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Optimizing a linear function over the nondominated set of multiobjective integer programs

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2021年第4期28卷 2248-2267页

作者： Lokman, Banu Univ Portsmouth Portsmouth Business Sch Richmond BldgPortland St Portsmouth PO1 3DE Hants England

In this paper, we develop two algorithms to optimize a linear function over the nondominated set of multiobjective integer programs. The algorithms iteratively generate nondominated points and converge to the optimal solution reducing the feasible set. The first algorithm proposes improvements to an existing algorithm employing a decomposition and search procedure in finding a new point. Differently, the second algorithm maximizes one of the criteria throughout the algorithm and generates new points by setting bounds on the linear function value. The decomposition and search procedure in the algorithms is accompanied by problem-specific mechanisms in order to explore the objective function space efficiently. The algorithms are designed to produce solutions that meet a prespecified accuracy level. We conduct experiments on multiobjective combinatorial optimization problems and show that the algorithms work well.

关键词： multiple objective programming integer programming nondominated set combinatorial optimization

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Semi-quasidifferentiability in nonsmooth nonconvex multiobjective optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第1期299卷 35-45页

作者： Kabgani, Alireza Soleimani-damaneh, Majid Urmia Univ Technol Appl Math Grp Orumiyeh Iran Inst Res Fundamental Sci IPM Sch Math POB 19395-5746 Tehran Iran Univ Tehran Sch Math Stat & Comp Sci Coll Sci Tehran Iran

In this paper, we extend the concept of quasidifferential to a new notion called semi-quasidifferential. This generalization is motivated by the convexificator notion. Some important properties of semiquasidifferentials are established. The relationship between semi-quasidifferentials and the Clarke sub differential is studied, and a mean value theorem in terms of semi-quasidifferentials is proved. It is shown that this notion is helpful to investigate nonsmooth optimization problems even when the objective and/or constraint functions are discontinuous. Considering a multiobjective optimization problem, a characterization of some cones related to the feasible set is provided. They are used for deriving necessary and sufficient optimality conditions. We close the paper by obtaining optimality conditions in multi objective optimization in terms of semi-quasidifferentials. Some outcomes of the current work generalize the related results existing in the literature. (c) 2021 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Nonsmooth optimization Semi-quasidifferentiable function Nonconvex programming

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A multiple criteria decision making framework for regional aquaculture development

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2001年第3期133卷 462-482页

作者： El-Gayar, OF Leung, P Univ Alexandria Inst Grad Studies Res Alexandria Egypt Univ Hawaii Manoa Dept Biosyst Engn Honolulu HI 96822 USA

Aquaculture development is considered as a viable sourer for providing high quality cheap protein, particularly, for developing countries where protein shortage already exists. However, complexities in such development planning can be difficult without the aid of modern decision-aids such as multiple criteria decision making (MCDM) models. MCDM models are already in use in the business and manufacturing sectors. However, their use in agriculture is limited and their use in aquaculture is almost nonexistent. This paper presents a MCDM framework for the planning of regional aquaculture development. The MCDM model seeks a desirable allocation of resources and activity levels that strikes an acceptable balance among the various development goals under consideration subject to resource constraints, market constraints, and pollution constraints. To accommodate different decision situations, three different MCDM solution techniques are implemented, namely, multiple objective programming (MOP, compromise programming (CP), and weighted goal programming (WGP). The applicability of the framework is demonstrated through applying it to a case study from northern Egypt where aquaculture is a viable industry for supplying cheap and good quality protein, balancing the foreign exchange deficits, and creating employment opportunities. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： multiple criteria decision making multiple objective programming compromise programming goal programming aquaculture development

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Holder continuity and upper estimates of solutions to vector quasiequilibrium problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2011年第2期210卷 148-157页

作者： Li, S. J. Chen, C. R. Li, X. B. Teo, K. L. Chongqing Univ Coll Math & Stat Chongqing 401331 Peoples R China Curtin Univ Technol Dept Math & Stat Perth WA 6845 Australia

In this paper, we establish the Holder continuity of solution mappings to parametric vector quasiequilibrium problems in metric spaces under the case that solution mappings are set-valued. Our main assumptions are weaker than those in the literature, and the results extend and improve the recent ones. Furthermore, as an application of Holder continuity, we derive upper bounds for the distance between an approximate solution and a solution set of a vector quasiequilibrium problem with fixed parameters. (C) 2010 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Vector quasiequilibrium problems Holder continuity Upper bounds Hausdorff distance

