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Designing bioreserve networks to satisfy multiple, conflicting demands

ECOLOGICAL APPLICATIONS 1999年第3期9卷 741-750页

作者： Rothley, KD Yale Univ Sch Forestry & Environm Studies New Haven CT 06511 USA

Reserve designers typically strive to create reserves that satisfy a variety of potentially conflicting criteria. Rather than optimizing with respect to just one criterion, reserve planners are likely to seek some compromise. To facilitate bioreserve design, I propose the use of multiobjective programming to identify these compromise alternatives, and then the use of the simple multiattribute rating technique to rank these alternatives and to explore the sensitivity of the rankings to the relative value placed on the individual criteria. An example is provided for the selection of a reserve system in Nova Scotia, Canada, based on three criteria: (1) connectedness, (2) area, and (3) rare species representation. First, multiobjective programming was used to reduce the set of over 15 000 potential reserve-system alternatives to a list of 36 candidate systems representing the optimal tradeoffs among the three criteria. The simple attribute-rating technique was then used to identify a single best solution for an arbitrary set of relative criteria values and to test the robustness of this solution to changes in relative preferences for the criteria. The techniques presented here can simplify the evaluation of reserve alternatives, enabling planners to refocus their efforts on the complex biological, social, and economic aspects of reserve design.

关键词： biodiversity preservation bioreserve design multiobjective programming Nova Scotia reserve network reserve selection selection algorithms reserves simple multiattribute rating technique

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THE LINEARIZATION METHOD - PRINCIPAL CONCEPTS AND PERSPECTIVE DIRECTIONS

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JOURNAL OF GLOBAL OPTIMIZATION 1993年第4期3卷 483-500页

作者： PSHENICHNYI, BN SOSNOVSKY, AA VM GLUSHKOV CYBERNET INST KIEV UKRAINE

The linearization method, for solving the general problem of nonlinear programming and its various modifications, is considered. On the basic ideas of the linearization method, the algorithms for solving the various problems of mathematical programming are constructed for (a) solving systems of equalities and inequalities, (b) multiobjective programming and (c) complementary problem.

关键词： THE LINEARIZATION METHOD, SYSTEMS OF EQUALITIES AND INEQUALITIES multiobjective programming COMPLEMENTARITY PROBLEM

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Generalisation of A-equitable preference in multiobjective optimisation problems

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OPTIMIZATION 2021年第9期70卷 1859-1874页

作者： Foroutannia, D. Merati, M. Vali E Asr Univ Rafsanjan Dept Math Rafsanjan Iran

The concept of A-equitable efficiency in solving the multiobjective optimisation problems have recently been introduced by Mut and Wiecek [Generalised equitable preference in multiobjective programming. Euro J Oper Res. 2011;212:535-551], where A is an arbitrary matrix with non-negative entries. The preference relation of this concept solution, , does not satisfy the strict monotonicity and strict principle of transfers axioms in general, therefore the set of A-equitably efficient solutions is not contained within the set of equitably efficient solutions and the set of Pareto-optimal solutions for the same problem. In this paper, we extend the work done by Mut and Wiecek and state the new conditions on the matrix A that guarantee to satisfy these axioms by the preference relation . The other contribution of this paper is the use of the preference relation to solve the multio objective optimisation problems instead of . This has the advantage that the decision-maker has more freedom to choose the preferences matrix A. The relation has become an equitable rational preference relation by imposing the weaker conditions on entries of A, in comparison to the relation <=(e(A)).

