In this article we consider the problem of nonessential objectives for multiobjective optimization problems (MOP) with linearobjective functions. In 1977 an approach based on the reduction of size of the matrix of ob...
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In this article we consider the problem of nonessential objectives for multiobjective optimization problems (MOP) with linearobjective functions. In 1977 an approach based on the reduction of size of the matrix of objective functions has been worked out by one of the present authors (Gal, T., Leberling, H., 1977. European Journal of Operations Research 1, 176-184). Although this method for dropping nonessential objectives leads to a mathematically equivalent MOP, problems concerning the application of MOP methods may arise. For instance, dropping some (or all) of the nonessential objectives the question is, how to ensure obtaining the same solution as with all objectives involved. We consider the problem of adapting the parameters of multiobjective optimization methods. For the case of weighting methods a simple procedure for adapting the weights is analyzed. For other methods, e.g. reference point approaches, such a simple possibility for adapting the parameters is not given. (C) 1999 Elsevier Science B.V. All rights reserved.
A multipleobjective model for manpower planning in a company sized, 100 person,military reserve unit was developed and tested. The model involves five objectives and consists of over 1150 decision variables and 650 c...
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A multipleobjective model for manpower planning in a company sized, 100 person,military reserve unit was developed and tested. The model involves five objectives and consists of over 1150 decision variables and 650 constraints over a 12 month planning horizon. US Army Reserve officers were used as subjects in an experiment in which model solutions were generated interactively using two different solution procedures. One procedure asked subjects-to identify their most preferred solution from a set of candidate solutions at each stage of the interactive process, while the other procedure asked subjects to identify their least preferred solution.
This paper proposes the use of an interior point algorithm for Multiobjectivelinearprogramming problems. At each iteration of the algorithm, the decision maker furnishes his precise trade-offs. From these trade-offs...
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This paper proposes the use of an interior point algorithm for Multiobjectivelinearprogramming problems. At each iteration of the algorithm, the decision maker furnishes his precise trade-offs. From these trade-offs, a cut is formed in the objective space. This cut induces a cut in the decision space that defines a half-space of promising points. We compute the analytic center of the restricted feasible region in the decision space and then we calculate the trade-offs of the decision maker at the image of the analytic center in the objective space. Therefore, we obtain a trajectory of analytic centers that converges to the best compromise solution. Since the proposed algorithm moves through the interior of the feasible region, it avoids the combinatorial difficulties of visiting extreme points and is less sensitive to problem size. We illustrate the method through a numerical example and provide computational experience. (C) 2000 Elsevier Science Ltd. All rights reserved.
作者：
Sayin, SBilkent University
Management Department Faculty of Business Administration 06533 Bilkent Ankara Turkey
We propose a method for finding the efficient set of a multipleobjectivelinear program based on the well-known facial decomposition of the efficient set. The method incorporates a simple linearprogramming test that...
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We propose a method for finding the efficient set of a multipleobjectivelinear program based on the well-known facial decomposition of the efficient set. The method incorporates a simple linearprogramming test that identifies efficient faces while employing a top-down search strategy which avoids enumeration of efficient extreme points and locates the maximally efficient faces of the feasible region. We suggest that discrete representations of the efficient faces could be obtained and presented to the Decision Maker. Results of computational experiments are reported.
The optimization of an economic indicator has traditionally been the sole objective function of mathematical programming models for power generation expansion planning. Recently, however, other evaluation aspects, suc...
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In multiple objective linear programming (MOLP) problems the extraction of all the efficient extreme points becomes problematic as the size of the problem increases. One of the suggested actions, in order to keep the ...
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In multiple objective linear programming (MOLP) problems the extraction of all the efficient extreme points becomes problematic as the size of the problem increases. One of the suggested actions, in order to keep the size of the efficient set to manageable limits, is the use of bounds on the values of the objective functions by the decision maker. The unacceptable efficient solutions are screened out from further investigation and the size of the efficient set is reduced. Although the bounding of the objective functions is widely used in practice, the effect of this action on the size of the efficient set has not been investigated. Ln this paper, we study the effect of individual and simultaneous bounding of the objective functions on the number of the generated efficient points. In order to estimate the underlying relationships, a computational experiment is designed in which randomly generated multiple objective linear programming problems of various sizes are systematically examined.
The planning of new units for electrical power generation is a problem which involves different and conflicting aspects. Besides cost, security issues and environmental concerns must be explicitly incorporated into th...
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The planning of new units for electrical power generation is a problem which involves different and conflicting aspects. Besides cost, security issues and environmental concerns must be explicitly incorporated into the models. In this way mathematical models become more realistic, and they enhance the decision maker's comprehension of the complex and conflicting nature of the distinct aspects of the problem. A multiple objective linear programming model for power generation expansion planning is presented. The model considers three objective functions (net present cost of the expansion plans, reliability of the supply system, and environmental impacts) and three categories of constraints (load requirements, operational restrictions and budget). Three generating technologies are considered for power system expansion: oil, nuclear and coal.
We propose a reference direction based interactive algorithm to solve multipleobjective integer linearprogramming (MOILP) problems. At each iteration of the solution procedure, the algorithm finds (weak) nondominate...
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We propose a reference direction based interactive algorithm to solve multipleobjective integer linearprogramming (MOILP) problems. At each iteration of the solution procedure, the algorithm finds (weak) nondominated solutions to the relaxed MOILP problem. Only at certain iterations, if the DM so desires, an additional mixed integer programming problem is solved to find an integer (weak) nondominated solution which is close to the current continuous (weak) nondominated solution to the relaxed MOILP problem. In the proposed algorithm, DM has to provide only the reference point at each iteration. No special software is required to implement the proposed algorithm. The algorithm is illustrated with an example.
In this paper, we propose the use of an interior-point linearprogramming algorithm for multiple objective linear programming (MOLP) problems. At each iteration, a Decision Maker (DM) is asked to specify aspiration le...
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In this paper, we propose the use of an interior-point linearprogramming algorithm for multiple objective linear programming (MOLP) problems. At each iteration, a Decision Maker (DM) is asked to specify aspiration levels for the various objectives, and an achievement scalarizing function is applied to project aspiration levels onto the nondominated set. The interior-point algorithm is used to find an interior solution path from a starting solution to a nondominated solution corresponding to the optimum of the achievement scalarizing function. The proposed approach allows the DM to re-specify aspiration levels during the solution process and thus steer the interior solution path toward different areas in objective space. We illustrate the use of the approach with a numerical example.
We present an interior multiple objective linear programming (MOLP) algorithm based on the path-following primal-dual algorithm. In contrast to the simplex algorithm, which generates a solution path on the exterior of...
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We present an interior multiple objective linear programming (MOLP) algorithm based on the path-following primal-dual algorithm. In contrast to the simplex algorithm, which generates a solution path on the exterior of the constraints polytope by following its vertices, the path-following primal-dual algorithm moves through the interior of the polytope. Interior algorithms lend themselves to modifications capable of addressing MOLP problems in a way that is quite different from current solution approaches. In addition, moving through the interior of the polytope results in a solution approach that is less sensitive to problem size than simplex-based MOLP algorithms. The modification of the interior single-objective algorithm to MOLP problems, as presented here, is accomplished by combining the step direction vectors generated by applying the single-objective algorithm to each of the cost vectors into a combined direction vector along which we step from the current iterate to the next iterate.
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