multiple objective linear programming (MOLP) models have been widely used in the energy sector for taking into account several conflicting objectives pursued in energy planning. However, continuous variables are not s...
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In this paper an aspiration-level method for multiple objective linear programming is developed. In this method, a quadratic distance function is minimized over an efficient face of a multipleobjectivelinear program...
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In this paper an aspiration-level method for multiple objective linear programming is developed. In this method, a quadratic distance function is minimized over an efficient face of a multiple objective linear programming problem. The solution to such quadratic programming model is an efficient point that is "nearest" to a given aspiration level. An efficient face is determined by an efficient weight vector generated by a weight-update algorithm. A combined weight-update and aspiration-level interactive method is then presented. The main purpose of the combined methods is to allow a decision maker to control the selection of preferred solution by jumping from one efficient face to another. A decision support system is also developed to implement the combined methods.
In this paper, we present a systematic approach to updating weights in multiple objective linear programming. We develop a number of extensions to the simplex theory which leads to the identification of (a) alternativ...
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In this paper, we present a systematic approach to updating weights in multiple objective linear programming. We develop a number of extensions to the simplex theory which leads to the identification of (a) alternative weight vectors for which a current efficient solution remains optimal, and (b) adjacent efficient solutions. We also give an example to illustrate the proposed approach.
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.
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.
multiple objective linear programming problems are solved with a variety of algorithms. While these algorithms vary in philosophy and outlook, most of them fall into two broad categories: those that are decision space...
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multiple objective linear programming problems are solved with a variety of algorithms. While these algorithms vary in philosophy and outlook, most of them fall into two broad categories: those that are decision space-based and those that are objective space-based. This paper reports the outcome of a computational investigation of two key representative algorithms, one of each category, namely the parametric simplex algorithm which is a prominent representative of the former and the primal variant of Bensons Outer-approximation algorithm which is a prominent representative of the latter. The paper includes a procedure to compute the most preferred nondominated point which is an important feature in the implementation of these algorithms and their comparison. Computational and comparative results on problem instances ranging from small to medium and large are provided.
This paper develops a data mining technique using multiple objective linear programming. This method replaces the applications of discriminant analysis, a tradition method, for data analysis. The multipleobjective li...
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This paper develops a data mining technique using multiple objective linear programming. This method replaces the applications of discriminant analysis, a tradition method, for data analysis. The multiple objective linear programming for this data analysis is solved by fuzzy programming method.
＜正＞ This paper focuses on fuzzy multiple objective linear programming （FMOLP） problems with fuzzy parameters in objective functions. B ased on the results of fuzzy linearprogramming （FLP） proposed by Zhang et ...
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＜正＞ This paper focuses on fuzzy multiple objective linear programming （FMOLP） problems with fuzzy parameters in objective functions. B ased on the results of fuzzy linearprogramming （FLP） proposed by Zhang et al, this paper firstly proposes related definitions and concepts about FMOLP problems with fuzzy parameters. It then extends scalarization-based approach for converting a FMOLP problem into a crisp programming problem, and uses the extended approach to solve the original FMOLP problem. Finally, an example is presented for demonstrating the proposed approach.
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.
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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