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On the transformation of lexicographic nonlinear multiobjective programs to single objective programs

MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2011年第2期74卷 217-231页

作者： Zarepisheh, M. Khorram, E. Amir Kabir Univ Technol Fac Math & Comp Sci Tehran 15914 Iran

This paper deals with multiobjective optimization programs in which the objective functions are ordered by their degree of priority. A number of approaches have been proposed (and several implemented) for the solution of lexicographic (preemptive priority) multiobjective optimization programs. These approaches may be divided into two classes. The first encompasses the development of algorithms specifically designed to deal directly with the initial model. Considered only for linear multiobjective programs and multiobjective programs with a finite discrete feasible region, the second one attempts to transform, efficiently, the lexicographic multiobjective model into an equvivalent model, i.e. a single objective programming problem. In this paper, we deal with the second approach for lexicographic nonlinear multiobjective programs.

关键词： multiobjective programming Vector optimization Preemptive priority Lexicographic ordering

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Coordination of transmission path transfers

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IEEE TRANSACTIONS ON POWER SYSTEMS 2004年第3期19卷 1607-1615页

作者： Li, Y Venkatasubramanian, V Washington State Univ Sch Elect Engn & Comp Sci Pullman WA 99163 USA

The transfer capability on a transmission path is limited by constraints on acceptability, voltage security, small-signal stability, and transient stability. For a large interconnected power grid, these constraints are influenced significantly by the interactions among path flows in different control areas. When a critical transmission path capability is limited by one of these constraints, it may be necessary to coordinate the interarea power transfers so as to improve the transfer capability on the constrained path without compromising on the security criteria. Based on such considerations, this paper presents a novel multiobjective methodology in which global strategies are developed for the improvement and coordination of transmission path transfers. The problem is formulated with respect to various constraints into suitable optimization problems. An efficient nonlinear programming algorithm with sufficient line search step is incorporated for finding optimal solutions while also incorporating security and stability constraints. The MW benefits for the transfer capability from the coordination procedure are explicitly demonstrated after the optimization process. The effectiveness of the methodology is illustrated by case studies on improving the capability of the California-Oregon Intertie (COI) for large-scale WECC western American power system models.

关键词： multiobjective programming nonlinear optimization small signal stability transfer capability transient stability voltage security

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Analysing the scalability of multiobjective evolutionary algorithms when solving the motif discovery problem

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JOURNAL OF GLOBAL OPTIMIZATION 2013年第2期57卷 467-497页

作者： Gonzalez-Alvarez, David L. Vega-Rodriguez, Miguel A. Univ Extremadura Escuela Politecn ARCO Res Grp Dept Technol Comp & Commun Caceres 10003 Spain

In this paper we analyse the scalability of seven multiobjective evolutionary algorithms when they solve large instances of a known biological problem, the motif discovery problem (MDP). The selected algorithms are a population-based and a trajectory-based algorithms (DEPT and MO-VNS, respectively), three swarm intelligence algorithms (MOABC, MO-FA, and MO-GSA), a genetic algorithm (NSGA-II), and SPEA2. The MDP is one of the most important sequence analysis problems related to discover common patterns, motifs, in DNA sequences. A motif is a nucleic acid sequence pattern that has some biological significance as being DNA binding sites for a regulatory protein, i.e., a transcription factor (TF). A biologically relevant motif must have a certain length, be found in many sequences, and present a high similarity among the subsequences which compose it. These three goals are in conflict with each other, therefore a multiobjective approach is a good way of facing the MDP. In addition, in recent years, scientists are decoding genomes of many organisms, increasing the computational workload of the algorithms. Therefore, we need algorithms that are able to deal with these new large DNA instances. The obtained experimental results suggest that MOABC and MO-FA are the algorithms with the best scalability behaviours.

关键词： Computer science Scalability analysis multiobjective programming Evolutionary algorithm DNA

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System Portfolio Selection for Large-Scale Complex Systems Construction

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IEEE SYSTEMS JOURNAL 2019年第4期13卷 3627-3638页

作者： Dou, Yajie Zhao, Danling Xia, Boyuan Zhang, Xiaoxiong Yang, Kewei Natl Univ Def Technol Coll Syst Engn Changsha 410073 Hunan Peoples R China

With the number of alternative systems increasing, the system portfolio selection problem for large-scale complex systems is an non-deterministic polynomial (NP)-hard problem. The time cost of the classification selection algorithm used for the portfolio selection is intolerable;thus, improving the algorithm is necessary. In this paper, first, the weapon system portfolio selection (WSPS) model is categorized into two types: single objective and multiobjective;the optimization difficulties are analyzed;and the feasible solution space reduction strategy is given. Second, a portfolio selection optimization algorithm based on the difference evolution technique for order preference by similarity to ideal solution (DE-TOPSIS) is proposed where the weapon system weighting method TOPSIS is integrated with the DE algorithm. Finally, considering different weapon system scales, the advantages of the proposed algorithm are illustrated by comparing it with two other algorithms in a single-target case and two other algorithms in a multiobjective case. The results indicate that the DE algorithm always has better performance with regard to optimal solution quality, convergence speed, and algorithm stability.

关键词： Difference evolution technique for order preference by similarity to ideal solution (DE-TOPSIS) multiobjective programming reduction strategy weapon system portfolio selection (WSPS)

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An η-approximation approach in nonlinear vector optimization with univex functions

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2006年第4期23卷 525-542页

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

In this paper, the so-called eta-approximation approach is used to obtain the sufficient conditions for a nonlinear multiobjective programming problem with univex functions with respect to the same function eta. In this method, an equivalent eta-approximated vector optimization problem is constructed by a modification of both the objective and the constraint functions in the original multiobjective programming problem at the given feasible point. Moreover, to find the optimal solutions of the original multiobjective problem, it sufficies to solve its associated eta-approximated vector optimization problem. Finally, the description of the eta-approximation algorithm for solving a nonlinear multiobjective programming problem involving univex functions is presented.