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A modified augmented max min model for weighted fuzzy goal programming

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2014年第1期27卷 339-350页

作者： Arikan, Feyzan Gazi Univ Dept Ind Engn TR-06570 Maltepe Turkey

Since Narasimhan's first application of Fuzzy Set Theory to Goal programming (GP) in 1980, much research into fuzzy GP has been carried out. In fuzzy GP studies, although several researchers remained loyal to using the traditional GP representation, the majority have followed the fuzzy programming approach. Among fuzzy-programming-based studies, only the studies of Tiwari et al. and Lin seem applicable when the objectives have relative importance. However, both have disadvantages. Because the former model uses the add operator, some of the objectives may not be preferred at the optimal solution even they have heavy weights. The latter model is based on the max-min approach, which does not guarantee a non-dominated solution. In this study, a weighted Fuzzy GP model is presented to overcome these disadvantages, along with the shortcomings of other existing models. The model is modified from Lai and Hwang's augmented max-min model, which is guaranteed to reach a non-dominated solution. The superiority of the model over the existing approaches is demonstrated using numerical examples chosen from the literature.

关键词： multiple objective programming fuzzy sets fuzzy goal programming non-dominated solution relative weights

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User equilibrium in traffic assignment problem with fuzzy N-A incidence matrix

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FUZZY SETS AND SYSTEMS 1999年第3期107卷 245-253页

作者： Wang, HF Liao, HL Natl Tsing Hua Univ Dept Ind Engn Hsinchu 30043 Taiwan

The user equilibrium in traffic assignment problem is to choose the minimum-cost path between every origin-destination pair and through this process, those utilized paths will have equal costs. In other words, giving cost and demand function for transportation between every origin-destination pair, the solution of the problem is to provide the minimum cost of which the flow is generated. In this study, we consider this problem when the N-A incidence matrix for transportation is fuzzy,, in the sense that, which arcs are chosen into the desired path for traveling is uncertain. Therefore, we apply the method and concept of the theory of variational inequality with fuzzy convex cone to establish a user equilibrium pattern. Finally, the proposed method is demonstrated with a numerical example. (C) 1999 Published by Elsevier Science B.V. All rights reserved.

关键词： user equilibrium problem variational inequality multiple objective programming fuzzy set theory

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Lexicographic multi-objective road pricing optimization considering land use and transportation effects

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第2期298卷 496-509页

作者： Zhong, Shaopeng Jiang, Yu Nielsen, Otto Anker Dalian Univ Technol Sch Transportat & Logist Dalian 116024 Peoples R China Tech Univ Denmark Dept Technol Management & Econ DTU Management DK-2800 Lyngby Denmark

This paper develops a bi-level multi-objective model for road pricing optimization considering land use and transportation effects. The upper-level problem determines a cordon-based road pricing scheme, while the lower-level problem models the interaction between land use and transportation. To facilitate decision-making in a scenario characterized by a hierarchical ordering of objectives, a novel alpha-conditional lexicographic optimization method is established, which uses an alpha value to capture the decision-maker's perceived acceptability of the trade-off between different objectives with respect to the hierarchical objective ordering. The properties associated with this approach are derived, and an algorithm to find the alpha-conditional lexicographic dominance solutions is developed. To solve the model, a revised genetic algorithm is further developed to illustrate how the proposed alpha-conditional lexicographic optimization method can be embedded into existing heuristic or metaheuristic methods. A case study using data from Jiangyin, China, demonstrates the significance of considering land use effects when evaluating road pricing scenarios. The results reveal the trade-off between transportation and various land use objectives and the variation of such a trade-off among different types of traffic analysis zones. It is demonstrated that the proposed alpha-conditional lexicographic approach can improve most of the land use objective values while ensuring that the total travel time is constrained within an acceptable range, enabling a balance between various land use and transportation objectives. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Transportation multiple objective programming Road pricing Land use and transportation interaction Lexicographic optimization

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Non-contour efficient fronts for identifying most preferred portfolios in sustainability investing

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2023年第2期306卷 742-753页

作者： Steuer, Ralph E. Utz, Sebastian Univ Georgia Dept Finance Athens GA 30602 USA Univ Augsburg Fac Business Adm & Econ Univ Str 12 D-86159 Augsburg Germany Ctr Climate Resilience Univ Str 12 D-86159 Augsburg Germany

