Fuzzy non-linear integer program by parametric programming approach. (English) Zbl 1019.90053
Summary: We propose a heuristic algorithm to analyze a differentiable nonlinear integer program when the fuzzy inequality constraint is considered. By defining a membership function, the fuzzy inequality constraint can be transformed into a parametric inequality of which a hybrid solution procedure incorporating a genetic algorithm is developed. Theoretical analysis and experimental investigation are presented.
MSC:
| 90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |
| 90C10 | Integer programming |
| 90C32 | Fractional programming |
| 90C59 | Approximation methods and heuristics in mathematical programming |
References:
| [1] | Bellman, R. E.; Zadeh, L. A., Decision-making in a fuzzy environment, Management Sci., 17, 141-164 (1970) · Zbl 0224.90032 |
| [2] | Chanas, S., The use of parametric analysis in fuzzy linear programming, Fuzzy Sets and Systems, 11, 243-251 (1983) · Zbl 0534.90056 |
| [3] | Dubois, D.; Prade, H., Fuzzy Sets and Systems: Theory and Application (1980), Academic Press: Academic Press New York · Zbl 0444.94049 |
| [4] | Geoffrion, A. M.; Nauss, R., Parametric and post-optimality analysis in integer linear programming, Management Sci., 23, 1270-1284 (1977) · Zbl 0358.90041 |
| [5] | Jekins, L., Parametric mixed integer programmingan application to solid waste management, Management Sci., 28, 1270-1284 (1982) · Zbl 0504.90069 |
| [6] | Klein, D.; Holm, S., Integer programming post-optimal analysis with cutting planes, Management Sci., 25, 64-72 (1979) · Zbl 0442.90067 |
| [7] | Roodman, G. M., Postoptimality analysis in zero-one programming by implicit enumeration, Naval Res. Logist. Quart., 19, 435-447 (1972) · Zbl 0262.90047 |
| [8] | Wang, H. F.; Horng, J. S., Structural approach to parametric analysis of an IP on the case of the right-hand side, European J. Oper. Res., 92, 148-156 (1996) · Zbl 0913.90248 |
| [9] | Wang, H. F.; Liao, Y. C., A hybrid approach to resolving a differentiable integer program, Comput. Oper. Res., 25, 6, 505-517 (1998) · Zbl 1042.90593 |
| [10] | Ward, J. E.; Wendell, R. E., Approaches of sensitivity analysis in linear programming, Ann. Oper. Res., 27, 23-38 (1990) · Zbl 0722.90075 |
| [11] | Zimmerman, H.-J., Fuzzy programming and linear programming with several objective functions, Fuzzy Sets and Systems, 1, 45-55 (1977) · Zbl 0364.90065 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
