In this paper we investigate two generalizations of the Pareto minimality concept: infimality and approximate minimality. It is shown that existence conditions for these optimality notions are much weaker and that the...
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In this paper we investigate two generalizations of the Pareto minimality concept: infimality and approximate minimality. It is shown that existence conditions for these optimality notions are much weaker and that they allow a more complete characterization via linear and nonlinear scalarization than Pareto minimality. We further study some relations between those optimality structures and apply the results to the image of a vector-valued mapping.
In this paper, a popular scalarization problem in multiobjective optimization, introduced by Benson, is considered. In the literature it was proved that, under convexity assumption, the set of properly efficient point...
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In this paper, a popular scalarization problem in multiobjective optimization, introduced by Benson, is considered. In the literature it was proved that, under convexity assumption, the set of properly efficient points is empty when the Benson's problem is unbounded. In this paper, it is shown that this result is still valid in general case without convexity assumption.
In this paper, a pair of multiobjective fractional variational symmetric dual problems over cones is formulated. Weak, strong and converse duality theorems are established under generalized F-convexity assumptions. Mo...
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In this paper, a pair of multiobjective fractional variational symmetric dual problems over cones is formulated. Weak, strong and converse duality theorems are established under generalized F-convexity assumptions. Moreover, self duality theorem is also discussed. (C) 2007 Elsevier B.V. All rights reserved.
Optimizing a function over the efficient set of a multiojective problem plays an important role in many fields of application. This problem arises whenever the decision maker wants to select the efficient solution tha...
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Optimizing a function over the efficient set of a multiojective problem plays an important role in many fields of application. This problem arises whenever the decision maker wants to select the efficient solution that optimizes his utility function. Several methods are proposed in literature to deal with the problem of optimizing a linear function over the efficient set of a multiobjective integer linear program MOILFP. However, in many real-world problems, the objective functions or the utility function are nonlinear. In this paper, we propose an exact method to optimize a quadratic function over the efficient set of a multiobjective integer linear fractional program MOILFP. The proposed method solves a sequence of quadratic integer problems. Where, at each iteration, the search domain is reduced s6uccessively, by introducing cuts, to eliminate dominated solutions. We conducted a computational experiment, by solving randomly generated instances, to analyze the performance of the proposed method.
A variety of approaches exist for the determination of a weighting scheme from a pairwise comparison matrix describing a scale-relation between objectives or alternatives. The most common context for such an algorithm...
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A variety of approaches exist for the determination of a weighting scheme from a pairwise comparison matrix describing a scale-relation between objectives or alternatives. The most common context for such an algorithm is that of the analytic hierarchy process (AHP), although uses in other areas of the field of multicriteria decision making (MCDM) can also be found. Typically, the eigenvalue method is the standard method employed in the AHP to determine weights, as in the ExpertChoice software. However, another class of techniques are the distance-metric-based approaches, which are frequently proposed as alternatives to the eigenvalue method. This paper evaluates such distance-metric-based approaches comparing their effectiveness, using the eigenvalue method as a benchmark. A common framework is introduced to establish an efficient frontier for method comparison. Journal of the Operational Research Society (2004).
In many real decision situations more than one objective has to be considered and different kinds of uncertainty must be handled. The uncertainty is generally of two natures: stochastic uncertainty related to environm...
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In many real decision situations more than one objective has to be considered and different kinds of uncertainty must be handled. The uncertainty is generally of two natures: stochastic uncertainty related to environmental data and fuzzy uncertainty related to expert judgement. This paper proposes a fuzzy chance constrained approach to solve mathematical programs integrating fuzzy and stochastic parameters with multiple objective aspects. Our approach is applied to determine reservoirs releases in the Echkeul basin in Tunisia.
An accurate prediction of asset prices is perhaps the biggest challenge of any study in portfolio optimization. Asset prices are affected by several random and nonrandom factors, which makes them difficult to forecast...
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An accurate prediction of asset prices is perhaps the biggest challenge of any study in portfolio optimization. Asset prices are affected by several random and nonrandom factors, which makes them difficult to forecast. This paper proposes a two-phase dynamic portfolio optimization approach. In the first phase, assets are clustered into buy, sell, and hold groups using technical indicators. We provide a methodology to integrate the investor attitude (optimistic, pessimistic, or neutral) during the clustering phase. In the second phase, we input the clustered groups into a portfolio optimization model to obtain the optimum asset allocations. We use coherent fuzzy numbers to model the asset returns to integrate the investor attitude in this phase. The optimization model is solved using a genetic algorithm. The portfolios are rebalanced at regular intervals as new data becomes available. We illustrate the proposed methodology on a 100-asset problem of the US stock market. We analyze the real-world performance of the obtained portfolios. We compare the performance of the proposed approach with the mean-variance model, and other portfolios, such as the naive portfolio and the NASDAQ-100 index.
In this work, Huard type converse duality theorems for scalar and multiobjective second-order dual problems in nonlinear programming are established. (C) 2007 Elsevier Ltd. All rights reserved.
In this work, Huard type converse duality theorems for scalar and multiobjective second-order dual problems in nonlinear programming are established. (C) 2007 Elsevier Ltd. All rights reserved.
This paper develops a multiobjective programming model for the optimal allocation of passenger train services on an intercity high-speed rail line without branches. Minimizing the operator's total operating cost a...
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This paper develops a multiobjective programming model for the optimal allocation of passenger train services on an intercity high-speed rail line without branches. Minimizing the operator's total operating cost and minimizing the passenger's total travel time loss are the two planning objectives of the model. For a given many-to-many travel demand and a specified operating capacity, the model is solved by a fuzzy mathematical programming approach to determine the best-compromise train service plan, including the train stop-schedule plan, service frequency, and fleet size. An empirical study on the to-be-built high-speed rail system in Taiwan is conducted to demonstrate the effectiveness of the model. The case study shows that an optimal set of stop-schedules can always be generated for a given travel demand. To achieve the best planning outcome, the number and type of stop-schedules should be flexibly planned, and not constrained by specific stopping schemes as often set by the planner. (C) 2000 Elsevier Science Ltd. All rights reserved.
In this paper, we show with a counterexample, that the method proposed by Sedeno-Noda and Gonzalez-Martin for the biobjective integer minimum flow problem is not able to find all efficient integer points in objective ...
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In this paper, we show with a counterexample, that the method proposed by Sedeno-Noda and Gonzalez-Martin for the biobjective integer minimum flow problem is not able to find all efficient integer points in objective space. (c) 2004 Elsevier Ltd. All rights reserved.
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