The paper focuses on investors whose strength of interest in sustainability issues (such as environmental, social, and governance) causes ESG to become a third criterion alongside risk and return in portfolio selection. This causes the efficient frontier to become an efficient surface. This means that an investor's optimal portfolio is no longer the point of most preferred risk/return tradeoff on the mean-variance (M-V) efficient frontier, but is the point of most preferred risk/return/ESG tradeoff on the investor's M-V-ESG efficient surface. However, to find such a point requires non-trivial ESG integration which is the name given to the process of integrating ESG into the portfolio construction process after screening. With the third objective transporting the problem into 3D-space, it is difficult to search the efficient surface in any kind of comprehensive fashion using M-V based or other bi-criterion techniques as this is akin to a 2 -dimensional being trying to view a 3-dimensional object. To remedy the situation, the paper proposes a tri-criterion approach that computes efficient surfaces and special non-contour curves (called NC-efficient fronts in the paper) that are stretched across the efficient surface so as to dragnet it for the points of best ESG integration within it. Using the methodology and data from the S&P500, the paper conducts computational tests on problems with up to 500 securities and under different constraint conditions so as to know what to expect from the new approach over a range of situations.(c) 2022 Elsevier B.V. All rights reserved.

关键词： multiple objective programming ESG in investing Efficient frontiers ESG integration Tri-criterion portfolio selection

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TRANSFORM-ANN for online optimization of complex industrial processes: Casting process as case study

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第1期264卷 294-309页

作者： Miriyala, Srinivas Soumitri Subramanian, Venkat Mitra, Kishalay Indian Inst Technol Hyderabad Dept Chem Engn Sangareddy 502285 Telangana India Univ Washington Dept Chem Engn 1410 NE Campus Pkwy Seattle WA 98195 USA

Artificial Neural Networks (ANNs) are well known for their credible ability to capture non-linear trends in scientific data. However, the heuristic nature of estimation of parameters associated with ANNs has prevented their evolution into efficient surrogate models. Further, the dearth of optimal training size estimation algorithms for the data greedy ANNs resulted in their overfitting. Therefore, through this work, we aim to contribute a novel ANN building algorithm called TRANSFORM aimed at simultaneous and optimal estimation of ANN architecture, training size and transfer function. TRANSFORM is integrated with three standalone Sobol sampling based training size determination algorithms which incorporate the concepts of hypercube sampling and optimal space filling. TRANSFORM was used to construct ANN surrogates for a highly non-linear industrially validated continuous casting model from steel plant. Multiobjective optimization of casting model to ensure maximum productivity, maximum energy saving and minimum operational cost was performed by ANN assisted Non-dominated Sorting Genetic Algorithms (NSGA-II). The surrogate assisted optimization was found to be 13 times faster than conventional optimization, leading to its online implementation. Simple operator's rules were deciphered from the optimal solutions using Pareto front characterization and K-means clustering for optimal functioning of casting plant. Comprehensive studies on (a) computational time comparisons between proposed training size estimation algorithms and (b) predictability comparisons between constructed ANNs and state of art statistical models, Kriging Interpolators adds to the other highlights of this work. TRANSFORM takes physics based model as the only input and provides parsimonious ANNs as outputs, making it generic across all scientific domains. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Artificial Intelligence multiple objective programming Neural Networks Online optimization Surrogate models

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Set-based robust optimization of uncertain multiobjective problems via epigraphical reformulations

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第3期313卷 871-882页

作者： Eichfelder, Gabriele Quintana, Ernest Tech Univ Ilmenau Inst Math PO 10 05 65 D-98684 Ilmenau Germany

In this paper, we study a method for finding robust solutions to multiobjective optimization problems under uncertainty. We follow the set-based minmax approach for handling the uncertainties which leads to a certain set optimization problem with the strict upper type set relation. We introduce, under some assumptions, a reformulation using instead the strict lower type set relation without sacrificing the compactness property of the image sets. This allows to apply vectorization results to characterize the optimal solutions of these set optimization problems as optimal solutions of a multiobjective optimization problem. We end up with multiobjective semi-infinite problems which can then be studied with classical techniques from the literature.

关键词： multiple objective programming Robustness and sensitivity analysis Set optimization Semi-infinite programming

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