关键词： Preference Pareto efficiency equitability multiobjective programming

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On optimality conditions for multiobjective optimization problems in topological vector space

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2007年第1期334卷 123-131页

作者： Fulga, Cristinca Preda, Vasile Acad Econ Studies Fac Cybernet Stat & Econ Informat Dept Math Bucharest Romania Univ Bucharest Fac Math & Comp Sci Bucharest 010014 Romania

In this paper, we are concerned with a differentiable multiobjective programming problem in topological vector spaces. An alternative theorem for generalized K subconvexlike mappings is given. This permits the establishment of optimality conditions in this context: several generalized Fritz John conditions, in line to those in Hu and Ling [Y Hu, C. Ling, The generalized optimality conditions of multiobjective programming problem in topological vector space, J. Math. Anal. Appl. 290 (2004) 363-372] are obtained and, in the presence of the generalized Slater's constraint qualification, the Karush-Kuhn-Tucker necessary optimality conditions. (c) 2006 Elsevier Inc. All rights reserved.

关键词： multiobjective programming optimality conditions topological vector spaces

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A CHARACTERIZATION OF WEAKLY EFFICIENT POINTS

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MATHEMATICAL programming 1995年第2期68卷 205-212页

作者： RUIZCANALES, P RUFIANLIZANA, A Departamento de Estadística e Investigación Operativa Facultad de Matemáticas Sevilla Spain

In this paper, we study a characterization of weakly efficient solutions of multiobjective Optimization Problems (MOPs). We find that, under some quasiconvex conditions of the objective functions in a convex set of constraints, weakly efficient solutions of an MOP can be characterized as an optimal solution to a scalar constraint problem, in which one of the objectives is optimized and the remaining objectives are set up as constraints. This characterization is much less restrictive than those found in the literature up to now.

关键词： WEAKLY EFFICIENT POINT multiobjective programming SCALAR OPTIMIZATION PROBLEM GENERALIZED CONVEXITY

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Definition and Characterization of Geoffrion Proper Efficiency for Real Vector Optimization with Infinitely Many Criteria

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2015年第2期165卷 439-457页

作者： Engau, Alexander Univ Colorado Dept Math & Stat Sci Denver CO 80202 USA

The concept and characterization of proper efficiency is of significant theoretical and computational interest, in multiobjective optimization and decision-making, to prevent solutions with unbounded marginal rates of substitution. In this paper, we propose a slight modification to the original definition in the sense of Geoffrion, which maintains the common characterizations of properly efficient points as solutions to weighted sums or series and augmented or modified weighted Tcheby-cheff norms, also if the number of objective functions is countably infinite. We give new proofs and counter examples which demonstrate that such results become invalid for infinitely many criteria with respect to the original definition, in general, and we address the motivation and practical relevance of our findings for possible applications in stochastic optimization and decision-making under uncertainty.

关键词： Proper efficiency Multicriteria optimization multiobjective programming Infinitely many criteria Weighted-sum method Tchebycheff norm Scalarization

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multiobjective Efficient Portfolio Selection with Bounded Parameters

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ARABIAN JOURNAL FOR SCIENCE AND ENGINEERING 2018年第6期43卷 3311-3325页

作者： Kumar, P. Panda, G. Gupta, U. C. SRM Inst Sci & Technol Dept Math Madras 603203 Tamil Nadu India Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

In this paper, a multiobjective portfolio selection model is studied, wherein all parameters like return, risk, etc., as well as decision variables are varying in intervals. A methodology is developed using interval analysis to derive an acceptable efficient portfolio. The theoretical developments are justified by assigning the degree of acceptability to every feasible portfolio as well as assigning goals to each objective function. This theoretical development is illustrated in a portfolio selection model with data from Bombay Stock Exchange, India, which justifies that the results obtained by the proposed method are close enough to the existing result.

