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Random approximations in multiobjective optimization

MATHEMATICAL programming 2017年第1-2期164卷 29-53页

作者： Vogel, Silvia Ilmenau Univ Technol Weimarer Str 25 D-98693 Ilmenau Germany

Often decision makers have to cope with a programming problem with unknown quantitities. Then they will estimate these quantities and solve the problem as it then appears-the 'approximate problem'. Thus there is a need to establish conditions which will ensure that the solutions to the approximate problem will come close to the solutions to the true problem in a suitable manner. Confidence sets, i.e. sets that cover the true sets with a given prescribed probability, provide useful quantitative information. In this paper we consider multiobjective problems and derive confidence sets for the sets of efficient points, weakly efficient points, and the corresponding solution sets. Besides the crucial convergence conditions for the objective and/or constraint functions, one approach for the derivation of confidence sets requires some knowledge about the true problem, which may be not available. Therefore also another method, called relaxation, is suggested. This approach works without any knowledge about the true problem. The results are applied to the Markowitz model of portfolio optimization.

关键词： multiobjective programming Stability Confidence sets Estimated functions Relaxation Markowitz model

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Hierarchical generation of Pareto optimal solutions in large-scale multiobjective systems

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COMPUTERS & OPERATIONS RESEARCH 2002年第11期29卷 1537-1558页

作者： Caballero, R Gómez, T Luque, M Miguel, F Ruiz, F Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain

In this paper, the problem of the determination of Pareto optimal solutions for certain large-scale systems with multiple conflicting objectives is considered. As a consequence, a two-level hierarchical method is proposed, where the global problem is decomposed into smaller multiobjective problems (lower level) which are coordinated by an upper level that has to take into account the relative importance assigned to each subsystem. The scheme that has been developed is an iterative one, so that a continuous information exchange is carried out between both levels in order to obtain efficient solutions for the initial global problem. The practical implementation of the developed scheme allows us to prove its efficiency in terms of processing time.

关键词： multiobjective programming non-dominated solutions hierarchical generating methods feasible decomposition

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multiobjective portfolio optimization using coherent fuzzy numbers in a credibilistic environment

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INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS 2021年第4期36卷 1560-1594页

作者： Mehlawat, Mukesh K. Gupta, Pankaj Khan, Ahmad Z. Univ Delhi Dept Operat Res RZ-26P-21St 34Indra Pk New Delhi 110045 India

In this paper, we propose a new credibility function for a fuzzy variable that can accommodate the attitude of the investor (pessimistic, optimistic, or neutral) along with capturing the return expectations. We use an adaptive index, which the investors can use to specify their general perception of the financial market. We extend the classic mean-variance model so that it provides greater flexibility to the investors in specifying their requirements viz., level of diversification, minimum and maximum level of investment in a particular asset, and the skewness requirement. We also replace variance with mean-absolute semideviation as a measure of quantifying risk, which is more realistic, and solve the resultant multiobjective credibility model with a real-coded genetic algorithm. Numerical examples have been provided at the end to illustrate the methodology and advantages of the model.

关键词： coherent fuzzy numbers credibility function mean– mean sabsolute‐ semideviation– skewness model multiobjective programming real‐ coded genetic algorithm

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Efficiency and generalized concavity

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1997年第1期94卷 147-153页

作者： Luc, DT Schaible, S UNIV CALIF RIVERSIDE GRAD SCH MANAGEMENTRIVERSIDECA 92521

In a recent paper on multiobjective maximization problems (Ref. 1), the authors use explicit quasiconcavity of the objective functions to prove a characterization of weakly efficient solutions and local-global properties. We provide results which are stronger in part and are derived with shorter proofs. We also present additional results.

关键词： multiobjective programming (weakly) efficient solutions local efficient solutions (semistrict) quasiconcavity

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Intractability of the dial-a-ride problem and a multiobjective solution using simulated annealing

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ENGINEERING OPTIMIZATION 1998年第2期30卷 91-123页

作者： Baugh, JW Kakivaya, GKR Stone, JR N Carolina State Univ Dept Civil Engn Raleigh NC 27695 USA

Numerous techniques for generating approximate solutions have been proposed in the last decade for routing and scheduling in multi vehicle dial-a-ride problems. While some of these techniques have mathematical foundations, it is often difficult to assess the global optimality of the generated solution due to the use of pure local improvement methods. In additon, most of these methods are based on a single objective, such as minimization of the number of vehicles used, and cannot account for different or competing objectives that characterize the problem. This paper proves the intractability of the dial-a-ride problem, and then describes a new approximate method based on simulated annealing that is used to solve these problems in the presence of multiple objectives.

关键词： dial-a-ride problem simulated annealing multiobjective programming decision-support systems

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Sustainable production technologies which take into account environmental constraints

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第3期193卷 730-740页

作者： Radulescu, Marius Radulescu, Sorin Radulescu, Constanta Zole Casa Acad Romane Inst Math Stat & Appl Math RO-050711 Bucharest 5 Romania Natl Inst Res & Dev Informat Bucharest 011455 1 Romania

We formulate and study a multiobjective programming approach for production processes which implements suitable constraints on pollutant emissions. We consider two alternative optimization problems: (a) minimum pollution risk;(b) maximum expected return. For each pollutant, we define three different contamination levels: (a) the desirable or the target pollution level, (b) the alarm (warning or critical) level and (c) the maximum admissible (acceptable) level, and introduce penalties proportional to the amounts of pollutants that exceed these levels. The objective function of the minimum pollution risk problem is not smooth since it contains positive parts of some affine functions, resulting in mathematical difficulties, which can be solved by formulating an alternative linear programming model, which makes use of additional variables and has the same solutions as the initial problem. We investigate various particular cases and analyze a numerical example for a textile plant. (C) 2007 Elsevier B.V. All rights reserved.

