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Satisfactory solution concepts and their relations for Stochastic Multiobjective programming problems

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2012年第2期220卷 430-442页

作者： Munoz, Maria M. Ben Abdelaziz, Fouad Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain Amer Univ Sharjah Grad Program Coll Engn Sharjah U Arab Emirates

This work deals with the concept of satisfactory solution for Stochastic Multiobjective programming (SMP) problems. Based on previous literature, we will introduce different concepts of satisfactory solutions for SMP problems, define a new concept of solution (where the decision maker (DM) sets his/her preferences in terms of two aspiration levels for the stochastic objective and two probabilities to reach those levels), and establish some relationship between these concepts. The results will aim at featuring these concepts and determine the differences between them. Moreover, the paper proposes a new step by step procedure to exchange information between the analyst and DM prior to solving the problem. Thus, the DM will be able to choose the transformation criterion for each stochastic objective and the aspiration level. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Stochastic programming multiple objective programming Goal programming Decision-maker's preferences Satisfactory solution Probabilistic goal

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Combined forecasts in portfolio optimization: A generalized approach

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COMPUTERS & OPERATIONS RESEARCH 2012年第4期39卷 805-819页

作者： Ustun, Ozden Kasimbeyli, Refail Izmir Univ Econ Fac Engn & Comp Sci Dept Ind Syst Engn TR-35330 Izmir Turkey Dumlupinar Univ Fac Engn Dept Ind Engn TR-43100 Kutahya Turkey

In this paper a general mathematical model for portfolio selection problem is proposed. By considering a forecasting performance according to the distributional properties of residuals, we formulate an extended mean-variance-skewness model with 11 objective functions. Returns and return errors for each asset obtained using different forecasting techniques, are combined in optimal proportions so as to minimize the mean absolute forecast error. These proportions are then used in constructing six criteria related to the mean, variance and skewness of return forecasts of assets in the future and forecasting errors of returns of assets in the past. The obtained multi-objective model is scalarized by using the conic scalarization method which guarantees to find all non-dominated solutions by considering investor preferences in non-convex multi-objective problems. The obtained scalar problem is solved by utilizing F-MSG algorithm. The performance of the proposed approach is tested on a real case problem generated on the data derived from Istanbul Stock Exchange. The comparison is conducted with respect to different levels of investor preferences over return, variance, and skewness and obtained results are summarized. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： multiple objective programming Risk management Global optimization Portfolio optimization Conic scalarization F-MSG algorithm

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PLANNING RELOCATION OF PEOPLE FOR DEVELOPING SURFACE MINES IN DENSELY POPULATED AREAS: OPTIMIZATION OF multiple objectiveS

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2011年第5期28卷 563-583页

作者： Zahir, Sajjad Sarker, Ruhul Univ Lethbridge Fac Management Lethbridge AB T1K 3M4 Canada Univ New S Wales Australian Def Force Acad Sch Engn & Informat Technol Canberra ACT 2600 Australia

Surface mining, often adopted for exploiting natural resources all over the world, is a major subject of debate as it causes major environmental impacts. It not only adversely alters the landscape but it also seriously hampers the traditional living conditions of numerous inhabitants, who may be displaced against their wishes without receiving necessary compensation. In this paper, goal programming is combined with the analytic hierarchy process to determine optimal decisions for the planned relocation of people where surface mining may take place in a densely populated environment, while addressing multiple conflicting objectives. The combined approach is illustrated with a numerical example highlighting its usage in other decision problems.

关键词： Goal programming environment multiple criteria analysis multiple objective programming OR in developing countries OR in strategic planning

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Redistribution of university budgets with respect to the status quo

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2004年第2期157卷 409-428页

作者： Tangian, A WSI Hans Bockler Stiftung D-40476 Dusseldorf Germany

University budgets are redistributed proportionally to five target criteria. The approach has been implemented in several models and applied to 15 North-Rhine Westfalia state universities. In the given paper, the problem is considered from the viewpoint of the general techniques for constructing objective functions for evaluating alternatives. It enables us to formulate three additional models aimed at best respecting the status quo: with minimizing absolute changes of actual budgets, with minimizing relative changes of actual budgets, and with minimizing changes of individual rules for budget accounting. The models are based on either linear, or quadratic objective functions, the latter being considered under several optional assumptions: local monotonicity, global monotonicity, concavity, and convexity. The paper is illustrated with computer results. (C) 2003 Elsevier B.V. All rights reserved.