关键词： multiobjective programming (weak) Pareto optimal point univex function with respect to eta, phi, and b eta-approximated vector optimization problem

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On multiobjective second order symmetric duality with cone constraints

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第3期204卷 402-409页

作者： Ahmad, I. Husain, Z. Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India

A pair of Wolfe type multiobjective second order symmetric dual programs with cone constraints is formulated and usual duality results are established under second order invexity assumptions. These results are then used to investigate symmetric duality for minimax version of multiobjective second order symmetric dual programs wherein some of the primal and dual variables are constrained to belong to some arbitrary sets, i.e., the sets of integers. This paper points out certain omissions and inconsistencies in the earlier work of Mishra [S.K. Mishra, multiobjective second order symmetric duality with cone constraints, European journal of Operational Research 126 (2000) 675-682] and Mishra and Wang [S.K. Mishra, S.Y. Wang, Second order symmetric duality for nonlinear multiobjective mixed integer programming, European journal of Operational Research 161 (2005) 673-682]. (C) 2009 Elsevier B.V. All rights reserved.

关键词： multiobjective programming Symmetric duality Minimax Second order invexity

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Convexificators and strong Kuhn-Tucker conditions

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2012年第4期64卷 550-557页

作者： Golestani, M. Nobakhtian, S. Univ Isfahan Dept Math Esfahan 81745163 Iran

This study is devoted to constraint qualifications and strong Kuhn-Tucker necessary optimality conditions for nonsmooth multiobjective optimization problems. The main tool of the study is the concept of convexificators. Mangasarian-Fromovitz type constraint qualification and several other qualifications are proposed and their relationships are investigated. In addition, sufficient optimality conditions are studied. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： multiobjective programming Optimality conditions Nonsmooth optimization Convexificator Constraint qualification

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A superlinearly convergent nonmonotone quasi-Newton method for unconstrained multiobjective optimization

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OPTIMIZATION METHODS & SOFTWARE 2020年第6期35卷 1223-1247页

作者： Mahdavi-Amiri, N. Sadaghiani, F. Sharif Univ Technol Fac Math Sci Tehran Iran

We propose and analyse a nonmonotone quasi-Newton algorithm for unconstrained strongly convex multiobjective optimization. In our method, we allow for the decrease of a convex combination of recent function values. We establish the global convergence and local superlinear rate of convergence under reasonable assumptions. We implement our scheme in the context of BFGS quasi-Newton method for solving unconstrained multiobjective optimization problems. Our numerical results show that the nonmonotone quasi-Newton algorithm uses fewer function evaluations than the monotone quasi-Newton algorithm.

关键词： multiobjective programming nonmonotone line search algorithm nonmonotone quasi-Newton method efficiency

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A combined MOIP-MCDA approach to building and screening atmospheric pollution control strategies in urban regions

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ENVIRONMENTAL MANAGEMENT 2006年第1期38卷 149-160页

作者： Mavrotas, George Ziomas, Ioannis C. Diakouaki, Danae Natl Tech Univ Athens Sch Chem Engn Lab Ind & Energy Econ Athens 15780 Greece Natl Tech Univ Athens Sch Chem Engn Lab Proc Anal & Design Athens 15780 Greece

This article presents a methodological approach for the formulation of control strategies capable of reducing atmospheric pollution at the standards set by European legislation. The approach was implemented in the greater area of Thessaloniki and was part of a project aiming at the compliance with air quality standards in five major cities in Greece. The methodological approach comprises two stages: in the first stage, the availability of several measures contributing to a certain extent to reducing atmospheric pollution indicates a combinatorial problem and favors the use of Integer programming. More specifically, Multiple Objective Integer programming is used in order to generate alternative efficient combinations of the available policy measures on the basis of two conflicting objectives: public expenditure minimization and social acceptance maximization. In the second stage, these combinations of control measures (i.e., the control strategies) are then comparatively evaluated with respect to a wider set of criteria, using tools from Multiple Criteria Decision Analysis, namely, the well-known PROMETHEE method. The whole procedure is based on the active involvement of local and central authorities in order to incorporate their concerns and preferences, as well as to secure the adoption and implementation of the resulting solution.

关键词： air pollution multiple criteria multiobjective programming integer programming

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multiobjective Allocation of Transboundary Water Resources: Case of the Euphrates and Tigris

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JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT 2010年第1期136卷 95-105页

作者： Kucukmehmetoglu, Mehmet Guldmann, Jean-Michel Ohio State Univ Dept City & Reg Planning Columbus OH 43210 USA Gebze Inst Technol Dept City & Reg Planning TR-41400 Gebze Kocaeli Turkey

The allocation of water in a multicountry river system necessarily involves conflicting objectives, where increasing water benefits for one country entails losses for other countries. This paper presents the formulation and application of a multiobjective linear programming model, where each objective represents the benefits for a country from using water for agriculture, urban consumption. and energy production, net of conveyance costs. This model is applied to the Euphrates and Tigris River basin and its three riparian countries-Turkey, Syria, and Iraq. The model is used to delineate the set of nondominated Solutions (Pareto frontier), and is extended to include political factors and distributional constraints, leading to ail allocation of basin water and resulting benefits.

关键词： Water resources allocation Economic benefits multiobjective programming Pareto frontier

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