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

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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Soil erosion and ground water pollution tradeoffs for nonirrigated farming systems

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JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 2002年第1期38卷 101-110页

作者： Akinsanmi, J Perry, GM Trinity Western Univ Langley BC V2Y 1Y1 Canada Oregon State Univ Dept Agr & Resource Econ Corvallis OR 97330 USA

Traditional focus on reducing one environmental externality may cause another externality to increase. This article examines the environmental and economic costs of abating soil loss and (or) nitrate leaching through alternative optimal production systems in the nonirrigated farming systems of Northeastern Oregon. Models estimating soil loss and nitrate-nitrogen leaching rates associated with current production processes, are linked to a Multi-objective programming (MOP) model. The results show that site specific conditions influence the level of abatement expenditures and optimal production strategies to reduce soil loss and leaching rates. Moreover while existing production strategies are effective in reducing soil loss at little cost, no strategies could be identified to reduce nitrate leaching rate on some soils.

关键词： economics multiple objective programming erosion nitrate nitrogen leaching nonpoint source pollution

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A characterization of pseudoinvexity for the efficiency in non-differentiable multiobjective problems. Duality

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2010年第4期73卷 1109-1117页

作者： Arana-Jimenez, Manuel Ruiz-Garzon, Gabriel Rufian-Lizana, Antonio Hernandez-Jimenez, Beatriz Univ Cadiz Dept Estadist & Invest Operat Escuela Super Ingn Cadiz 11002 Spain Univ Cadiz Dept Estadist & Invest Operat Fac Ciencias Sociales & Comunicac Cadiz 11405 Spain Univ Seville Dept Estadist & Invest Operat Fac Matemat E-41012 Seville Spain Univ Pablo de Olavide Dept Econ Metodos Cuantitat & H Econ Seville Spain

We prove that in order for the Kuhn-Tucker or Fritz John points to be efficient solutions, it is necessary and sufficient that the non-differentiable multiobjective problem functions belong to new classes of functions that we introduce here: KT-pseudoinvex-II or FJ-pseudoinvex-II, respectively. We illustrate it by examples. These characterizations generalize recent results given for the differentiable case. We study the dual problem and establish weak, strong and converse duality results. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： multiple objective programming Pseudoinvexity Kuhn-Tucker and Fritz John optimality conditions Efficient solutions

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A two stage fuzzy piecewise logistic model for penetration forecasting

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APPLIED SOFT COMPUTING 2014年 21卷 149-158页

作者： Tseng, Fang-Mei Yu, Jing-Rung Yuan Ze Univ Coll Management Taoyuan 320 Taiwan Natl Chi Nan Univ Dept Informat Management Puli Nantou 545 Taiwan

It is undeniably crucial for a firm to be able to make a forecast regarding the sales volume of new products. However, the current economic environments invariably have uncertain factors and rapid fluctuations where decision makers must draw conclusions from minimal data. Previous studies combine scenario analysis and technology substitution models to forecast the market share of multigenerational technologies. However, a technology substitution model based on a logistic curve will not always fit the S curve well. Therefore, based on historical data and the data forecast by both the Scenario and Delphi methods, a two stage fuzzy piecewise logistic growth model with multiple objective programming is proposed herein. The piecewise concept is adopted in order to reflect the market impact of a new product such that it can be possible to determine the effective length of sales forecasting intervals even when handling a large variation in data or small size data. In order to demonstrate the model's performance, two cases in the Television and Telecommunication industries are treated using the proposed method and the technology substitution model or the Norton and Bass diffusion model. A comparison of the results shows that the proposed model outperforms the technology substitution model and the Norton and Bass diffusion model. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Fuzzy piecewise regression Logistic model multiple objective programming Delphi method

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An exact penalty on bilevel programs with linear vector optimization lower level

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第1期197卷 36-41页

作者： Ankhili, Z. Mansouri, A. Univ Cadi Ayyad Dept Math Fac Sci Semlalia MAD Marrakech Morocco

We are interested in a class of linear bilevel programs where the upper level is a linear scalar optimization problem and the lower level is a linear multi-objective optimization problem. We approach this problem via an exact penalty method. Then, we propose an algorithm illustrated by numerical examples. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Bilevel programming Linear programming multiple objective programming Penalty methods

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A polynomial-time-delay and polynomial-space algorithm for enumeration problems in multi-criteria optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2011年第1期210卷 48-56页

作者： Okamoto, Yoshio Uno, Takeaki Tokyo Inst Technol Grad Sch Informat Sci & Engn Meguro Ku Tokyo 1528552 Japan Res Org Informat & Syst Natl Inst Informat Chiyoda Ku Tokyo 1018430 Japan

We propose a polynomial-time-delay polynomial-space algorithm to enumerate all efficient extreme solutions of a multi-criteria minimum-cost spanning tree problem, while only the bi-criteria case was studied in the literature. The algorithm is based on the reverse search framework due to Avis and Fukuda. We also show that the same technique can be applied to the multi-criteria version of the minimum-cost basis problem in a (possibly degenerated) submodular system. As an ultimate generalization, we propose an algorithm to enumerate all efficient extreme solutions of a multi-criteria linear program. When the given linear program has no degeneracy, the algorithm runs in polynomial-time delay and polynomial space. To best of our knowledge, they are the first polynomial-time delay and polynomial-space algorithms for the problems. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Combinatorial optimization Complexity theory Linear programming multiple objective programming

