied to randomly generated simulated forests to compare its performance in other contexts. As the problem is a multiobjective binary nonlinear model, a metaheuristic procedure is used in order to solve it. (C) 2014 Department of Forest Economics, Swedish University of Agricultural Sciences, Umea. Published by Elsevier GmbH. All rights reserved.

关键词： Forest planning multiobjective programming Adjacency constraints CO2 captured Nonlinear binary models Metaheuristic

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Vector continuous-time programming without differentiability

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第3期234卷 924-933页

作者： de Oliveira, Valeriano Antunes Univ Fed Uberlandia Fac Ciencias Integradas Pontal BR-38032000 Ituiutaba MG Brazil

In this work continuous-time programming problems of vector optimization are considered. Firstly, a nonconvex generalized Gordan's transposition theorem is obtained. Then, the relationship with the associated weighting scalar problem is studied and saddle point optimality results are established. A scalar dual problem is introduced and duality theorems are given. No differentiability assumption is imposed. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Continuous-time programming multiobjective programming Preinvex functions Scalarization Saddle point optimality Duality

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Pattern classification by linear goal programming and its extensions

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JOURNAL OF GLOBAL OPTIMIZATION 1998年第2期12卷 111-126页

作者： Nakayama, H Kagaku, N Konan Univ Dept Appl Math Kobe Hyogo 658 Japan

Pattern classification is one of the main themes in pattern recognition, and has been tackled by several methods such as the statistic one, artificial neural networks, mathematical programming and so on. Among them, the multi-surface method proposed by Mangasarian is very attractive, because it can provide an exact discrimination function even for highly nonlinear problems without any assumption on the data distribution. However, the method often causes many slits on the discrimination curve. In other words, the piecewise linear discrimination curve is sometimes too complex resulting in a poor generalization ability. In this paper, several trials in order to overcome the difficulties of the multi-surface method are suggested. One of them is the utilization of goal programming in which the auxiliary linear programming problem is formulated as a goal programming in order to get as simple discrimination curves as possible. Another one is to apply fuzzy programming by which we can get fuzzy discrimination curves with gray zones. In addition, it will be shown that using the suggested methods, the additional learning can be easily made. These features of the methods make the discrimination more realistic. The effectiveness of the methods is shown on the basis of some applications.

关键词： multiobjective programming pattern classification goal programming portfolio selection

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