Ralph E. Steuer. Multiple criteria optimization: theory, computation and application. Wiley, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... In domains involving goals with explicit expressions, one could formulate the design problem using an optimization methodology [17] Such single objective formulations have been argued to be constraining for actual design problems [32] Instead, multi objective function formulations could be used [12, 28, 32]. The methodology presented here is compatible with these multi objective function algorithms, in that one can use them to solve the formulations presented here, when the domain has sufficient formalization (performance parameter equations) 28] The focus of this paper is on formally specifying ....

.... function formulations could be used [12, 28, 32] The methodology presented here is compatible with these multi objective function algorithms, in that one can use them to solve the formulations presented here, when the domain has sufficient formalization (performance parameter equations) [28]. The focus of this paper is on formally specifying the multi criteria objective function, not methods for finding its global peak. In the preliminary design domain, the degree of specification of candidate models is usually incomplete. The method of imprecision can still be used, however, to ....

[Article contains additional citation context not shown here]

STEUER,R.Multiple Criteria Optimization: Theory, Computation, and Application. J. Wiley, New York, NY, 1986.

....that the trade o# curves may include non convex parts. The results obtained from the case studies in Section 5 also proves the possibility for the non convexity of the Pareto front. Instead of the weighted sum method, the lexicographic weighted Chebyshev metric method, introduced by Steuer [7], is employed to plot the Pareto front of each subproblem P (N ) This method makes it possible to compute the whole Pareto front [7] regardless of its shape, by minimizing the distance to a reference point. The reference point selection is based on the ideal point, z where z i = min x#S f i ....

....possibility for the non convexity of the Pareto front. Instead of the weighted sum method, the lexicographic weighted Chebyshev metric method, introduced by Steuer [7] is employed to plot the Pareto front of each subproblem P (N ) This method makes it possible to compute the whole Pareto front [7] regardless of its shape, by minimizing the distance to a reference point. The reference point selection is based on the ideal point, z where z i = min x#S f i (v) Then the reference point is given by i = z # i where # i 0 for all i = 1, Q. In this study, each # i is selected ....

R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Application, John Wiley and Sons, New York, 1985.

....3. 1.000 15. 0.957 7, 1.000 12. 1.000 7 Lossy Dielectric Materials ( lr=l. j0. e(1 GHz) 1 GHz) e(f) f e=er je, er(f) f e(1 GHz) g e(l GHz) 5. 0.861 8. 0.569 8, 0.778 10. 0.682 10. 0.778 6, 0. 861 Relaxation type Magnetic Materials #]2 #ff (fandf in GHz) e r = 15 jO 9 35. 0.8 10 35. 0.5 11 30. 1.0 12 18. 0.5 13 20. 1.5 2.5 14 30. 15 30. 16 25. 2.0 3.5 variety in the behavior of the multilayer, but not necessarily in its physical construction. III. NUMERICAL PESTJETS In this section, we present the results of applying the aforementioned Pareto GA ....

....15. 0.957 7, 1.000 12. 1.000 7 Lossy Dielectric Materials ( lr=l. j0. e(1 GHz) 1 GHz) e(f) f e=er je, er(f) f e(1 GHz) g e(l GHz) 5. 0.861 8. 0.569 8, 0.778 10. 0.682 10. 0.778 6, 0.861 Relaxation type Magnetic Materials #]2 #ff (fandf in GHz) e r = 15 jO 9 35. 0. 8 10 35. 0.5 11 30. 1.0 12 18. 0.5 13 20. 1.5 2.5 14 30. 15 30. 16 25. 2.0 3.5 variety in the behavior of the multilayer, but not necessarily in its physical construction. III. NUMERICAL PESTJETS In this section, we present the results of applying the aforementioned Pareto GA algorithms as ....