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A model for ordinally constructing additive objective functions

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第2期159卷 476-512页

作者： Tangian, A WSI D-40476 Dusseldorf Germany

We investigate a method for constructing piecewise-linear approximations of an additive (called also separable) objective function in n target variables from a few indifference points in two-dimensional planes. It is shown that (a) the data used by the method are ordinal.. simplest, and minimal;(b) the limit ordinal preference is independent of the cardinal utility scale used in intermediate computations, since the accuracy of the approximations is estimated in the Hausdorff metric on the space of binary relations. The method is illustrated with an example of constructing an additive objective function of German economic policy in four target variables: Inflation, Unemployment, GNP Growth, and Increase in Public Debt. We provide some modifications of the model aimed at user's convenience. (C) 2003 Elsevier B.V. All rights reserved.

关键词： multiple criteria analysis multiple objective programming decision support systems additive objective function additive utility

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Interactive Nonconvex Pareto Navigator for multiobjective optimization

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期275卷 238-251页

作者： Hartikainen, Markus Miettinen, Kaisa Klamroth, Kathrin Univ Jyvaskyla Fac Informat Technol POB 35 Agora FI-40014 Jyvaskyla Finland Univ Wuppertal Sch Math & Nat Sci Gaussstr 20 D-42119 Wuppertal Germany

We introduce a new interactive multiobjective optimization method operating in the objective space called Nonconvex Pareto Navigator. It extends the Pareto Navigator method for nonconvex problems. An approximation of the Pareto optimal front in the objective space is first generated with the PAINT method using a relatively small set of Pareto optimal outcomes that is assumed to be given or computed prior to the interaction with the decision maker. The decision maker can then navigate on the approximation and direct the search for interesting regions in the objective space. In this way, the decision maker can conveniently learn about the interdependencies between the conflicting objectives and possibly adjust one's preferences. To facilitate the navigation, we introduce special cones that enable extrapolation beyond the given Pareto optimal outcomes. Besides handling nonconvexity, the new method contains new options for directing the navigation that have been inspired by the classification-based interactive NIMBUS method. The Nonconvex Pareto Navigator method is especially well-suited for computationally expensive problems, because the navigation on the approximation is computationally inexpensive. We demonstrate the method with an example. Besides proposing the new method, we characterize interactive navigation based methods in general and discuss desirable properties of navigation methods overall and in particular with respect to Nonconvex Pareto Navigator. (C) 2018 Elsevier B.V. All rights reserved.

关键词： multiple objective programming Interactive multiobjective optimization Navigation Nonconvex problems Pareto optimality

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Necessary and sufficient second order optimality conditions for multiobjective problems with C¹ data

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2013年 85卷 192-203页

作者： Santos, L. B. Osuna-Gomez, R. Hernandez-Jimenez, B. Rojas-Medar, M. A. Univ Fed Parana Ctr Politecn Dpto Matemat BR-81531980 Curitiba Parana Brazil Univ Seville Fac Matemat Dept Estat & Invest Operat E-41012 Seville Spain Univ Pablo de Olavide Area Estat & Invest Operat Dept Econ Metodos Cuantitat & Ha Econ Seville 41013 Spain Univ Bio Bio Fac Ciencias Dpto Ciencias Basicas Grp Matemat Aplicada Chillan Chile

In this paper, we obtain necessary and sufficient second order optimality conditions for multiobjective problems using second order directional derivatives. We propose the notion of second order KT-pseudoinvex problems and we prove that this class of problems has the following property: a problem is second order KT-pseudoinvex if and only if all its points that satisfy the second order necessary optimality condition are weakly efficient. Also we obtain second order sufficient conditions for efficiency. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： multiple objective programming Generalized convexity Optimality conditions

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On solving bi-objective constrained minimum spanning tree problems

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JOURNAL OF GLOBAL OPTIMIZATION 2023年第1期87卷 301-323页

作者： Carvalho, Iago A. Coco, Amadeu A. Univ Fed Alfenas Comp Sci Dept Ave Jovino Fernandes Sales 2600 BR-37133840 Alfenas MG Brazil Univ Lille ORKAD CRIStAL UMR 9189CNRSCent Lille Lille France

This paper investigates two approaches for solving bi-objective constrained minimum spanning tree problems. The first seeks to minimize the tree weight, keeping the problem's additional objective as a constraint, and the second aims at minimizing the other objective while constraining the tree weight. As case studies, we propose and solve bi-objective generalizations of the Hop-Constrained Minimum Spanning Tree Problem (HCMST) and the Delay-Constrained Minimum Spanning Tree Problem (DCMST). First, we present an Integer Linear programming (ILP) formulation for the HCMST. Then, we propose a new com-pact mathematical model for the DCMST based on the well-known Miller-Tucker-Zemlin subtour elimination constraints. Next, we extend these formulations as bi-objective models and solve them using an Augmented e-constraints method. Computational experiments per-formed on classical instances from the literature evaluated two different implementations of the Augmented e-constraints method for each problem. Results indicate that the algorithm performs better when minimizing the tree weight while constraining the other objective since this implementation finds shorter running times than the one that minimizes the additional objective and constrains the tree weight.

关键词： multiple objective programming Hop-constrained minimum spanning tree Delay-constrained minimum spanning tree Augmented e-constraint Bottleneck objective function MTZ constraints

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