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Existence of χ-efficient solution of multiobjective fractional programming problem with bounded parameters

INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH 2018年第6期25卷 1947-1971页

作者： Jana, Mrinal Panda, Geetanjali Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India

In this paper, a methodology is developed to solve a multiobjective fractional programming problem in which the coefficients of the objective functions and constraints are intervals. This model is transformed into an interval-free equivalent optimization problem. A new partial ordering is introduced and the relation between the original problem and the transformed problem is established using this partial ordering. The proposed methodology is illustrated through a numerical example.

关键词： constraint programming fractional programming multiple objective programming uncertainty modeling

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Implementation aspects of interactive multiobjective optimization for modeling environments: the case of GAMS-NIMBUS

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2014年第3期58卷 757-779页

作者： Ojalehto, Vesa Miettinen, Kaisa Laukkanen, Timo Univ Jyvaskyla Dept Math Informat Technol FI-40014 Jyvaskyla Finland Aalto Univ Sch Engn Dept Energy Technol FI-00076 Aalto Finland

Interactive multiobjective optimization methods have provided promising results in the literature but still their implementations are rare. Here we introduce a core structure of interactive methods to enable their convenient implementation. We also demonstrate how this core structure can be applied when implementing an interactive method using a modeling environment. Many modeling environments contain tools for single objective optimization but not for interactive multiobjective optimization. Furthermore, as a concrete example, we present GAMS-NIMBUS Tool which is an implementation of the classification-based NIMBUS method for the GAMS modeling environment. So far, interactive methods have not been available in the GAMS environment, but with the GAMS-NIMBUS Tool we open up the possibility of solving multiobjective optimization problems modeled in the GAMS modeling environment. Finally, we give some examples of the benefits of applying an interactive method by using the GAMS-NIMBUS Tool for solving multiobjective optimization problems modeled in the GAMS environment.

关键词： multiple objective programming Interactive methods NIMBUS method Modeling languages Pareto optimality

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A multiobjective hub-airport location problem for an airline network design

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第2期277卷 412-425页

作者： Soylu, Banu Katip, Hatice Erciyes Univ Dept Ind Engn TR-38039 Kayseri Turkey

This paper presents a biobjective multiple allocation p-hub median problem, discusses the properties of the Pareto frontier and proposes exact and heuristic algorithms for finding the Pareto frontier. Our motivation emanates from airline networks and their new hub investment strategies. The first objective minimizes the total transportation cost of the network, while the second one minimizes 2-stop journeys in order to improve customer satisfaction, which is negatively affected by the multiple-transit routes of airlines. Although using hubs reduces operating costs in networks, a cost-effective hub network may not imply minimum individual travel times for passengers, or happy passengers. It is well-known that airline customers prefer flights with fewer stops. However, reducing 2-stop routes increases the number of arcs, non-stop and 1-stop routes, and thus the total cost in the network. We analyzed the tradeoff between these objective functions. We performed experiments on well-Known data sets from the literature. We were able to find the Pareto frontier exactly for small/medium size instances. A variable neighborhood search (VNS) heuristic is presented to approximate the Pareto frontier of large size instances. We also performed an application on the current Turkish aeronautics network. The results are presented and discussed. (C) 2019 Elsevier B.V. All rights reserved.

关键词： multiple objective programming p-hub median problem Mixed-integer linear programming Multiobjective VNS Hub location

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Evolutionary, constructive and hybrid procedures for the bi-objective set packing problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2010年第2期204卷 206-217页

作者： Delorme, Xavier Gandibleux, Xavier Degoutin, Fabien Ecole Natl Super Mines Ctr Genie Ind & Informat F-42023 St Etienne 2 France Univ Nantes LINA F-44322 Nantes 03 France INRETS ESTAS F-59650 Villeneuve Dascq France

