A multiple objective linear programming problem (F') involves the simultaneous maximization of two or more conflicting linearobjective functions over a nonempty polyhedron X. Many of the most popular methods for ...
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A multiple objective linear programming problem (F') involves the simultaneous maximization of two or more conflicting linearobjective functions over a nonempty polyhedron X. Many of the most popular methods for solving this type of problem, including many well-known interactive methods, involve searching the efficient set X-E of the problem. Generally however, X-E is a complicated, nonconvex set. As a result, concepts and methods from global optimization may be useful in searching X-E. In this paper, we will explain in theory, and show via an actual application to citrus rootstock selection in Florida, how the potential usefulness of the well-known interactive method STEM for solving problem (P) in this way, can depend crucially upon how accurately certain global optimization problems involving minimizations over X-E are solved. In particular, we will show both in theory and in practice that the choice of whether to use the popular but unreliable "payoff table" approach or to use one of the lesser known, more accurate global optimization methods to solve these problems can determine whether STEM succeeds or fails as a decision aid. Several lessons and conclusions of transferable value derived from this research are also given.
作者：
Jorge, JMUniv La Laguna
Dept Estadist Invest Operat & Computac San Cristobal la Laguna 38271 Tenerife Spain
In this paper we present the concept of maximal descriptor set as a way of identifying faces of a polyhedron in a unique form. This concept is based on the implicit representation of a face through its maximal set of ...
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In this paper we present the concept of maximal descriptor set as a way of identifying faces of a polyhedron in a unique form. This concept is based on the implicit representation of a face through its maximal set of binding inequalities. By making use of this notion it is possible to derive new practical tests to characterize the efficiency of arbitrary faces in a multipleobjectivelinear program, some of which can be seen as extensions of other well-known results on efficiency for general points (not necessarily vertices). (C) 2002 Elsevier Science B.V. All rights reserved.
In this paper we consider the problem of incorporating qualitative data in multiple objective linear programming. We show how the weight assessment technique in the Analytic Hierarchy Process (AHP) can be utilized in ...
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In this paper we consider the problem of incorporating qualitative data in multiple objective linear programming. We show how the weight assessment technique in the Analytic Hierarchy Process (AHP) can be utilized in multiple objective linear programming, when only qualitative (subjective, judgemental) data is available. Using the AHP, we first quantify the qualitative relationships between the row variables and the decision variables for our model. The row variables may have the status of an objective function or a constraint. Then we apply our visual and dynamic decision support system called VIG for solving the resulting multiple objective linear programming problem. We develop the approach and describe an application to strategic management. [ABSTRACT FROM AUTHOR]
Because a rational decision maker should only select an efficient alternative in multiple criterion decision problems, the efficient frontier defined as the set of all efficient alternatives has become a central solut...
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Because a rational decision maker should only select an efficient alternative in multiple criterion decision problems, the efficient frontier defined as the set of all efficient alternatives has become a central solution concept in multiple objective linear programming. Normally this set reduces the set of available alternatives of the underlying problem. There are several methods, mainly based on the simplex method, for computing the efficient frontier. This paper presents a quite different approach which uses a nonlinear parametric program, solved by Wolfe's algorithm, to determine the range of the efficient frontier.
We present an algorithm for solving bilevel linear programs that uses simplex pivots on an expanded tableau. The algorithm uses the relationship between multipleobjectivelinear programs and bilevel linear programs a...
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We present an algorithm for solving bilevel linear programs that uses simplex pivots on an expanded tableau. The algorithm uses the relationship between multipleobjectivelinear programs and bilevel linear programs along with results for minimizing a linearobjective over the efficient set for a multipleobjective problem. Results in multipleobjectiveprogramming needed are presented. We report computational experience demonstrating that this approach is more effective than a standard branch-and-bound algorithm when the number of leader variables is small.
The article deals with operations defined on convex polyhedra or polyhedral convex functions. Given two convex polyhedra, operations like Minkowski sum, intersection and closed convex hull of the union are considered....
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The article deals with operations defined on convex polyhedra or polyhedral convex functions. Given two convex polyhedra, operations like Minkowski sum, intersection and closed convex hull of the union are considered. Basic operations for one convex polyhedron are, for example, the polar, the conical hull and the image under affine transformation. The concept of a P-representation of a convex polyhedron is introduced. It is shown that many polyhedral calculus operations can be expressed explicitly in terms of P-representations. We point out that all the relevant computational effort for polyhedral calculus consists in computing projections of convex polyhedra. In order to compute projections we use a recent result saying that multiple objective linear programming (MOLP) is equivalent to the polyhedral projection problem. Based on the MOLP solver bensolve a polyhedral calculus toolbox for Matlab and GNU Octave is developed. Some numerical experiments are discussed.
In this paper, we provide a mixed-integer programming approach for solving the problem of minimizing a real-valued function over the efficient set of a multipleobjectivelinear program problem. Instead of solving the...
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In this paper, we provide a mixed-integer programming approach for solving the problem of minimizing a real-valued function over the efficient set of a multipleobjectivelinear program problem. Instead of solving the problem directly, we introduce a new problem of minimizing the objective function subject to some linear constraints with additional binary variables. We show under certain conditions that the two problems are equivalent. When the objective function of the original problem is a linear or convex function, the new problem is a linear or convex programming problem, respectively, with some binary variables. These problems can be solved as mixed-integer programs with current state-of-art mixed-integer programming solvers.
A primal-dual infeasible-interior-point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm, moving through the interior of polytope but not con...
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A primal-dual infeasible-interior-point algorithm for multiple objective linear programming (MOLP) problems was presented. In contrast to the current MOLP algorithm, moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size, so providing the potential to dramatically improve the practical computation effectiveness.
In this paper we study the problem of multiple objective linear programming (MOLP). We introduce a new solution concept which is related to that of the nucleolus of n-person cooperative game theory. We prove that a ge...
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In this paper we study the problem of multiple objective linear programming (MOLP). We introduce a new solution concept which is related to that of the nucleolus of n-person cooperative game theory. We prove that a general MOLP problem always has a solution in the new sense. The points in the nucleolus are efficient in the classic way. We prove existence and at the same time we introduce a constructing algorithm for computing it.
multiple objective linear programming is used to evaluate a simulated two-participant maize/cassava/leucaena/teak agroforestry system. Examples using two different price ratios are presented along with possible method...
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multiple objective linear programming is used to evaluate a simulated two-participant maize/cassava/leucaena/teak agroforestry system. Examples using two different price ratios are presented along with possible methods to optimize the system with regard to the interests of the two profit seeking participants. A third example examines possible solutions to a system involving a profit seeking forester and a non-monetary subsistence farmer.
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