[Article contains additional citation context not shown here]

R. E. Steuer, Multiple Criteria Optimization: Theory, Computation, Application. Malabar, FL: Krieger, 1989.

....weight W(x) is assigned to auction to scale the risk value according to the probability of having risk. 4. 2 Heuristic search for best gain and risk Since there are two goals (safety and profitability) to optimize, the core of the Gain Risk model is a multiple criteria optimization problem [Steuer, 1986]. One possible solution is to use multiple objective linear programming (MOLP) The alternative solutions are classical AI search techniques, such as A or beam search. The UMBCTAC agent runs a relatively simple heuristic search which has two stages. In the first stage, we prune those ....

Steuer, R. Multiple criteria optimization: Theory, Computation and Application. Chichester, John Wiley & Sons: New York.

....algorithm for one gives an exact algorithm that solves the other. For instance, if we only need a solution for a xed k or a xed c, using binary search we can give an answer to one problem using a routine for the other. In fact, the whole feasible region can be described by the Pareto points [Ste86] that is, the undominated pairs of k and c that induce feasible colorings. For the case of approximations, that is not true anymore. Having an approximation algorithm for one problem does not imply the same for the other. This situation is evident for this pair of problems because one ....

R. E. Steuer. Multiple Criteria Optimization: Theory, Computation and Application. Wiley, New York, 1986.

....Figure 1. Illustration of the objective functions on an edge. notation generalizes to the nondominated set Z Par de ned below. Solving the Q criteria semi obnoxious network location problem means nding the set of ecient points. For an introduction to multiple criteria analysis see Steuer [12]. The de nition of eciency is as follows. De nition 1. A solution x 2 G(V; E) to (4) is ecient (Pareto optimal) i there does not exist another solution x 2 G(V; E) to (4) such that f ( x) x) 8q 2 Q and 9q 2 Q s:t: f ( x) f (x) Otherwise x is inecient. The set of all ....

R.E. Steuer. Multiple criteria optimization: Theory, Computation, and Application. Wiley, New York, 1986.

....problem could be solved. 4.4 Formulating the objective As most optimization problems are multiobjective in nature, there are many methods available to tackle this kind of problems. References to multiobjective optimization could be found in Hwang et al. 40] Ringuest [69] and Steuer [82] and with applications to engineering design in Eschenauer et al. 22] and Osyczka [61] Generally, the multiobjective optimization problem (MOOP) can be handled in four different ways depending on when the decision maker articulates his preference concerning the different objectives: never, ....

....to prototype driven. A more thorough discussion of these methods is presented in Paper [XIII] 4.4. 1 No preference articulation There are methods that do not use any preference information, e.g. the Min Max formulation and global criterion method, see Hwang et al. 40] Osyczka [61] and Steuer [82]. The Min Max formulation is based on minimization of the relative distance from a candidate solution to the utopian solution F , see Figure 7. The distance between a solution vector and the utopian vector is typically expressed as a v p norm. 4.4.2 Priori articulation of preference ....

[Article contains additional citation context not shown here]

STEUER R., Multiple criteria optimization: theory, computation and application, John Wiley & Sons, Inc, New York, 1986.

....has been significant interest in using genetic programming for problems with multiple objectives [2] In general these solvers are aimed for small problems. GAMS and the solvers supported by GAMS does not have facilities for these solution procedures. More information can be found in for instance [12], 1] 2. Goal programming A special form of multiple objective programming is goal programming[4] Goal programming deals with multiple, possibly conflicting goals, which may be measured in nonhomogeneous units. An objective f i (x) is reformulated into a goal by considering an aspiration level ....

Ralph E. Steuer, Multiple criteria optimization : Theory, computation, and application, Wiley, 1986.

.... Such applications include neural network learning, digital signal and image processing, structural optimization, engineering design, computer aided design (CAD) for VLSI, database design and processing, nuclear power plant design and operation, mechanical design, and chemical process control [68, 145, 180]. Due to the availability of a lot of unconstrained optimization algorithms, many real applications that are inherently nonlinear and constrained have been solved in various unconstrained forms. Optimal or good solutions to these applications have significant impacts on system performance, such as ....