The bi-objective set packing problem is a multi-objective combinatorial optimization problem similar to the well-known set covering/partitioning problems. To our knowledge and surprise, this problem has not yet been studied whereas several applications have been reported. Unfortunately, solving the problem exactly in a reasonable time using a generic solver is only possible for small instances. We designed three alternative procedures for approximating solutions to this problem. The first is derived from the original 'Strength Pareto Evolutionary Algorithm', which is a population-based metaheuristic. The second is an adaptation of the 'Greedy Randomized Adaptative Search Procedure', which is a constructive metaheuristic. As underlined in the overview of the literature summarized here, almost all the recent, effective procedures designed for approximating optimal solutions to multi-objective combinatorial optimization problems are based on a blend of techniques, called hybrid metaheuristics. Thus, the third alternative, which is the primary subject of this paper, is an original hybridization of the previous two metaheuristics. The algorithmic aspects, which differ from the original definition of these metaheuristics, are described, so that our results can be reproduced. The performance of our procedures is reported and the computational results for 120 numerical instances are discussed. (C) 2009 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Metaheuristics Set packing problem Hybrid method

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A novel multi-objective particle swarm optimization with multiple search strategies

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2015年第3期247卷 732-744页

作者： Lin, Qiuzhen Li, Jianqiang Du, Zhihua Chen, Jianyong Ming, Zhong Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen 518060 Peoples R China

Recently, multi-objective particle swarm optimization (MOPSO) has shown the effectiveness in solving multi-objective optimization problems (MOPs). However, most MOPSO algorithms only adopt a single search strategy to update the velocity of each particle, which may cause some difficulties when tackling complex MOPs. This paper proposes a novel MOPSO algorithm using multiple search strategies (MMOPSO), where decomposition approach is exploited for transforming MOPs into a set of aggregation problems and then each particle is assigned accordingly to optimize each aggregation problem. Two search strategies are designed to update the velocity of each particle, which is respectively beneficial for the acceleration of convergence speed and the keeping of population diversity. After that, all the non-dominated solutions visited by the particles are preserved in an external archive, where evolutionary search strategy is further performed to exchange useful information among them. These multiple search strategies enable MMOPSO to handle various kinds of MOPs very well. When compared with some MOPSO algorithms and two state-of-the-art evolutionary algorithms, simulation results show that MMOPSO performs better on most of test problems. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

关键词： multiple objective programming Particle swarm optimization Evolutionary computation multiple search strategies

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Extension of Zoutendijk method for solving constrained multiobjective optimization problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期273卷 44-57页

作者： Morovati, Vahid Pourkarimi, Latif Amirkabir Univ Technol Fac Math & Comp Sci Dept Appl Math Tehran Iran Razi Univ Fac Sci Dept Math Kermanshah Iran

This paper extends the use of Zoutendijk method for constrained multiobjective optimization problems. This extension is a nonparametric direction-based algorithm. More precisely, considering all objective functions and binding constraints, this algorithm proposes a convex quadratic subproblem for generating a convenient improving feasible direction. Then, by using some elementary computation, the step length corresponding to the current direction is obtained. Some useful theoretical results corresponding to the proposed method are demonstrated. Using some of these theoretical results and under some mild conditions, the convergence of the proposed method is proved. The Zoutendijk multiobjective optimization (ZMO) method is not a population-based method. However, in order to find an approximation of the nondominated frontier, we need to have an appropriate population of initial feasible solutions. To achieve this aim, in this paper a cutting plane-like procedure which can generate an appropriate population of feasible solutions over the feasible set is proposed. Finally, in order to show its superiority, the proposed method is implemented for some well-known test problems. By employing some performance assessment criteria, the obtained numerical results are compared with the NSGA II method for all test problems. To have a more convenient comparison, the results are depicted in some performance profiles. Moreover, the obtained nondominated frontiers of these methods are compared for some test problems. The numerical results confirm the high performance of the ZMO method. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Zoutendijk's method Nonparametric methods Efficient solution Nondominated point

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Bicriteria train scheduling for high-speed passenger railroad planning applications

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2005年第3期167卷 752-771页

作者： Zhou, XS Zhong, M Univ Maryland Dept Civil & Environm Engn College Pk MD 20742 USA Univ Maryland Maryland Transportat Initiat College Pk MD 20742 USA Univ Maryland Robert H Smith Sch Business College Pk MD 20742 USA

