Many real world decision making problems are multi objective in nature. However, in some cases the model parameters are imprecise in nature. Such type of problems cannot be solved using classical techniques. These mod...
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Many real world decision making problems are multi objective in nature. However, in some cases the model parameters are imprecise in nature. Such type of problems cannot be solved using classical techniques. These modelling complications can be handled with the help of the concept developed in the theory of fuzzy sets. For the imprecise parameters the model users are normally able to give realistic intervals. Using parametric approach the fuzzy multi objective model may be reduced to multi objective linear programming (MOLP) with crisp parameters. Genetic algorithm (GA) is a powerful technique to solve multi objective decision making problems. A set of non-dominated pareto optimal solutions may be obtained with this approach. In this paper the MOLP with imprecise parameter has been considered and solved using parametric approach and GA. To illustrate the procedure a numerical example has been solved. A case study has been done for the allocation of coal and its by-products from a mine establishment to different consumption sites. The transportation cost, availability and the demands are defined by a realistic interval. The problem is solved by GA approach and efficient numerical solution has been found.
The multiparametric 0-1-Integer Linear programming (0-1-ILP) problem relative to the constraint matrix is a family of 0-1-ILP problems in which the problems are related by having identical objective and right-hand-sid...
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The multiparametric 0-1-Integer Linear programming (0-1-ILP) problem relative to the constraint matrix is a family of 0-1-ILP problems in which the problems are related by having identical objective and right-hand-side vectors. In this paper we present an algorithm to perform a complete multiparametric analysis. (C) 2000 Elsevier Science B.V. All rights reserved.
The Balanced Linear programming Problem (BLPP) arises in situations which require equitable distribution of a scarce resource. The BLPP can be transformed to the standard form of the linear programming problem by intr...
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The Balanced Linear programming Problem (BLPP) arises in situations which require equitable distribution of a scarce resource. The BLPP can be transformed to the standard form of the linear programming problem by introducing 2\N\+2 additional variables and 2\N\ additional constraints. This transformation is not desirable from the computational point of view for larger values of \N\ as it increases the problem size substantially. It is also undesirable from a theoretical perspective as it might affect the special structure of the constraint matrix. In this paper, we develop an algorithm for the BLPP which does not require problem enlargement. The algorithm is based on the relationship between the BLPP and the minimax linear programming problem, and solving the latter problem parametrically. Our algorithm, in essence, performs steps that are similar to those performed in the parametric simplex method with parametric right hand side. We then adapt our algorithm for the network flow problem and this specialized algorithm can be applied on the network directly without maintaining the simplex tableau. (C) 1997 Elsevier Science B.V.
Traditional sensitivity and parametric analysis in linear optimization was based on preserving optimal basis. Interior point methods, however, do not converge to a basic solution (vertex) in general Recently., there a...
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Traditional sensitivity and parametric analysis in linear optimization was based on preserving optimal basis. Interior point methods, however, do not converge to a basic solution (vertex) in general Recently., there appeared new techniques in sensitivity analysis, which consist in preserving so called support set invariancy and optimal partition invariancy. This paper reflects the renascence of sensitivity and parametric analysis and extends single-parametric results to the case when there are multiple parameters in the objective function and in the right-hand side of equations. Multiparametric approach enables us to study more complex perturbation occurring in linear programs than the simpler sensitivity analysis does. We present a description of the set of admissible parameters under the mentioned invariances, and compare them with the classical optimal basis concept. (C) 2009 Elsevier B.V. All rights reserved.
Constraint programming models appear in many sciences including mathematics, engineering and physics. These problems aim at optimizing a cost function joint with some constraints. Fuzzy constraint programming has been...
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Constraint programming models appear in many sciences including mathematics, engineering and physics. These problems aim at optimizing a cost function joint with some constraints. Fuzzy constraint programming has been developed for treating uncertainty in the setting of optimization problems with vague constraints. In this paper, a new method is presented into creation fuzzy concept for set of constraints. Unlike to existing methods, instead of constraints with fuzzy inequalities or fuzzy coefficients or fuzzy numbers, vague nature of constraints set is modeled using learning scheme with adaptive neural-fuzzy inference system (ANFIS). In the proposed approach, constraints are not limited to differentiability, continuity, linearity;also the importance degree of each constraint can be easily applied. Unsatisfaction of each weighted constraint reduces membership of certainty for set of constraints. Monte-Carlo simulations are used for generating feature vector samples and outputs for construction of necessary data for ANFIS. The experimental results show the ability of the proposed approach for modeling constrains and solving parametric programming problems. (c) 2010 Elsevier Inc. All rights reserved.
The design processes based on parametric design and generative design allows multiple alternatives to be generated, analysed and corrected. The aim of the developed program was to automate the urban design concept dev...
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The design processes based on parametric design and generative design allows multiple alternatives to be generated, analysed and corrected. The aim of the developed program was to automate the urban design concept development process for selected land units with a local development plan. This document, ordinances and other sources were the guidelines for the program to be developed. The solution-generating program starts by taking in the data, and then geometrical objects are created that have the right relationships to each other. Finally, results are evaluated on the basis of calculated indices and further generations are created taking into account the best options. This process must be overseen by a human, but with the development of machine learning and artificial intelligence, automation will progress, reducing human effort. The results of the study were collated and compared with other experiments in an in-depth literature review.
This paper deals with multiobjective nonlinear programming problems with random variables in the objective functions. These random variables are characterized by possibility density functions. The existing results con...
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This paper deals with multiobjective nonlinear programming problems with random variables in the objective functions. These random variables are characterized by possibility density functions. The existing results concerning the qualitative analysis of basic notions in parametric nonlinear programming problems are reformulated to study the stability sets of the first, second, third and fourth kind for multiobjective nonlinear programming problems under the concept of a-possibility efficient. (C) 1999 Elsevier Science B.V. All rights reserved.
The tolerance approach to sensitivity analysis in linear programming aims at finding a unique numerical value (tolerance) representing the maximum absolute perturbation which can be applied simultaneously and independ...
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The tolerance approach to sensitivity analysis in linear programming aims at finding a unique numerical value (tolerance) representing the maximum absolute perturbation which can be applied simultaneously and independently on each right-hand-side or objective coefficient without affecting the optimality of the given basis. Some extensions have been proposed in the literature, which allow for individual tolerances for each coefficient, thus enlarging the tolerance region. In this paper we review the main results concerning the approach, giving new and simpler proofs, and we propose an efficient geometric algorithm returning a tolerance region that is maximal with respect to inclusion. We compare our method with the existing ones on two examples, showing how a priori information can be naturally exploited by our algorithm to further enlarge individual tolerances. (c) 2004 Elsevier B.V. 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.
In this paper we present a pivotal-based algorithm for the global minimization of composite concave quadratic functions subject to linear constraints. It is shown that certain subclasses of this family yield easy-to-s...
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In this paper we present a pivotal-based algorithm for the global minimization of composite concave quadratic functions subject to linear constraints. It is shown that certain subclasses of this family yield easy-to-solve line search subproblems. Since the proposed algorithm is equivalent in efficiency to a standard parametric complementary pivoting procedure, the implication is that conventional parametric quadratic programming algorithms can now be used as tools for the solution of much wider class of complex global optimization problems. (C) 1998 Elsevier Science B.V. All rights reserved.
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