We discuss the use of a quadratic norm for departures from the bliss value of a decision problem under conflicting objectives. The use of a quadratic norm is, for example, of interest within the dynamic framework of o...
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In this paper we show how to incorporate efficient feasible directions into interactive line search algorithms for multiple objective linear programming problems. The resulting new line search is guaranteed to generat...
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In this paper we show how to incorporate efficient feasible directions into interactive line search algorithms for multiple objective linear programming problems. The resulting new line search is guaranteed to generate points that lie in the efficient set. In addition, the new line search automatically corrects possible errors in judgement that the decision maker may inadvertently commit in giving some of his responses. These two improvements are achieved without sacrificing the key property of typical interactive line search algorithms, namely that they yield a new point at each iteration more preferred by the decision maker than the current point. The only additional computational requirement of the new line search is the solution of a single linear programming problem at each iteration. For these reasons, we advocate the incorporation of efficient feasible directions into interactive line search algorithms for multiple objective linear programs in the manner shown in this paper.
Complete efficiency in multiple objective programming may be more common than has been thought, especially for problems whose feasible regions have no interior. In view of this, we present methods for testing for comp...
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Complete efficiency in multiple objective programming may be more common than has been thought, especially for problems whose feasible regions have no interior. In view of this, we present methods for testing for complete efficiency in multiple objective programming, with special attention to the linear case. These tests do not require the feasible region to have a nonempty interior. For typical linear problems, including those with compact feasible regions, the test not only checks for complete efficiency, but also generates both an initial efficient and an initial extreme point efficient solution for use in vector maximum or interactive algorithms.
In this paper, several interactive procedures for solving multiple criteria nonlinear programming problems have been developed. These are based on the generalized reduced gradient method for solving single objective n...
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In this paper, several interactive procedures for solving multiple criteria nonlinear programming problems have been developed. These are based on the generalized reduced gradient method for solving single objective nonlinear programming problems. They can handle maximization problems with nonlinear concave objectives, nonlinear convex constraints and an implicit quasi-concave preference function of the decision maker. The interactive procedures work with information of varying degrees of accuracy from the decision maker, thereby extending and strengthening a number of existing methods. [ABSTRACT FROM AUTHOR]
Optimization algorithms or heuristics in which the user interacts significantly either during the solution process or as part of post-optimality analysis are becoming increasingly popular. An important underlying prem...
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Optimization algorithms or heuristics in which the user interacts significantly either during the solution process or as part of post-optimality analysis are becoming increasingly popular. An important underlying prem...
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The purpose of this paper is to develop an interactive system for supporting the decision making process under multiple objectives and to empirically evaluate its performance. An interactive algorithm underlying the s...
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The purpose of this paper is to develop an interactive system for supporting the decision making process under multiple objectives and to empirically evaluate its performance. An interactive algorithm underlying the system is proposed with emphasis on the psychological aspects of the decision maker (DM). A choice process model is developed, based on pairwise comparison judgments of alternatives, because the judgments are basic and easy for a DM. A corresponding interactive algorithm is implemented and compared with other existing algorithms. Two kinds of comparative experiments, numerical and subject experiments, are conducted to verify the validity of the choice model as well as the practical effectiveness and the convergence of the algorithm.
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