This paper presents a new approach towards parametric analysis of MINLP models in the context of process synthesis problems under uncertainty. The approach is based on the idea of High Dimensional Model Representation...
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This paper presents a new approach towards parametric analysis of MINLP models in the context of process synthesis problems under uncertainty. The approach is based on the idea of High Dimensional Model Representation technique which utilize a reduced number of model runs to build an uncertainty propagation model that expresses the variability of optimal solution in the uncertain space. Based on this idea, a systematic procedure is developed where in the first step the possible changes in the optimal design configurations due to parametric uncertainty are identified. In the next step, the variability of optimal solution with parameter uncertainty for each design is captured. Having obtained a parametric expression of optimal objective for each design, the optimal solution can be determined by comparing the solutions for different designs. The proposed approach provides information about variation of the optimal objective and optimal design configuration over the entire uncertain space. This information can then be judiciously utilized in any decision making depending on specific process requirements. The main advantage of the proposed approach is that it does not depend on the nature or existence of a mathematical model to describe the input-output relationship of the process. (C) 2003 Elsevier Science Ltd. All rights reserved.
We designed an algorithm for the multiparametric 0-1-integer linear programming (ILP) problem with the perturbation of the constraint matrix, the objective function and the right-hand side vector simultaneously consid...
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We designed an algorithm for the multiparametric 0-1-integer linear programming (ILP) problem with the perturbation of the constraint matrix, the objective function and the right-hand side vector simultaneously considered. Our algorithm works by choosing an appropriate finite sequence of non-parametric mixed integer linear programming (MILP) problems in order to obtain a complete multiparametrical analysis. The algorithm may be implemented by using any software capable of solving MILP problems. (C) 2002 Elsevier Science B.V. All rights reserved.
The problem of optimally allocating the resources to competing activities where the amounts of the resources are not only previosly given but are also to be determined subject to certain linear constraints is consider...
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The problem of optimally allocating the resources to competing activities where the amounts of the resources are not only previosly given but are also to be determined subject to certain linear constraints is considered. The objective is to find such activity levels such that their weighted deviation from a prespecified target is as small as possible. A primal decomposition approach for the problem and derive an explicit formula for the piecewise affine-linear convex objective function of the upper level problem are suggested. The lower level problem is a parametric optimization problem with a bottleneck objective function. If the constraints on the amounts of the resources are all of knapsack type or if there is only one such constraint, then the upper level problem is equivalent to the lower level problem with fixed right-hand sides. In the general case, the problem can efficiently be solved by means of the level method. (C) 2002 Elsevier Science B.V. All rights reserved.
We designed and implemented an algorithm to solve the parametric 0-1 -integer linear programming (ILP) problem relative to the constraint matrix that is, to solve a family of 0-1-ILP problems in which the problems are...
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We designed and implemented an algorithm to solve the parametric 0-1 -integer linear programming (ILP) problem relative to the constraint matrix that is, to solve a family of 0-1-ILP problems in which the problems are related by having identical objective and right-hand-side vectors. Our algorithm works by choosing in appropriate finite sequence of non-parametric 0-1-mixed integer linear programming (MILP) problems in order to obtain it complete parametric analysis. The algorithm may be implemented by using any software capable of solving MILP problems. (C) 2002 Elsevier Science B.V. All rights reserved.
In some applications a minimum cost transportation model arises where supplies are fixed while demands may simultaneously vary. In this paper we analyse the structure of such a model and propose several techniques to ...
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In some applications a minimum cost transportation model arises where supplies are fixed while demands may simultaneously vary. In this paper we analyse the structure of such a model and propose several techniques to describe its behaviour. Our approach is founded on the concept of optimal region, i.e., the subset of demand vectors where a given basic tree is optimal. The proposed algorithm consists in different pivoting strategies designed to: 1. build up a minimal list of basic trees such that the associated optimal regions cover the set of feasible demand vectors;2. analyse the effects of either opening a new supplier or closing an existing one;3. suitably treat the dual degenerate case by building up a minimal representation of every maximal region where the optimal value is linear in the demand vector. Computational complexity is discussed and numerical examples are given. (C) 2002 Elsevier Science B.V. All rights reserved.