关键词： Interval optimization Liquidity multiobjective programming Partial order Portfolio selection

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multiobjective BLOCKMODELING FOR SOCIAL NETWORK ANALYSIS

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PSYCHOMETRIKA 2013年第3期78卷 498-525页

作者： Brusco, Michael Doreian, Patrick Steinley, Douglas Satornino, Cinthia B. Florida State Univ Coll Business Tallahassee FL 32306 USA Univ Pittsburgh Dept Sociol Pittsburgh PA 15260 USA Univ Ljubljana Fac Social Sci Ljubljana 61000 Slovenia Univ Missouri Dept Psychol Sci Columbia MO 65211 USA

To date, most methods for direct blockmodeling of social network data have focused on the optimization of a single objective function. However, there are a variety of social network applications where it is advantageous to consider two or more objectives simultaneously. These applications can broadly be placed into two categories: (1) simultaneous optimization of multiple criteria for fitting a blockmodel based on a single network matrix and (2) simultaneous optimization of multiple criteria for fitting a blockmodel based on two or more network matrices, where the matrices being fit can take the form of multiple indicators for an underlying relationship, or multiple matrices for a set of objects measured at two or more different points in time. A multiobjective tabu search procedure is proposed for estimating the set of Pareto efficient blockmodels. This procedure is used in three examples that demonstrate possible applications of the multiobjective blockmodeling paradigm.

关键词： social networks blockmodeling multiobjective programming heuristics tabu search

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Using fuzzy operators to address the complexity in decision making of water resources redistribution in two neighboring river basins

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ADVANCES IN WATER RESOURCES 2010年第6期33卷 652-666页

作者： Chen, Ho-Wen Chang, Ni-Bin Univ Cent Florida Dept Civil Environm & Construct Engn Orlando FL 32816 USA Chaoyang Univ Technol Dept Environm Engn & Management Taichung Taiwan

This paper emphasizes the use of fuzzy sets for incorporating objective and subjective uncertainties to address coevolutionary alignment of a suite of water resources redistribution alternatives in a transboundary channel-reservoir system. The highlighted decision making complexity arises from the interactions between two neighboring water systems (i.e., the Tseng-Wen and Kao-Ping River Basins, South Taiwan) where a pending diversion plan has been under intensive debate for over a decade. While the local stakeholders make uncertain science linked with uncertain politics resulting in endless delay of the diversion plan, the environmental advocacy groups stress the increasing concern of loss of biological integrity due to changes of land use when sharing water resources across the boundary. Consequently, there is a need to generate a novel integration that enables us to consider a vast number of internal weirs, water intakes, reservoirs, drainage ditches, and transfer pipelines within the basin and bring out the connectivity via diversion between these two neighboring river basins under uncertainty. To explore the managerial implications with varying risk perception and risk attitude, four types of fuzzy operators tailored for the fuzzy multi-objective decision analysis depict greater flexibility in representing the complexity of possible trade-offs among those alternatives. These trade-offs in the multi-objective evaluation context are constrained by physical, chemical, socioeconomic, managerial, and technical factors reflecting the needs for adaptive water resources management. Findings indicates that the use of fuzzy operators is instructive, which could provide unique guidance for enlightening the potential barriers in sustainable water resources management at the regional scale. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Water resources Systems analysis multiobjective programming Fuzzy set theory Decision science Environmental sustainability

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Selecting compact habitat reserves for species with differential habitat size needs

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COMPUTERS & OPERATIONS RESEARCH 2008年第2期35卷 475-487页

作者： Marianov, Vladimir ReVelle, Charles Snyder, Stephanie Pontificia Univ Catolica Chile Coll Engn Vicuna Mackenna 4860 Santiago Chile USDA Forest Serv N Cent Res Stn St Paul MN 55108 USA

We propose a model for the design of protected habitat reserves, which maximizes the number of species represented at least once in a limited set of reserved sites or parcels. Most models for reserve design do not differentiate eligible habitat sites by their size. Also, they assume that protection is guaranteed through the selection of one site for any species, not taking into consideration that habitat needs vary from species to species. Our model acknowledges the fact that different species require reserves of different sizes, and that these reserves should be compact areas, as opposed to a set of disconnected parcels. Computational experience is shown on a landscape modeled as a regular grid, in which individual species require 1-, 2- or 4-parcel compact reserves. The results are compared to output from a Maximum Species Covering Model. (C) 2006 Elsevier Ltd. All rights reserved.

关键词： habitat protection species preservation multiobjective programming integer programming biodiversity

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