Unified Interactive Approach for Solving Multiobjective Nonlinear Programming Problems | ||||
| The Egyptian Statistical Journal | ||||
| Article 4, Volume 58, Issue 1, June 2014, Page 75-86 | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.2014.314440 | ||||
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| Abstract | ||||
| In general, there is no single optimal solution in multiobjective problems, but rather a set of non-inferior (or pareto optimal) solutions from which the DM must select the most preferred solution as the one to implement. The generation of the entire non- inferior (or pareto optimal) solution set is not practical for most real world problems. This paper deals with a unified interactive approach for solving multiobjective nonlinear programming (MONLP) problems. This approach unified the reference direction (RD) method introduced by Narula et al., [9] and all of there reference point (RP) method introduced by Wierzbicki [14], Tchebycheff method introduced by Steuer [12] and the satisficing trade-off method (STOM) introduced by Nakayama [8] combined in ARP method introduced by Wang et al., [13]. The main development of the new approach as, we still starting with "weak efficient solution say xv corresponding to fvas the first step and use fvto improve the weighting coefficients of the (augmented) lexicographic weighted Tchebycheff problem where we improve the value f-fv inserted in ARP by the value f-f* and hence modify the reference point in the case of an unsatisfactory solution for the DM as he wishes. The positive features of the improvement are: the reduction of the number of iterations, the reduction of the computational effort and the role of the DM is only to compare the solution resulted from the first step with the reference attainable point (ARP) and the solution resulted from solving the lexicographic weighted Tchebycheff programming problem with calculating weights. An illustrative numerical example is given to demonstrate the theory developed and the quality and effectiveness of the presented approach in this paper. | ||||
| Keywords | ||||
| Multiobjective Nonlinear Programming Problems; Pareto Optimal Solution; Reference Point (RP) Method; Reference Direction (RD) Method; Satisfying Trad; off Method (STOM); Tehebycheff Method; Unified Interactive Approach; Satisfactory Solution | ||||
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