关键词： decision support systems multiple criteria analysis polynomial regression in several variables multiple objective programming quadratic programming budgeting resource allocation

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Time-cost trade-off via optimal control theory in Markov PERT networks

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ANNALS OF OPERATIONS RESEARCH 2007年第1期150卷 47-64页

作者： Azaron, Amir Katagiri, Hideki Sakawa, Masatoshi Hiroshima Univ Grad Sch Engn Hiroshima 7398527 Japan Dalhousie Univ Dept Ind Engn Halifax NS Canada Univ Bu Ali Sina Fac Engn Dept Ind Engn Hamadan Iran

We develop a new analytical model for the time-cost trade-off problem via optimal control theory in Markov PERT networks. It is assumed that the activity durations are independent random variables with generalized Erlang distributions, in which the mean duration of each activity is a non-increasing function of the amount of resource allocated to it. Then, we construct a multi-objective optimal control problem, in which the first objective is the minimization of the total direct costs of the project, in which the direct cost of each activity is a non-decreasing function of the resources allocated to it, the second objective is the minimization of the mean of project completion time and the third objective is the minimization of the variance of project completion time. Finally, two multi-objective decision techniques, viz, goal attainment and goal programming are applied to solve this multi-objective optimal control problem and obtain the optimal resources allocated to the activities or the control vector of the problem.

关键词： project management multiple objective programming optimal control theory Markov processes

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On the use of the distance in reference point-based approaches for multiobjective optimization

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ANNALS OF OPERATIONS RESEARCH 2015年第1期235卷 559-579页

作者： Luque, Mariano Ruiz, Ana B. Saborido, Ruben Marcenaro-Gutierrez, Oscar D. Univ Malaga Dept Appl Econ Math E-29071 Malaga Spain Ecole Polytech Polytech Montreal Researchers Software Engn Montreal PQ H3C 3A7 Canada Univ Malaga Dept Appl Econ Stat & Econometr E-29071 Malaga Spain

Reference point-based methods are very useful techniques for solving multiobjective optimization problems. In these methods, the most commonly used achievement scalarizing functions are based on the Tchebychev distance (minmax approach), which generates every Pareto optimal solution in any multiobjective optimization problem, but does not allow compensation among the deviations to the reference values given that it minimizes the value of the highest deviation. At the same time, for any , compromise programming minimizes the distance to the ideal objective vector from the feasible objective region. Although the ideal objective vector can be replaced by a reference point, achievable reference points are not supported by this approach, and special care must be taken in the unachievable case. In this paper, for , we propose a new scheme based on the distance, in which different single-objective optimization problems are designed and solved depending on the achievability of the reference point. The formulation proposed allows different compensation degrees among the deviations to the reference values. It is proven that, in the achievable case, any optimal solution obtained is efficient, and, in the unachievable one, it is at least weakly efficient, although it is assured to be efficient if an augmentation term is added to the new formulation. Besides, we suggest an interactive algorithm where the new formulation is embedded. Finally, we show the empirical advantages of the new formulation by its application to both numerical problems and a real multiobjective optimization problem, for achievable and unachievable reference points.