关键词： multiobjective programming Production planning Environmental constraints Pollutant emission

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Research on the optimization of proportions for synchronous grouting material in composite muck during shield tunneling

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JOURNAL OF CLEANER PRODUCTION 2024年 484卷

作者： Zhang, Jian Zhu, Cheng Kuang, Mengxiang Xu, Tao Wang, Xiaohu Feng, Tugen Xu, Jingmin Hohai Univ Key Lab Minist Educ Geomech & Embankment Engn 1 Xikang Rd Nanjing 210024 Peoples R China Yangtze Ecol & Environm Co Ltd 88 Sanyang Rd Wuhan 430014 Peoples R China Southeast Univ Inst Geotech Engn Sch Transportat Nanjing 211189 Peoples R China China State Railway Investment Construct Grp Co Lt 1 Chuangzhi Rd Nanjing 210019 Peoples R China Jiangxi Univ Sci & Technol Sch Civil Engn & Surveying & Mapping Engn 1958 Kejiadadao Rd Ganzhou 341000 Peoples R China

To tackle the challenge of onsite resource reuse of composite muck, which relies on a shield tunneling section in the case of Nanjing Metro Line 7, this paper examines the effects of component substitution and varying proportions of factors on slurry properties through laboratory tests and multiobjective modeling. From a practical application perspective, the potential of using composite muck as a synchronous grouting material for shield tunneling was explored. In reference to the common mixed strata encountered in shield tunneling construction in the Nanjing area, a general slurry mixing ratio suitable for various mixed strata conditions was derived. The research results indicate the following optimized mixing ratios for the composite muck slurry: a water-to-binder (cement + fly ash) ratio of 0.76, a cement-to-fly ash ratio of 0.53, a binder-to-soil (silty clay + silty fine sand + river sand) ratio of 0.67, a clay (i.e., silty clay)-to-sand (i.e., silty fine sand + river sand) ratio of 0.4, and a substitution ratio (i.e., silty fine sand/silty fine sand + river sand) of 0.2. This slurry is feasible for practical applications and can reduce construction costs by 38.13%. The obtained general mixing ratio for the composite muck slurry, suitable for various mixed stratigraphic conditions, essentially meets onsite construction requirements (the bleeding rate is controlled within a low range of 1.1-3.1%, and the maximum compressive strength reaches up to 6.76 MPa at 28 days), with reasonable costs. It streamlines construction by eliminating the need for onsite screening of muck, allowing for the direct onsite reuse of composite muck in shield tunneling.

关键词： Composite muck for shield tunneling Disposal of soil Synchronous grouting material multiobjective programming General mixing ratio

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AN INTERACTIVE MULTIGOAL programming-MODEL FOR DETERMINING LIVESTOCK RATIONS - AN APPLICATION TO DAIRY-COWS IN ANDALUSIA, SPAIN

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1992年第10期43卷 945-953页

作者： LARA, P ROMERO, C CIDA DEPT ANIM PRODCORDOBASPAIN UNIV CORDOBA DEPT AGR ECON MANAGEMENT & STATCORDOBASPAIN

This paper addresses an important problem in the field of livestock ration formulation: the rigidity of the right-hand sides of the model. Thus, instead of considering the nutritional requirements as fixed values they are considered as targets which may or may not be achieved. In this way a multigoal programming model is formulated. The preferences of the ration-formulator are elicited resorting to the interactive method proposed by Zionts and Wallenius. The approach proposed is applied to a ration formulation problem for dairy cows in the Pedroches Valley in Andalusia, Spain.

关键词： AGRICULTURE multiobjective programming

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Nondifferentiable multiobjective Mond-Weir type second-order symmetric duality over cones

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OPTIMIZATION LETTERS 2010年第2期4卷 293-309页

作者： Gulati, T. R. Mehndiratta, Geeta Indian Inst Technol Dept Math Roorkee 247667 Uttar Pradesh India

In this paper, a pair of Mond-Weir type nondifferentiable multiobjective second-order symmetric dual programs over arbitrary cones is formulated. Weak, strong and converse duality theorems are established under second-order K-F-convexity/K-eta-bonvexity assumptions. A self duality theorem is also obtained by assuming the functions involved to be skew-symmetric.

关键词： Second-order symmetric duality Second-orderK-F-convexity K-eta-bonvexity Cones multiobjective programming Efficient solutions

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A novel approach for solving stochastic problems with multiple objective functions

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RAIRO-OPERATIONS RESEARCH 2021年第4期55卷 2413-2422页

作者： Kasri, Ramzi Bellahcene, Fatima Mouloud Mammeri Univ Fac Sci LAROMAD Lab BP 17 RP Tizi Ouzou 15000 Algeria

In this paper we suggest an approach for solving a multiobjective stochastic linear programming problem with normal multivariate distributions. Our approach is a combination between a multiobjective method and a nonconvex technique. The problem is first transformed into a deterministic multiobjective problem introducing the expected value criterion and an utility function that represents the decision makers preferences. The obtained problem is reduced to a mono-objective quadratic problem using a weighting method. This last problem is solved by DC (Difference of Convex) programming and DC algorithm. A numerical example is included for illustration.

关键词： multiobjective programming stochastic programming DCA DC programming utility function expected value criterion

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