This paper proposes a general procedure to construct the membership functions of the performance measures in queueing systems when the interarrival time and service time are fuzzy numbers. The basic idea is to reduce ...
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This paper proposes a general procedure to construct the membership functions of the performance measures in queueing systems when the interarrival time and service time are fuzzy numbers. The basic idea is to reduce a fuzzy queue into a family of crisp queues by applying the alpha-cut approach. A pair of parametric programs is formulated to describe th at family of crisp queues, via which the membership functions of the performance measures are derived. To demonstrate the validity of the proposed procedure, four fuzzy queues, namely, M/F/1, F/M/1, F/F/1, and FM/FM/1, are exemplified. The discussion of this paper is confined to systems with one and two fuzzy variables: nevertheless, the procedure can be extended to systems with more than two fuzzy variables. (C) 1999 Elsevier Science B.V. All rights reserved.
All practical implementations of model-based predictive control (MPC) require a means to recover from infeasibility. We propose a strategy designed for linear state-space MPC with prioritized constraints. It relaxes o...
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All practical implementations of model-based predictive control (MPC) require a means to recover from infeasibility. We propose a strategy designed for linear state-space MPC with prioritized constraints. It relaxes optimally an infeasible MPC optimization problem into a feasible one by solving a single-objective linear program (LP) online in addition to the standard online MPC optimization problem at each sample. By optimal, it is meant that the violation of a lower prioritized constraint cannot be made less without increasing the violation of a higher prioritized constraint. The problem of computing optimal constraint violations is naturally formulated as a parametric preemptive multiobjective LP. By extending well-known results from parametric LP, the preemptive multiobjective LP is reformulated into an equivalent standard single-objective LP. An efficient algorithm for offline design of this LP is given, and the algorithm is illustrated on an example.
This paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average. Based on the alpha -cut representation of fuzzy sets and the extension principle, a pair of fracti...
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This paper proposes a fractional programming approach to construct the membership function for fuzzy weighted average. Based on the alpha -cut representation of fuzzy sets and the extension principle, a pair of fractional programs is formulated to find the alpha -cut of fuzzy weighted average. Owing to the special structure of the fractional programs, in most cases, the optimal solution can be found analytically. Consequently, the exact form of the membership function can be derived by taking the inverse function of the alpha -cut. For other cases, a discrete but exact solution to fuzzy weighted average is provided via an efficient solution method. Examples are given for illustration. (C) 2001 Elsevier Science BY. All rights reserved.
A family of linear semi-infinite problems depending on a parameter tau epsilon= [0, tau*] is considered. For fixed tau = tau (0)epsilon [0, omega*], a sensitivity analysis of the problem solution is carried out and ru...
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A family of linear semi-infinite problems depending on a parameter tau epsilon= [0, tau*] is considered. For fixed tau = tau (0)epsilon [0, omega*], a sensitivity analysis of the problem solution is carried out and rules constructing the solutions of this family for tau in a right-side neighborhood of tau (0) are described. Results on the one-sided derivatives of the solution with respect to the parameter are presented. On the basis of the results, an active-set-strategy and a path-following algorithm are suggested.
This paper presents a solution method for multiobjective nonlinear programming (MONLP) problems and the stability of this solution. The method. called interactive stability compromise programming (ISCP), offers a prac...
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This paper presents a solution method for multiobjective nonlinear programming (MONLP) problems and the stability of this solution. The method. called interactive stability compromise programming (ISCP), offers a practical solution to MONLP problems by deriving the compromise weights and combining judgement with an automatic optimization technique in fuzzy decision making. This is achieved by using the method of compromise programming and the method of compromise weights and we obtain the stability for the solution in each step of the algorithm. A numerical example illustrates various aspects of the results developed in this paper. (C) 2001 Published by Elsevier Science B.V.
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