关键词： Reference point multiple objective programming Compromise programming Distance-based multiobjective optimization approaches

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Interactive multiobjective optimization with NIMBUS for decision making under uncertainty

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OR SPECTRUM 2014年第1期36卷 39-56页

作者： Miettinen, Kaisa Mustajoki, Jyri Stewart, Theodor J. Univ Jyvaskyla Dept Math Informat Technol Jyvaskyla 40014 Finland Tampere Univ Technol Dept Automat Sci & Engn FIN-33101 Tampere Finland Finnish Environm Inst Freshwater Ctr Helsinki 00251 Finland Univ Cape Town Dept Stat Sci ZA-7701 Rondebosch South Africa

We propose an interactive method for decision making under uncertainty, where uncertainty is related to the lack of understanding about consequences of actions. Such situations are typical, for example, in design problems, where a decision maker has to make a decision about a design at a certain moment of time even though the actual consequences of this decision can be possibly seen only many years later. To overcome the difficulty of predicting future events when no probabilities of events are available, our method utilizes groupings of objectives or scenarios to capture different types of future events. Each scenario is modeled as a multiobjective optimization problem to represent different and conflicting objectives associated with the scenarios. We utilize the interactive classification-based multiobjective optimization method NIMBUS for assessing the relative optimality of the current solution in different scenarios. This information can be utilized when considering the next step of the overall solution process. Decision making is performed by giving special attention to individual scenarios. We demonstrate our method with an example in portfolio optimization.

关键词： multiple objective programming Interactive methods Scenarios Uncertainty handling Pareto optimality Classification of objectives

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An Ant Colony Optimization algorithm to solve a 2-machine bicriteria flowshop scheduling problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2002年第2期142卷 250-257页

作者： T'kindt, V Monmarché, N Tercinet, F Laügt, D Ecole Ingenieurs Informat Ind Lab Informat F-37200 Tours France

Consider the 2-machine flowshop scheduling problem with the objective of minimizing both the total completion time and the makespan criteria. The latter is assumed to be optimized prior to the former. In view of the N P-hardness of the problem an Ant Colony Optimization approach is proposed to solve it. The heuristic also uses feature of Simulated Annealing search and local search algorithms. Computational experiments show its effectiveness compared to existing heuristics. The extension to the total completion time problem is also studied. (C) 2002 Published by Elsevier Science B.V.

关键词： scheduling multiple objective programming Ant Colony Optimization

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An extended goal programming model for site selection in the offshore wind farm sector

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ANNALS OF OPERATIONS RESEARCH 2016年第1-2期245卷 121-135页

作者： Jones, Dylan F. Wall, Graham Univ Portsmouth Dept Math Ctr Operat Res & Logist Lion Terrace Portsmouth PO1 3HF Hants England

This paper presents an application of extended goal programming in the field of offshore wind farm site selection. The strategic importance of offshore shore wind farms is outlined, drawing on the case of the United Kingdom proposed round three sites as an example. The use of multi-objective modelling methodologies for the offshore wind farm sector is reviewed. The technique of extended goal programming is outlined and its flexibility in combining different decision maker philosophies described. An extended goal programming model for site selection based on the United Kingdom future sites is then developed and a parametric analysis undertaken at the meta-objective level. The results are discussed and conclusions are drawn.

关键词： multiple objective programming Extended goal programming Offshore wind Renewable energy

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On the Lexicographic Centre of multiple objective Optimization

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2016年第2期168卷 600-614页

作者： Zhang Jiangao Yang, Shitao Chongqing Univ Fac Construct Management & Real Estate Chongqing 400045 Peoples R China Sichuan Univ State Key Lab Hydraul & Mt River Engn Chengdu 610064 Peoples R China Florida Inst Technol Nathan M Bisk Coll Business 150 W Univ Blvd Melbourne FL 32901 USA

We study the lexicographic centre of multiple objective optimization. Analysing the lexicographic-order properties yields the result that, if the multiple objective programming's lexicographic centre is not empty, then it is a subset of all efficient solutions. It exists if the image set of multiple objective programming is bounded below and closed. The multiple objective linear programming's lexicographic centre is nonempty if and only if there exists an efficient solution to the multiple objective linear programming. We propose a polynomial-time algorithm to determine whether there is an efficient solution to multiple objective linear programming, and we solve the multiple objective linear programming's lexicographic centre by calculating at most the same number of dual linear programs as the number of objective functions and a system of linear inequalities.

关键词： multiple objective programming Lexicographic order Lexicographic centre Efficient solution Image set theta-image set

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