This paper is concerned with a double-track train scheduling problem for planning applications with multiple objectives. Focusing on a high-speed passenger rail line in an existing network, the problem is to minimize both (1) the expected waiting times for high-speed trains and (2) the total travel times of high-speed and medium-speed trains. By applying two practical priority rules, the problem with the second criterion is decomposed and formulated as a series of multi-mode resource constrained project scheduling problems in order to explicitly model acceleration and deceleration times. A branch-and-bound algorithm with effective dominance rules is developed to generate Pareto solutions for the bicriteria scheduling problem, and a beam search algorithm with utility evaluation rules is used to construct a representative set of non-dominated solutions. A case study based on Beijing-Shanghai high-speed railroad in China illustrates the methodology and compares the performance of the proposed algorithms. (C) 2004 Elsevier B.V. All rights reserved.

关键词： scheduling multiple objective programming transportation railway

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A cutting-plane method to non-smooth multiobjective optimization problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第3期275卷 822-829页

作者： Vieira, D. A. G. Lisboa, A. C. ENACOM Belo Horizonte MG Brazil CEFET Grad Program Math Modeling Belo Horizonte MG Brazil Gaia Solut Demand Belo Horizonte Technol Pk Belo Horizonte MG Brazil

The cutting-plane optimization methods rely on the idea that any subgradient of the objective function or the active/violated constraints defines a halfspace to be excluded from a set that contains an optimal solution: the localizing set. This algorithm converges towards a global minimum of any pseudoconvex subdifferentiable function. A naive extension for multiobjective optimization would be using simultaneously some subgradients of all objective functions for a given feasible point. However, as demonstrated in this paper, this approach can lead to a convergence towards non-optimal points. This paper introduces an optimization strategy for cutting-plane methods to cope with multiobjective problems without any scalarization procedure. The proposed strategy guarantees that its optimal solution is a Pareto Optimal solution of the original problem, which is also no worse than the starting point, and that any Pareto Optimal solution can be sampled. Moreover, the auxiliary problem is infeasible only if the original problem is also infeasible. The new strategy inherits the original theoretical guarantees of cutting planes methods and it can be applied to build other strategies. (C) 2019 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Cutting-plane method Pseudoconvex functions Subdifferencial Nonsmooth optimization

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An extended goal programming methodology for analysis of a network encompassing multiple objectives and stakeholders

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2016年第3期255卷 845-855页

作者： Jones, Dylan Florentino, Helenice Cantane, Daniela Oliveira, Rogerio Univ Portsmouth Dept Math Ctr Operat Res & Logist Portsmouth PO1 2UP Hants England Univ Estadual Paulista Dept Biostat Sao Paulo Brazil

This paper proposes a goal programming methodology to ensure that a mix of balance and optimisation is achieved across a hierarchical decision network. The extended goal programming principle is used for this purpose. A model is constructed that provides consideration of balance and efficiency of multiple objectives and stakeholders at each network node level. A goal programming formulation to provide the decision that best meets the goals of the network is given. The proposed model is controlled by three key parameters that represent the level of non-compensation between objectives, level of non-compensation between stakeholders, and level of centralisation in the network. The methodology is demonstrated on an example pertaining to regional renewable energy generation and the results are discussed. Conclusions are drawn as to the effect of different attitudes towards compensatory behaviour between objectives and stakeholders in the network. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Extended goal programming multiple objective programming Renewable energy

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A relaxed projection method for solving multiobjective optimization problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2017年第1期256卷 17-23页

作者： Brito, A. S. Cruz Neto, J. X. Santos, P. S. M. Souza, S. S. DM Univ Estadual Piaui Teresina Brazil Univ Fed Piaui DM BR-64049500 Teresina PI Brazil Univ Fed Piaui CMRV BR-64049500 Parnaiba PI Brazil

In this paper, we propose an algorithm for solving multiobjective minimization problems on nonempty closed convex subsets of the Euclidean space. The proposed method combines a reflection technique for obtaining a feasible point with a projected subgradient method. Under suitable assumptions, we show that the sequence generated using this method converges to a Pareto optimal point of the problem. We also present some numerical results. (C) 2016 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Pareto optimality Projected subgradient method

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