R. E. Steuer. Multiple Criteria Optimization: Theory, Computation and Application. Krieger Publishing Company, 1989.

..... 131 vii List of Tables viii List of Figures ix Introduction Many engineering applications can be formulated as constrained nonlinear programming problems (NLPs) Examples include production planning, computer integrated manufacturing, chemical control processing, and structure optimization [65, 121, 148]. 1.1 Problem Definition Constrained NLPs can be solved by existing methods if they are specified in well defined formulae that are di#erentiable and continuous. However, only special cases can be solved when they do not satisfy the required assumptions. For instance, sequential quadratic ....

R. E. Steuer. Multiple Criteria Optimization: Theory, Computation and Application. Krieger Publishing Company, 1989.

....and constraint functions are nonlinear. Typical applications include signal processing, structural optimization, neuralnetwork design, VLSI design, database design and processing, nuclear power plant design and operation, mechanical engineering, physical sciences, and chemical process control [144, 193, 17, 47, 56]. A general goal in solving nonlinear constrained optimization problems is to find feasible solutions that satisfy all the constraints. This is not an easy task because nonlinear constrained optimization problems are normally NP hard [63] In practice, the di#culties in solving a nonlinear ....

R. E. Steuer. Multiple Criteria Optimization: Theory, Computation and Application. Krieger Publishing Company, 1989.

....points (and corresponding solutions) such that 3z,z: A such that z z: i.e. set A is composed of mutually nondominated points. The point z composed of the best attainable objective function values is called the ideal point: z = max f (x)lx D j = 1 . J. Range equalization factors ([26], ch. 8.4.2) are defined in the following way: 7r = j=l . J R where R i is the (approximate) range of objective zi in the nondominated set, or D or A. Objective function values multiplied by range equalization factors are called normalized objective function values. 2 Weighted linear ....

....if the optimum is not unique then some of the optima may be dominated, but must have at least one objective component equal to a Pareto optimal solution. For each Pareto optimal solution x there exists a weighted Tchebycheff scalarizing function s such that x is a global optimum (minimum) of s ([26], ch. 14.8) Weight vectors that meet the following conditions: J j=l are called normalized weight vectors. Minimization of the weighted Tchebycheff scalarizing function corresponds to a min max problem. The problem can be, however, transformed to the following one: minimize c (P2) s.t. ....

Steuer R.E. (1986), Multiple Criteria Optimization - Theory, Computation and Application, Wiley, New York.

No context found.

Ralph E. Steuer. Multiple criteria optimization: theory, computation and application. Wiley, 1986.

No context found.

Steuer Ralph E. Multiple Criteria Optimization: Theory, Computation and Application. Wiley, 1986.

No context found.

Steuer Ralph E. (1986). Multiple Criteria Optimization: Theory, Computation and Application. Wiley.

No context found.

R.E. Steuer (1985). Multiple Criteria Optimization: Theory, Computation and Application. Wiley, NewYork.

No context found.

Steuer, R., E. Multiple Criteria Optimization - Theory, Computation and Application, Wiley, 1986.

No context found.

Steuer, R. E. (1986). Multiple Criteria Optimization: Theory, Computation, and Application. John Wiley & Sons, New York.

No context found.

R. E. Steuer, Multiple Criteria Optimization: Theory, Comutation and Applicaion, Wiley, New York, 1986.

No context found.

Steuer R., Multiple criteria optimization: theory, computation and application. New York, John Wiley & Sons, Inc., 1986.

No context found.

Steuer, R. E. (1986). Multiple criteria optimization: Theory, computation, and application. New York: Wiley.

No context found.

R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Application, Wiley, ]986.

No context found.

Steuer, R. (1986), Multiple criteria optimization: Theory, Computation and Application. Chichester, John Wiley & Sons: New York.

No context found.

Steuer, R., Multiple Criteria Optimization: Theory, Computation, and Application , New York: Wiley, 1986.

No context found.

Steuer RE (1986). Multiple Criteria Optimization: Theory, Computation, and Application. Wiley: New York.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC